tag:blogger.com,1999:blog-320796762024-03-07T16:02:16.860-08:00RRResearchNot your typical science blog, but an 'open science' research blog. Watch me fumbling my way towards understanding how and why bacteria take up DNA, and getting distracted by other cool questions.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.comBlogger1101125tag:blogger.com,1999:blog-32079676.post-33975751637746692222020-07-19T13:41:00.000-07:002020-07-19T17:27:43.318-07:00Thinking about a post-pandemic worldI've been trying to think carefully about what our world will be like once the current pandemic is over. Most people are rightly focused on the current situation and on short term measures to limit the spread of the virus and the harm it causes, but we should also be thinking about, and planning for, what the world is likely to be like once populations reach some sort of equilibrium. How many people will the virus be infecting or killing every year? How much difference will a vaccine really make? Will we still need to wear masks?<br />
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<blockquote class="tr_bq">
<span style="color: #cc0000;"><span style="background-color: white;"><span style="font-size: large;"><b><span style="background-color: yellow;"> What follows is my non-rigorous back-of-the-envelope analysis. I made some big assumptions (spelled out) and did some simple arithmetic of a few simple scenarios. There's no proper modeling here.</span></b></span></span></span></blockquote>
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<br />
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What kind of equilibrium we get will depend on how much immunity develops as a result of Covid-19 infection, how rapidly the immunity fades, and whether or not researchers can develop a vaccine that gives the same immunity. So first we should consider some very broad-brush scenarios.<br />
<br />
These outcomes range from very bad (no immunity, no
vaccine) to quite good (lifelong immunity from a vaccine). But how
likely are they? What kind of future should we plan for?<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqCvEH_hqETE_xyFCwOuq4_mseubKyj37Ciq6df76dTm41xgW_jGQJ8BLaa7-eyt65Jc5fiEjE8_WiSZNdVBDWJ5fMYjiIqF5_L3Vlcx-OPgild3wpXuwtMUUpnO87KQhYRFMC9w/s1600/Covid-19+longterm+fig1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="725" data-original-width="1489" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqCvEH_hqETE_xyFCwOuq4_mseubKyj37Ciq6df76dTm41xgW_jGQJ8BLaa7-eyt65Jc5fiEjE8_WiSZNdVBDWJ5fMYjiIqF5_L3Vlcx-OPgild3wpXuwtMUUpnO87KQhYRFMC9w/s640/Covid-19+longterm+fig1.png" width="640" /></a></div>
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Based on what vaccine scientists have discovered and accomplished so far, I think that we will get a vaccine. I also think that both ‘no immunity’ and ‘lifelong immunity’ are so unlikely that we shouldn’t waste time thinking about their consequences.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYU8kQFCjQhxt-P-GjmzvhshEz4lzwRzaX4fXKrD68AL9aoWaxr-QrSahIpEQz-2Eo-dwGfhPeyndO3jIZT3-QHhiWS6F-s7LIHU2SehxJPU6qff9tA0yhpLg1BstE_p57p0YiPw/s1600/Covid-19+longterm+fig1B2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="727" data-original-width="1512" height="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYU8kQFCjQhxt-P-GjmzvhshEz4lzwRzaX4fXKrD68AL9aoWaxr-QrSahIpEQz-2Eo-dwGfhPeyndO3jIZT3-QHhiWS6F-s7LIHU2SehxJPU6qff9tA0yhpLg1BstE_p57p0YiPw/s640/Covid-19+longterm+fig1B2.png" width="640" /></a></div>
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Now let’s do some planning for the most likely scenario.<br />
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Below I add more detail to the most likely outcome, that both infection and a vaccine confer moderate immunity. I consider the effect of many people refusing (or being unable to pay for) vaccination, and of wearing masks and practicing some social distancing.<br />
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Let’s assume that the vaccine is a lot like our current flu vaccine, so it reduces your chance of being infected by about 50%, and your chance of having a severe infection or dying by 90%. If you do get infected, it also reduces your contagiousness by about 50%. Let’s also assume that you need to be re-vaccinated every year, both because the immunity fades over time and because in some years a virus mutation makes the current vaccine less effective.<br />
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What might the annual Covid-19 infection rates and death rates be in a typical year? Let’s consider four scenarios that capture the most important possibilities: <br />
<ul>
<li><b>Scenario A:</b> Many people refuse to be vaccinated (I assume 44% vaccine uptake, like the current flu vaccine), and social interactions return to normal.</li>
<li><b>Scenario B:</b> 44% of people refuse to be vaccinated, as in <b>A</b>. However most people practice some social distancing and wear masks when in crowds, which reduces the number of infections by about 50%. </li>
<li><b>Scenario C:</b> Most people are vaccinated annually, and social interactions return to normal. </li>
<li><b>Scenario D:</b> Most people are vaccinated annually, as in <b>C</b>. Most people also practice some social distancing and wear masks when in crowds, as in <b>B</b>., which reduces the number of infections by about 50%. </li>
</ul>
To estimate how much Covid-19 infection we might expect, I decided to use the CDC’s influenza data (https://www.cdc.gov/flu/about/burden/index.html). The CDC estimates that influenza has caused 2,400-14,000 infections and 4-19 deaths per 100,000 people each year since 2010. So I assumed that if Covid-19 vaccine works as well as the flu vaccine but with poor uptake and social interactions returned to normal, we would have about 7000 Covid-19 infections per 100,000 annually. Initially I used the current Covid-19 death rate of 1% for unvaccinated people, and 0.1% for vaccinated people.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhImBRKGbvHqSrJcDs8hVHUMNsNWNEX8ipaO0Jvnso4HqmtpFKOngRePGzb52Mhcl4i0CWByj9Izxrj6FMurXytMb0g4dn2RAa6504mFS8EYZ63JPw5bCS9EUJEIDWUAmYRchYqLw/s1600/Covid-19+longterm+fig2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="685" data-original-width="1483" height="294" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhImBRKGbvHqSrJcDs8hVHUMNsNWNEX8ipaO0Jvnso4HqmtpFKOngRePGzb52Mhcl4i0CWByj9Izxrj6FMurXytMb0g4dn2RAa6504mFS8EYZ63JPw5bCS9EUJEIDWUAmYRchYqLw/s640/Covid-19+longterm+fig2.png" width="640" /></a></div>
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For comparison here are the extremes of the CDC’s estimates of the current influenza burden, drawn to the same scale:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS-tHAcduSiddjtzt3GbbQoddhmGKzPTT9mPobt8RoxRx_WRCH_hyMF4DsvhBs6ICXnfrCMnggM3FRLhuAYXtijh6no_7Tdw3PVYAUZz78ayki2lETRaBYfxLIztkoPVcg7Dcfdg/s1600/Covid-19+longterm+fig3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="289" data-original-width="1295" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS-tHAcduSiddjtzt3GbbQoddhmGKzPTT9mPobt8RoxRx_WRCH_hyMF4DsvhBs6ICXnfrCMnggM3FRLhuAYXtijh6no_7Tdw3PVYAUZz78ayki2lETRaBYfxLIztkoPVcg7Dcfdg/s640/Covid-19+longterm+fig3.png" width="640" /></a></div>
So, if we get a vaccine that works only as well as the influenza vaccine, but most people get vaccinated, we could have an ultimate Covid-19 death burden lower than the current influenza death burden, even without social distancing and masks.<br />
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<b>Some qualifications:</b><br />
<br />
<b>How soon will things stabilize? </b> Covid-19 is spreading rapidly in many parts of the world, and well controlled in others. A vaccine like the one I consider will probably be available within a year or so. It might then take a couple more years for vaccination and infection levels to settle into some kind of equilibrium. But this will not be even across populations, and local outbreaks will continue to occur, since both vaccination rates and infection rates are likely to differ a lot between communities and between societies.<br />
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<b>Covid-19 treatments may get better: </b> The analysis above assumes that the death rate from Covid-19 infection remains about 1%. But Covid-19 treatments will probably continue to improve, reducing the death rate in both vaccinated and unvaccinated people.<br />
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<b>Covid-19 infections often make people sicker than the flu, and for longer: </b> The analysis above doesn’t consider the disease burden of non-lethal Covid-19 infections, which appears to be much higher than that of influenza. Although most people who get the flu feel lousy for a week or less, and return to full health within a few weeks, many Covid-19 infections cause more severe effects, with a wide range of debilitating symptoms that may linger for at least several months. Because infections in vaccinated people are expected to be much less severe, employers (or insurers) might require proof of vaccination.<br />
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<b>It's hard to predict the effects of changing contagiousness:</b> Above I've assumed that having been vaccinated reduces an infected person's ability to transmit the infection by 50%, and my calculations then assumed that this will reduce the overall number of infections at equilibrium by 50%. But the dynamics of infection spread are complex, and the actual equilibrium reduction might be much stronger.<br />
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{page:WordSection1;}</style>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com1tag:blogger.com,1999:blog-32079676.post-56455741642155507372020-05-26T14:21:00.000-07:002020-05-26T14:21:06.774-07:00Response to Ambur et al.
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";"> The points in purple are objections raised by <a href="https://royalsocietypublishing.org/doi/full/10.1098/rstb.2015.0528" target="_blank">Ambur <i>et al</i>.</a> to the hypothesis that the main function of DNA uptake by competent bacteria is acquisition of DNA as a nutrient:</span></b></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";"><span style="color: black;">These points are typical of those raised when the goal is to dismiss the nutrient hypothesis rather than to carefully consider all the issues.</span></span></b></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";"><span style="color: black;"> </span> </span></b></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";">(i) As yet, there is no clear evidence that the integration of nucleotides
taken up by transformation become routed into DNA metabolism.</span></b></div>
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<span lang="EN-US" style="mso-bidi-font-family: "Times New Roman";">Yes.
Competence has mainly been studied in mucosal commensals, where investigations
of metabolism are difficult.<span style="mso-spacerun: yes;"> </span>In these
organisms absence of evidence is not evidence of absence.</span></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";">(ii) The presence of exogenous DNA does not appear to induce
competence in any transformable species.</span></b></div>
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<span lang="EN-US" style="mso-bidi-font-family: "Times New Roman";">Yes,
but I don’t see why this is more relevant for the nutrient hypothesis than for
other hypotheses.<span style="mso-spacerun: yes;"> </span>(Also, <i>Vibrio</i> does use
chitin as a signal for competence; its presence indicates biofilms and abundant
DNA.)</span></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";">(iii) Competence in streptococci, like <i>S. pneumoniae</i>, is induced
for only a short time period during exponential growth when other resources are
highly abundant.</span></b></div>
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<span lang="EN-US" style="mso-bidi-font-family: "Times New Roman";">Because
laboratory growth conditions for human commensals and pathogens are so
different from natural growth conditions, lab cultures are very poor guides to
what matters in the real world.<span style="mso-spacerun: yes;"> </span>That’s
why our work focused on understanding the regulatory machinery.</span></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";">(iv) Transported DNA is heavily protected against nuclease
digestion within the cell, potentially enabling transported fragments to remain
intact as a substrate for recombination.</span></b></div>
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<span lang="EN-US" style="mso-bidi-font-family: "Times New Roman";">And
yet most competent bacteria take up all DNAs they encounter, and DNA that cannot
be recombined is efficiently degraded.<span style="mso-spacerun: yes;"> </span>The
proteins that protect the DNA are also common in non-competent species and so
must function outside of transformation.</span></div>
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<b><span lang="EN-US" style="color: #660066; mso-bidi-font-family: "Times New Roman";">(v) The hypothesis does not explain why several competent species
only take up DNA from close relatives due to conserved DNA uptake sequences (USS
and DUS) despite the fact that non-homologous DNA could be used as a source of nucleotides
for direct use or degradation. </span></b></div>
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<span lang="EN-US" style="mso-bidi-font-family: "Times New Roman";">On
the flip side, almost all competent bacteria take up DNA indiscriminately, so DNA’s
benefit can’t depend on its information content.<span style="mso-spacerun: yes;"> </span>For these exceptions, we have hypothesized that sequence-dependent
uptake constraints exist in these species, and have shown that these create molecular drive that causes uptake sequences to
accumulate in genomes at frequencies and distributions corresponding to those seen in real genomes with DUS and USS.</span></div>
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{page:WordSection1;}</style>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-50356457830655685182020-05-24T12:58:00.003-07:002020-05-24T13:52:08.277-07:00Designing better masks<br />
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-US">Optimizing
design of masks to prevent spread of COVID-19:</span></b></div>
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<i><span style="mso-bidi-font-weight: normal;"><span lang="EN-US">(Originally a series of tweets that came out in the wrong order)</span></span></i></div>
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<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">COVID-19 is transmitted mainly
by droplets and particles in the air we breathe, not by contact with
contaminated surfaces.</span></div>
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</span></span></span><span lang="EN-US">Surgical and cloth masks only
poorly protect an uninfected wearer from becoming infected. </span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">But these masks CAN reduce virus
release by an infectious person, because exhalation produces large wet droplets
that are relatively easy to trap on their way out but that rapidly evaporate to
smaller dry particles that are hard to trap on their way in (see <a href="https://en.wikipedia.org/wiki/Wells_curve" target="_blank">Wells Curve</a>). </span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">So the general public should
wear masks not to protect themselves from infection but to protect other
members of the community, in case the wearer is unknowingly infected. But
design of surgical and cloth face masks has not been optimized for this
function. </span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">What properties should such a
mask have?</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">a.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">The fabric should block passage
of most respiratory droplets.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">b.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">Most exhaled air should pass
through the mask, not around it, even after a cough or sneeze.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">c.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">Any exhaled air that escapes
should escape downward, not upward. </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">d.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">Air and water molecules should
pass easily through the mask fabric. </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">e.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">For ease of breathing, exhaled
and inhaled air should be filtered over a large area of mask. The mask should
not be tightly pressed to the nostrils and mouth. </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">f.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">To maximize air exchange, the
mask should not normally enclose a large volume of air.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">g.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">The space inside the mask
should expand in the event of a cough or sneeze, to trap the large volume of air
and allow it to be gradually released through the mask (not around it). </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 72.0pt; mso-add-space: auto; mso-list: l0 level2 lfo1; text-indent: -18.0pt;">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Cambria; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Cambria; mso-fareast-theme-font: minor-latin;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">These goals may best be met by long
lightweight scarf-type masks that fit snugly around the nose, cheeks and ears,
and settle loosely on the shoulders. </span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqassZvS-5YUdIVi_uCUhH2CnZpiiOiz6A7EGiH1L4fm6idldJU3KXTDF4ToVdG8vg_IHFD3ZoljHlD76RgwRInk3YGdA_KDO8AtEuJAKOq5hJrKPfg3wHB8y1VtkLdesa86MVw/s1600/Scarf+mask.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="337" data-original-width="295" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqassZvS-5YUdIVi_uCUhH2CnZpiiOiz6A7EGiH1L4fm6idldJU3KXTDF4ToVdG8vg_IHFD3ZoljHlD76RgwRInk3YGdA_KDO8AtEuJAKOq5hJrKPfg3wHB8y1VtkLdesa86MVw/s320/Scarf+mask.png" width="280" /></a></div>
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<br /></div>
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ul
{margin-bottom:0cm;}</style>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-40986444075503673942020-03-16T15:10:00.001-07:002020-03-16T21:38:09.281-07:00A semi-quantitative framework for long-term thinking about the COVID-19 pandemicI think the current rush to invoke extreme flatten-the-curve measures needs to be accompanied by careful thought about what we'll do once the measures have had the desired effect. In particular, how long would restrictive measures need to remain in force, and how will we decide when they can be lifted? And how can we mitigate the personal, social and economic harms of the measures while they remain in place?<br />
<br />
So I've created a series of semi-quantitative graphs to help. ('Semi-quantitative means that there are numbers on the axes and specific doubling times for periods of exponential growth, but the finer details are rough approximations.)<br />
<br />
<b>Here's the tl;dr for the first 6 months:</b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs58Hq2byruKl6doGaQc0GHDoyS3-Z79jqhxsxRkw0O8j5XwvOgsxOB2K3ir1-dwNk6n9VGtH9KyrsaubKF_I7e87-qI0XA0hPvcGdy8rxY7MqoPndcp2g63smwJdQBMNc8ETixw/s1600/tldr.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="770" data-original-width="1354" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs58Hq2byruKl6doGaQc0GHDoyS3-Z79jqhxsxRkw0O8j5XwvOgsxOB2K3ir1-dwNk6n9VGtH9KyrsaubKF_I7e87-qI0XA0hPvcGdy8rxY7MqoPndcp2g63smwJdQBMNc8ETixw/s400/tldr.png" width="400" /></a></div>
<br />
<b>Points to note: </b><br />
<br />
<ul>
<li>The Y-axis is log-scale, so small differences in height indicate big differences in numbers of infected people.</li>
<li>Five different scenarios are considered, with plausible effects on doubling time of % infected.</li>
<li>Restrictive measures are assumed to reduce peak % infected and eventual equilibrium.</li>
<li>For all but the most extreme scenario, infection levels remain high (≥1%) even after 6 months.</li>
<li>It will be very hard to justify lifting restrictions that have been effective.</li>
</ul>
<div>
<b><br /></b></div>
<div>
<b>Here's the tl;dr if the costly restrictions are lifted after 7 months of misery:</b></div>
<div>
<b><br /></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUkUyxgT8hctRa2F3DRZ0_DvPKO-L_h_Q9B1hRowoMHCZmcVivbPxFz5GXcQcjzG1A_3VjeQ0S3InkqFKdalWdNttREKnPTkHgtv8qDWsIMM-yjfwfBJcX_191tMVFQNZksXNcog/s1600/tldr-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1022" data-original-width="1600" height="255" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUkUyxgT8hctRa2F3DRZ0_DvPKO-L_h_Q9B1hRowoMHCZmcVivbPxFz5GXcQcjzG1A_3VjeQ0S3InkqFKdalWdNttREKnPTkHgtv8qDWsIMM-yjfwfBJcX_191tMVFQNZksXNcog/s400/tldr-2.png" width="400" /></a></div>
<div>
<b>Points to note:</b></div>
<div>
<ul>
<li>In all cases, lifting restrictions makes % infected much worse (remember, log-scale...).</li>
<li>The more effective the restrictions were in limiting total infections, the worse the second wave on infection is, and the longer it drags on.</li>
</ul>
<div>
<b>Below are the individual graphs:</b></div>
<div>
<br /></div>
<div>
<b>If no action were taken (doubling time 3 days):</b></div>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghLAJfWhCiwOq15jV24J9Ue4Yr7BK4WB8RDZGJdK-7gZpuOaCpttHgc0m_DUS9w12p4ovL8bCDOEq8BhbkOzaR2QvselGhoDuvzZhv8Zsax3XsVugB3NIx62k5VC4EfGN4cLC2XQ/s1600/Slide06.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="398" data-original-width="705" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghLAJfWhCiwOq15jV24J9Ue4Yr7BK4WB8RDZGJdK-7gZpuOaCpttHgc0m_DUS9w12p4ovL8bCDOEq8BhbkOzaR2QvselGhoDuvzZhv8Zsax3XsVugB3NIx62k5VC4EfGN4cLC2XQ/s400/Slide06.png" width="400" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRQPJcfPMm2cd3t2X-5H1uhv7u6NFAikL6ja4C_aU0hoGiJ1b6guKRZDlTOhb-UcepHg8Ej1f7dHCxP_yao1K31TP4SxOQiGsT9a2W9aRn66hann0MLcEl5hv3I7o4O6qtUMxKBQ/s1600/Slide07.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="389" data-original-width="704" height="220" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRQPJcfPMm2cd3t2X-5H1uhv7u6NFAikL6ja4C_aU0hoGiJ1b6guKRZDlTOhb-UcepHg8Ej1f7dHCxP_yao1K31TP4SxOQiGsT9a2W9aRn66hann0MLcEl5hv3I7o4O6qtUMxKBQ/s400/Slide07.png" width="400" /></a></div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Infections are assumed to peak at about 30% of the population at weeks 6-10, and then to decline to about 1% of the population since about half of the population will remain susceptible.</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div>
<b>If we take actions that have no or low personal cost (doubling time 6 days):</b></div>
<div>
<ul>
<li><span style="background-color: white; font-family: "calibri";">Reduce physical contact
with other people</span></li>
<li><span style="background-color: white;"><span style="font-family: "calibri";">Don’t</span><span style="font-family: "calibri";"> </span><span style="font-family: "calibri";">touch</span><span style="font-family: "calibri";"> </span><span style="font-family: "calibri";">your</span><span style="font-family: "calibri";"> </span><span style="font-family: "calibri";">face</span></span></li>
<li><span style="background-color: white;"><span style="font-family: "calibri";">Wash your hands</span></span></li>
<li><span style="background-color: white;"><span style="font-family: "calibri";">Avoid large groups and
crowded places</span></span></li>
<li><span style="background-color: white;"><span style="font-family: "calibri";">Work from home if this is
possible</span></span></li>
<li><span style="background-color: white;"><span style="font-family: "calibri";">Reduce travel</span></span></li>
</ul>
</div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhvJqLAxXP5TXJd3OCBx_WTJiDJWEdKhEtn-cWlEF5OnyVKjAYP0P3avR0V-S3r_cQwiUjh12XFPRxHmZyc3UnhBSLOtsdDRAF-6YA5xajU0LfSrXqTseeZ-rKK-GsETrljtEYng/s1600/no-low.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="892" data-original-width="1600" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhvJqLAxXP5TXJd3OCBx_WTJiDJWEdKhEtn-cWlEF5OnyVKjAYP0P3avR0V-S3r_cQwiUjh12XFPRxHmZyc3UnhBSLOtsdDRAF-6YA5xajU0LfSrXqTseeZ-rKK-GsETrljtEYng/s400/no-low.png" width="400" /></a></div>
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<div>
The peak % infected is lower, maybe 20%, occurs at weeks 11-16, and declines to about 0.3% provided the restrictions remain in place.</div>
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<b>If we take actions that have moderate cost (doubling time 10 days):</b></div>
<br />
<ul>
<li><span style="background-color: white; font-family: "calibri";">Cancel pro-sports, concerts, conferences and other large gatherings</span></li>
<li><span style="background-color: white; font-family: "calibri";">Close bars and restaurants</span></li>
<li><span style="background-color: white; font-family: "calibri";">Cancel university classes</span></li>
</ul>
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The peak % infected is lower, maybe 15%, occurs at weeks 18-25, and declines to about 0.15% provided the restrictions remain in place.</div>
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<br />
<div>
<b>If we take actions that have high cost (doubling time 20 days):</b></div>
<br />
<ul>
<li><span style="background-color: white; font-family: "calibri";">Close all schools and universities</span></li>
<li><span style="background-color: white; font-family: "calibri";">Close close non-essential shops and workplaces</span></li>
<li>Close all public buildings</li>
<li>Ban all non-essential travel</li>
</ul>
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The peak % infected is lower, about 10%%, occurs at weeks 35-40, and falls to about 1% by week 52 provided the restrictions remain in place.</div>
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<div>
<br /></div>
<div>
<div>
<b>If we take extreme actions (R0 <1 b=""></1></b></div>
<br />
<ul>
<li>Lock down the entire population</li>
<li>Enforce by police or the National Guard</li>
</ul>
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The % infected slows its increase and begins to decline by week 15. It continues declining provided the restrictions remain in place.</div>
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<!--EndFragment--><b></b>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com4tag:blogger.com,1999:blog-32079676.post-21987983143843993172018-06-23T09:45:00.001-07:002018-06-23T09:45:08.971-07:00Planning the GTA workMy goal for the rest of my time in Andrew Lang's GTA lab is to gather data that constrains estimates of the efficiency of GTA transduction. I have lots of ideas but they're not very well organized, and I keep getting distracted by the minutiae of GTA biology (and our general ignorance of same). So this post is an attempt to get a sensible plan written out.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg12qqLDbbqd-fnT0GBD_bvbvmp3RXJecqAdOYUbk0aoL6utdVbiyAB6q93hxFPSgtTbdmP2KQR4kZq3z1EeMwx6SuQnCcdRSt7RV9-y6P5lqHGt4CyE6YEwSXxRSynOq_4oGaGMQ/s1600/chalkboard.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg12qqLDbbqd-fnT0GBD_bvbvmp3RXJecqAdOYUbk0aoL6utdVbiyAB6q93hxFPSgtTbdmP2KQR4kZq3z1EeMwx6SuQnCcdRSt7RV9-y6P5lqHGt4CyE6YEwSXxRSynOq_4oGaGMQ/s640/chalkboard.JPG" width="640" /></a></div>
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The bottom line for efficiency is how many transductants are generated for each cell that produces GTA and then dies. This depends on many factors, so I'm going to try to break down the steps and evaluate their limitations.<br />
<br />
Here are some of the questions I'd like to know the answers to. (Some of these questions overlap with others, and some of them are addressed by data we already have.)<br />
<br />
<ol>
<li>How many functional GTA particles does a cell produce under 'normal' conditions? </li>
<li>Are lots of defective particles produced too?</li>
<li>Do individual cells of 'overproducer' mutants produce more GTA particles than normal cells, or is overproduction due only to more cells being producers? </li>
<li>How stable are GTA particles in the cultures where they are produced?</li>
<li>How stable are GTA particles in more dilute solutions?</li>
<li>Do GTA particles bind to free capsule or to cell-envelope components released by lysed cells?</li>
<li>Do cells in producer cultures bind the GTA particles produced by other cells and take up ands recombine their DNA? </li>
<li>How good are recipient cells at finding GTA particles when cells and particles are scarce?</li>
<li>Do cells die if they are exposed to too high a concentration of GTA particles?</li>
</ol>
<div>
<b>Experiments I'm going to do:</b></div>
<div>
<ol>
<li>Measure stability of GTA titers in culture filtrates stored at room temperature.</li>
<li>Measure growth of wildtype and overproducer strains by plating dilutions and counting colonies, in addition to measuring culture density by its turbidity. At the same time measure accumulation of GTA (see <a href="http://rrresearch.fieldofscience.com/2018/06/marc-soliozs-1975-phd-thesis-on-gta.html" target="_blank">this post</a> and <a href="http://rrresearch.fieldofscience.com/2018/06/summary-of-r-capsulatus-bioscreen.html" target="_blank">this post</a>).</li>
<li>Compete an overproducer mutant against its isogenic parent during growth under GTA-producing conditions, to estimate the cost of GTA production. This is especially important since my most recent growth curves don't show much difference between ovverproducer and wildtype strains. This requires that one strain carry an antibiotic resistance marker the other lacks, so I'm using GTA to transfer a kanamycin-resistance marker from a derivative of the 'wildtype' strain into its overproducer sibling. Then I can do the competition both ways, starting with the kanR overproducer at low frequency in a background of kanS wildtype cells, or starting with the kanR wildtype at low frequency in a background of kanS overproducer. I have all these strains now (just confirming that the kanR overproducer does overproduce GTA), so I can start the experiment as soon as I grow up the cultures. I should also Do a complete growthtiter the amounts fo GTA produced, since the goal is to get the ration of GTA produced to cells died.</li>
<li>Do the same competitions, but between an overproducer and a no-GTA mutant, or between wildtype and no-GTA mutant</li>
<li>Add marked GTA to a producer culture (to multiple different producer cultures) to see how efficiently the cells take up GTA. The producer strains are all rifR, so this needs a GTA prep carrying a different marker. I've made a GTA filtrate that transduces kanR, but this transduction is very inefficient compared to rifR, no doubt partly because the kanR is a big insertion, not a point mutation.</li>
<li>To get an independent antibiotic resistance point mutation, I've just started selecting for a spontaneous mutation giving resistance to streptomycin, by plating GTA-producer strains on streptomycin plates. Mutations giving strR are common and this selection has been successful for <i>R. capsulatus</i> in the past.</li>
<li>Do a GTA-producer time course analysis that distinguishes between GTA production and GTA accumulation. Experiments to date have just assayed the amount of GTA in the culture at different times, and there are unexplained peculiarities about the results (see this post: http://rrresearch.fieldofscience.com/2018/06/summary-of-r-capsulatus-bioscreen.html)</li>
</ol>
<div>
<br /></div>
</div>
<div>
<b>Scheduling complication: </b> I'm here until August 12, but I'll be tied up with visitors for part of the time, next week and for the last two weeks of July. Because <i>R. capsulatus</i> grows slowly, I need to wait two days to see the result of each experiment. </div>
<div>
<br /></div>
<div>
I could do the first 'quick-and-dirty' version of the competition experiment now, starting the cell mixtures tomorrow (Friday) morning and growing them for only 24 or 48 hr, taking time point samples at t=0, t=24 and t=48 (Sunday morning). Then I could count the colonies on Tuesday morning. Will I also measure the amount of GTA in each mixture, by its ability to transduce rifR and kanR?</div>
Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-56556248648460557622018-06-15T08:25:00.000-07:002018-06-15T08:25:29.207-07:00Why doesn't all the GTA get taken up?I've been modelling the production and uptake of GTA particles in a culture, hoping to understand the cause of the <a href="http://rrresearch.fieldofscience.com/2018/06/marc-soliozs-1975-phd-thesis-on-gta.html" target="_blank">surprising GTA-accumulation curve</a> I described in the previous post. But this has led me to a more fundamental surprise.<br />
<blockquote class="tr_bq">
<span style="color: #990000; font-family: "verdana" , sans-serif;">Only a very small fraction of the cells in a GTA+ culture produce GTA particles and lyse, and all the other cells are able to bind GTA particles and take up their DNA. So why doesn't all the new GTA quickly get taken up by all the surviving cells?</span></blockquote>
Here are the basic principles I've been assuming, based on what's in the literature: <b>GTA production: </b> Cells in exponential growth don't produce GTA. The GTA genes are turned on as the culture density gets high and growth slows. Once the culture reaches its stationary-phase density GTA production stops. <b>GTA uptake: </b> Cells in exponential growth express the capsule genes at a low level and bind GTA particles with moderate efficiency. The capsule genes are turned up when culture density reaches a quorum-sensing threshold, and ability to bind GTA particles gradually increases. Stationary phase cells bind GTA particles efficiently. <b>GTA decay: </b>BTA particles are moderately unstable, so they fall apart with some unknown probability.<br />
<br />
Let's put some numbers to this:<br />
<br />
<ol>
<li>Assume that 1% of cells produce GTA over the course of the permissive stage.</li>
<li>Assume that each producer cell produces 100 particles and then dies.</li>
<li>Assume that each non-producer cell can take up 1 GTA particle.</li>
</ol>
<br />
Result: All the GTA particles are taken up. The concentration of GTA particles in the medium falls to zero.<br />
<br />
In reality, assumption 1 is likely to be an overestimate, and assumption 3 an underestimate. I'm going to do some experiments to see if I can clarify what's going on.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-57374877223094670292018-06-06T07:39:00.000-07:002018-06-06T07:39:59.842-07:00Marc Solioz's 1975 PhD thesis on GTAPhD students, don't assume that your thesis will moulder unread in the library. More than 40 years after he submitted it, I'm reading <a href="https://www.researchgate.net/profile/Marc_Solioz" target="_blank">Marc Solioz</a>'s PhD thesis (The Gene Transfer Agent of <i>Rhodopseudomonas capsulata</i>). I want to understand the kinetics of GTA production, and his is the only good data I can find.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2XbsgP7q5Ar_RxCWOponN1r7sU79Uzb0zicTGMEr_wAsz7dcZGFUjEA3y_3QuGChUv5tAGjTLXh6qypR17SBt__D-FN0QyErtTbNbtI0ahcrsPWzkdhDZEIIMyK5bK8GcC1yRbA/s1600/Solioz+thesis.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="338" data-original-width="596" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2XbsgP7q5Ar_RxCWOponN1r7sU79Uzb0zicTGMEr_wAsz7dcZGFUjEA3y_3QuGChUv5tAGjTLXh6qypR17SBt__D-FN0QyErtTbNbtI0ahcrsPWzkdhDZEIIMyK5bK8GcC1yRbA/s400/Solioz+thesis.png" width="400" /></a></div>
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<br />
Here's what he reported:<br />
<br />
<b><span style="color: #741b47;">A. Stability of and transduction by GTA in various solutions: </span></b> He tested a wide range of solutions. In these studies he didn't try to distinguish between conditions that stabilize GTA for storage and conditions that maximize its ability to attach to cells and inject its DNA. It's happiest in 1mM each of Na+, Mfg+ and Ca++. This can be buffered with 10 mM Tris, with or without gelatin or BSA (no effect). It's destabilized by 10% gycerol, even for freezing. GTA preps made by filtering culture supernatants should be diluted at least 10-fold to reduce the destabilizing effect of the medium constituents.<br />
<b><br /></b>
<b><span style="color: #741b47;">B. Inactivation by other factors: </span></b> GTA's stability is not affected by temperatures up to 50°C. Keeping it on ice is not better than room temperature, and there was no difference between partially purified and purified stocks. It's inactivated by proteases but not RNase or DNase. It's not inactivated by ether or chloroform, or by phospholipases, consistent with the absence of any membrane.<br />
<br />
<b><span style="color: #741b47;">C. Inactivation by UV: </span></b> UV damages DNA so it is expected to inactivate the transducing activity of GTA particles. To control for experimental variation (a big concern with UV experiments), he compared GTA inactivation to inactivation of phage T2 UV'd together in the same solution. The action spectra are the same for GTA and T2, but GTA inactivation requires much higher doses, consistent with the small amount of DNA in each particle.<br />
<br />
<b style="background-color: white;"><span style="color: #741b47;">D. Conditions and kinetics of GTA production: </span></b> 1<b>. Production kinetics:</b> This is the same surprising result (Solioz's term) I showed in the previous post. Cells were grown photosynthetically/anaerobically in a yeast extract + peptone medium. The dashed line approximates the combined growth curves seen in the four independent experiments, but it's in 'arbitrary units' (I think on a log scale) so I have to infer the cell densities from how my cells grow.<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFsgHclWAsQrHo_aRytof420MGZh3fxk4VR994KaGritXLMKu9R8wCN88W4aMNucxsokFcP_coNpwMYcH0oiBPgDraBX-YmlWplMSKwsVY7KCKUPpgB-UH7ksHIBwVHMVban866A/s1600/Solioz+fig.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="639" data-original-width="497" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFsgHclWAsQrHo_aRytof420MGZh3fxk4VR994KaGritXLMKu9R8wCN88W4aMNucxsokFcP_coNpwMYcH0oiBPgDraBX-YmlWplMSKwsVY7KCKUPpgB-UH7ksHIBwVHMVban866A/s400/Solioz+fig.png" width="310" /></a><br />
<br />
He reports that the initial peak and drop were consistently seen across all his experiments, but that sometimes the drop was not followed by the final high-GTA stage. He saw a similar pattern using a strain that does not absorb GTA (strain H9), so the changes in GTA titre are not due to changes in the removal of GTA particles from the medium. However this conclusion is weakened by the description of strain H9 in the methods, which just says 'does not act as a recipient of GTA, with no reference'.) Other tests he did could not rule out effects of transient inhibitory/inactivating factors in the culture supernatant.<br />
<br />
<b>2. Effects of growth conditions on production.</b> Defined medium RCV gave low titres of GTA. Yields with different concentrations of yeast extract and/or peptone were variuable, apparently depending even on the batch no. of ingredient used. Variation sin culture growth rate and final density did not correlate with GTA titres.<br />
<br />
<b>3. Isolation of mutants:</b> He attempted to isolate an overproducer mutant but failed. The original producer strain B10 carried two phages, so he made a derivative strain, SB1003, that was cured of the phages and carried the convenient RifR point mutation. This new strain is the one I have been using as the standard donor; it's good to know its provenance.<br />
<b><br /></b>
<b>4. Radiolabelling: </b> He put in a lot of work to find a way to radioactively label GTA. This was used to guide the purification studies.<br />
<br />
<b><span style="color: #741b47;">E. Purification of GTA particles: </span></b> This is a long section that's not of much interest to me. He tested a wide range fo the available biochemical techniques used for purification of organelles, phage and molecules.<br />
<br />
<span style="color: #741b47;"><b>F. Characterization of the nucleic acid:</b> </span>He used the single-strand-specific nuclease S1 to show that the DNA in GTA particles is double-stranded. He used CsCl ultracentrifugation to estimate its base composition as 65% G+C, the same as that of the R. capsulatus genome. Repeating this analysis with heat-denatured DNA confirmed that the DNA is linear, not closed-circular like plasmid DNA. Banding in a CsSO4 gradient showed that it is not extensively modified. In sucrose gradients it co-sedimented with SV40 DNA, suggesting a size of 3.6 x 10^6 Daltons. How big is this in base pairs or kb, you ask - about 5.5 kb. He says it would be better to run the DNA in an agarose gel, but this emerging technology wasn't available to him yet.<br />
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<b><span style="color: #741b47;">G. Examination of GTA with the Electron Microscope: </span></b> He saw lots of tails, and empty heads, some with tails. Apparently-full heads came in different sizes, from 150-600 Angstroms in diameter (15-60 nm). But he thinks much of this may be artefacts of the purification and EM-preparation procedures.<br />
<br />Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-19391677254275348922018-06-03T10:38:00.002-07:002018-06-21T12:41:52.977-07:00Summary of R. capsulatus Bioscreen growth curvesThe previous post (<a href="http://rrresearch.fieldofscience.com/2018/06/gta-competition-experiments.html" target="_blank">GTA competition experiments</a>) described the results of the follow-up set of R. capsulatus growth curves that I planned at the end of the previous experiment (<a href="http://rrresearch.fieldofscience.com/2018/04/r-capsulatus-growth-curves-in-rcv-medium.html" target="_blank">R. capsulatus growth curves in RCV medium</a>). But it didn't pull together the results of all the Bioscreen growth curves, nor integrate them with what was previously known/thought). So here goes:<br />
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First, what's already been reported about growth in liquid culture? Not a lot. The graphs below are all I could find. (I asked my colleague here - he says he doesn't know of any others.)<br />
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<b>GTA production: </b></div>
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The only work that measured GTA production along with growth is Solioz et al. 1975, and their 'growth curve' is just a schematic. The titers of GTA this shows are very peculiar. The titer is very low while the culture is growing, and rises to about 3x10^4 just before culture density levels off. But then it dips sharply, falling to about 10^3 over a few hours, and then rises again to its final stable level of about 4x10^5.<br />
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I don't understand how the titer can fall that quickly. Where do the GTA particles go? The titers are transformants to RifR or StrR, so the total number of active GTA particles per ml is about 1000-fold higher, so ~4x10^7 at he first peak, and 10^6 at the valley. Perhaps there's an initial burst of GTA production that stops abruptly, and most of the released GTAs are quickly lost because they attach to the remaining cells. There would be at least 10^8 cells at that stage so this could easily happen. After a few hours the second wave of GTA production begins. This produces at least 4x10^8 GTA particles that remain free (and possibly many that attach to cells and are not detected).<br />
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10="">
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Are the GTA titers from my last Bioscreen run comparable? I got 780 RifR transductants per ml, from a culture that had about 10^9 cells/ml; this is about 20-fold lower than Solioz <i>et al</i>. reported, and about 3-fold lower than I saw in an earlier (not-Bioscreen) culture. The difference may partly be due to the different culture conditions in the Bioscreen.</10><br />
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10=""><br /></10>
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10=""><b>Effects of PO4: </b></10><br />
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10=""><br /></10>
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10="">The Westbye graphs on the lower right come from a study of the effects of phosphate levels on GTA production. This is in the defined medium RCV, either with its normal 10 mM PO4 or with only 0.5 mM PO4. Low PO4 allowed higher GTA production. Differences in PO4 did not affect the culture density of the normal strain SB1003, probably because less than 1% of the cells in a culture produce GTA, but low PO4 caused a drop in the density of the overproducer strain DE442, where up to 20% of cells are thought to produce GTA. The phosphate effect is thought to be on release of GTA particles from the producer cells, not on GTA synthesis or on stability of parrticles in the medium.</10><br />
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10=""><br /></10>
<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10="">In my Bioscreen runs I saw the effect of low PO4 on GTA levels, but no the predicted drop in culture density of DE442. Instead both DE442 cultures levelled off at densities well below that of both SB1003 cultures.</10><br />
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<10 100-fold="" 20-fold="" 3="" a="" about="" again="" and="" are="" as="" but="" cells="" exponentially="" falls="" final="" going="" growing="" hrs.="" is="" it="" its="" just="" level="" linear="" ml="" nbsp="" of="" on="" over="" p="" quickly="" rapidly="" rises="" scale...="" schematic="" the="" then="" to="" was="" while="" write="" x10=""><br /></10>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-47317814822471434742018-06-01T06:09:00.004-07:002018-06-02T10:07:36.801-07:00GTA competition experimentsI'm in St. John's for the 'summer'*, doing GTA-related experiments in Andrew Lang's lab at Memorial University of Newfoundland ('MUN').<br />
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The first experiments I'm going to do are growth competitions between GTA-producing strains and otherwise-identical non-producer strains created by deleting the GTA genes. Because GTA production requires cell lysis, we predict that the non-producers should outcompete the producers.<br />
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While I was still in Vancouver I did detailed growth curves of the various strains. Preliminary ones are described <a href="http://rrresearch.fieldofscience.com/2018/04/r-capsulatus-growth-curves-in-rcv-medium.html" target="_blank">here</a>, and I'll paste the graph from the latest ones below:<br />
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I wanted to check the effect of phosphate concentration in GTA production and culture growth, so I only used two strains, SB1003 (wildtype) and DE442 (a GTA overproducer). I used two PO4 concentrations; 0.1 mM, which should allow high GTA production and reduced growth, and 10 mM, which should cause low GTA production and better growth. The growth differences should be detectable only for DE442. (I also used three different cell densities. I'm only showing the results for cultures started at the highest density, but the others grew similarly with the expected delays.)<br />
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I measured GTA production at two times, by removing cultures from some wells, filtering out the cells, and using the cell-free supernatants to transduce an RifS strain to RifR.<br />
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The results are below. (The upper graph is plotted on a linear scale, and the lower graph is the same data plotted on a log scale, for easier comparison of growth rates.) The growth curves are very similar to those from a previous experiment (RR#1438) where I didn't measure GTA production.<br />
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The GTA production happened as expected. SB1003 produced no significant GTA in high PO4, and a modest amount (780 transductants per ml) in low PO4. DE442 produced lots more GTA under all conditions, but about 4-fold more in low PO4 than in high PO4.<br />
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On the linear scale the two strains appear to have very similar exponential growth rates, but the log scale reveals that DE442 (the GTA overproducer) is slower in exponential growth. DE442 also reaches a lower final densities (SB1003, OD ~ 1 - 1.08; DE442 OD ~ 0.7).<br />
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The growth differences are unlikely to be directly due to the lysis required by GTA production, because the GTA differences caused by the different PO4 levels do not correlate with OD differences.<br />
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DE442 is not isogenic with SB1003; it carries a mutation that blocks synthesis of the red accessory pigment. Could DE4432’s pigment phenotype be responsible for its poorer growth? These were aerobic cultures in a dark room, so the growth difference is not a direct consequence of differences in photosynthesis.<br />
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I don't think it would be straightforward to transfer the ‘overproducer’ mutation into the SB1003 background, since typical transduction frequencies are less than 1/1000, and we have no way to select for overproducer colonies against the background of normal colonies. If the pigment difference causes the growth difference, we could transfer the wildtype pigment allele into DE442 or the mutant allele into SB1003. I wonder how the parent strain of DE442 (Y262, I think) grows.<br />
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* It's definitely not summer yet here. Icy winds anywhere near the coast, and several thin snowfalls in the last few days. I remain hopeful, because most of the trees are finally getting their leaves, and the spring bulbs are blooming.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-4108699736746667692018-05-12T18:11:00.000-07:002018-05-13T06:33:26.233-07:00Wait, there's a much simpler explanation! (For CRISPR-Cas, not for GTA)I'm in Halifax for a couple of weeks, visiting Ford Doolittle and his philosophical colleagues, We've spent much of the time considering the extent to which CRISPR-Cas systems can or should be considered 'Lamarckian'. I started with the simplistic perspective that of course it is, because an acquired character (immunity to future phage or plasmid infection) becomes inherited because the Cas proteins insert short phage- or plasmid-derived DNA sequences as a CRISPR 'spacer' into the chromosome.<br />
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Here's a very detailed diagram I made of the evolutionary events (mutation and selection) affecting CRISPR-Cas systems (click to embiggen):<br />
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We ended up concluding that 'directed mutation' was a better perspective.<br />
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But, once our ideas started settling down, this detailed diagram got me thinking about how uncertain and far in the future the 'immunity to future infection' benefit is. That's a problem for CRISPR-Cas evolution, since this uncertainty greatly weakens the selection maintaining and refining the system. Iv selection is too weak, the system shouldn't be maintained at all.<br />
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A more urgent problem is that the cell needs to survive the immediate infection/invasion before it has any chance of benefiting from the long-term immunity. This becomes especially important if the bias against potentially-lethal self-spacers arises because the cell contains many copies of the invader genome.<br />
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But the cell does have a very nice mechanism to clear the invader, because it has just created an invader-specific spacer in its CRISPR array. Transcribing this new spacer would give it many copies of an invader-specific crRNA with which Cas9 can destroy all the copies of the invader genome. <br />
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<b>So here's my new hypothesis:</b><br />
<blockquote class="tr_bq">
<span style="font-size: large;">The primary function of CRISPR-Cas systems is the detection and <b><i>immediate</i></b> destruction of phage and /or plasmid DNA. Benefits from immunity to future infection are relatively unimportant.</span> <b></b> </blockquote>
<b><b>Things I need to find out:</b></b><br />
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<b><b> </b>Is this a new idea? </b> I don't remember seeing it anywhere, but if any reader knows of a prior proposal please let me know in the comments or via Twitter (@rosieredfield).<br />
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<b>Is relevant data available? </b> The basic experiment is, in principle at least, quite simple. Do cells with an intact CRISPR-Cas system survive phage infection better than cells with a defective system? Do they become transformed less efficiently by plasmids? These tests would be most sensitively done under sub-optimal infection conditions.<br />
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<b>How is transcription of the Cas genes and CRISPR array regulated?</b> In particular, how efficiently is the CRISPR array transcribed and processed immediately after a new spacer has been added? In the context of my GTA-as-CRISPR-vaccine ideas (see <a href="http://rrresearch.fieldofscience.com/2018/01/might-gta-be-vaccination-system-for.html" target="_blank">this post </a>from
a few months ago) I'd been looking for reports that new CRISPR
spacers can be immediately transcribed, creating crRNAs that can
immediately attack the original invader. I didn't find any solid data,
but neither did I find anything that ruled this out. <br />
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<br />Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-87998398624974212742018-04-22T16:06:00.002-07:002018-06-03T08:13:18.326-07:00R. capsulatus growth curves in RCV mediumMy upstairs GTA colleague and I were surprised that the Bioscreen growth curves in the previous post didn't show a dip in OD600 of the GTA-overproducer strain like that seen in manual (non-automated) growth curves. This dip is thought to be caused by the lysis of GTA-producing cells as GTA production peaks when cells hit stationary phase.<br />
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We thought part of the problem might be that I used the standard YPS medium which is based on modest concentrations of yeast extract and peptone. The clearest/most-recent published demonstration that GTA-producing cultures used RCV, a simpler 'defined' medium based on malate, and showed that the apparent lysis occurred in medium with 0.5 mM PO4 but not in medium with 10 mM PO4.<br />
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So I redid the growth curves for all 6 strains, using both high-P and low-P versions of RCV (kindly supplied by my upstairs colleague). The results are not inconsistent with the Westbye results, but they're not at all compelling. None of the strains decreases in OD600<br />
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The problem is that there's quite a bit of between-strain variation in growth and in the stability of the stationary phase OD. (Within each strain the replicate wells give very similar results, with one exception.)<br />
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The graph below shows growth in the high-phosphate medium. The main graph shows OD600 on a log scale (appropriate to exponential growth), and all the strains appear to stably reach similar densities. But the inset shows the same data on a linear scale, which makes the variation look more significant. The overproducer strain stops growing abruptly at OD600 = 0.7 a lower density than the other strains.<br />
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Here's the cells in the low-phosphate medium. There's an initial drop in OD600, over the first 10 hours, but then all the strains grow steadily except strain YW1, where the individual wells grew at different rates for no apparent reason. Again the linear-scale inset shows the substantial variation at stationary phase. The overproducer DE442 again stops growing, this time at OD600 = 0.8, and now its OD falls by about 20% over the next 40 hours.<br />
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I really don't feel comfortable drawing any solid conclusions from this one experiment, especially since there's a blip in many of the growth curves at a point where I stopped and restarted the runs to add more time when I realized that 3 days wasn't going to be long enough. Even though the shaking only stopped for 2-3 minutes, and the trays of cells remained in their holder with the lid closed, most of the strains had an abrupt change in OD600. (You can see the blips at hour 63.)</div>
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<b>Plan: Do the run again. </b> This time I'll pre-grow the cells into log phase in high-P and low-P RCV. medium (the upstairs colleague has offered me enough medium to do this). And I'll plan on pausing the run at key times to take samples that I can assay for GTA production.</div>
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<br />Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-87439679653556007032018-04-16T14:08:00.000-07:002018-04-17T10:20:09.990-07:00What can we learn from growth curves?Here's the results of the Bioscreen growth curves I ran for <i>Rhodobacter capsulatus</i> strains:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPfI90YZzws69f0wA-BnFaJ0DYH9qOFY8Uv67KdVIhEVq02bm0kmXmCynYskE28V-rqm14K84vWnaBVhIQMhsvsP0Q32Mm4ksyVqJqahYN3eGnnkUma-O25KpZexG5n0WHhHIDEA/s1600/Rc+Bioscreen.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1091" data-original-width="1318" height="330" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPfI90YZzws69f0wA-BnFaJ0DYH9qOFY8Uv67KdVIhEVq02bm0kmXmCynYskE28V-rqm14K84vWnaBVhIQMhsvsP0Q32Mm4ksyVqJqahYN3eGnnkUma-O25KpZexG5n0WHhHIDEA/s400/Rc+Bioscreen.png" width="400" /></a></div>
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Each dot is the mean OD600 of 15 replicate wells, each containing 300 µl of culture, with ODs read every 20 minutes for 45 hours. The cultures all grew up at about the same times, but I've shifted the X-axes so the curves don't overlap. OD values below about 0.015 are not significantly above the backround absorption of the culture medium. The Y-axis is a log scale, so when doubling time is constant the dots will fall in a straight line.</div>
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I did these runs 'just-in-case', because I'm going to be working with <i>Rhodobacter capsulatus</i> at Memorial University in Newfoundland for the next few months (on sabbatical leave) and thought they probably wouldn't have a convenient Bioscreen that I could use.<br />
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Now I need to figure out what we learn from these, and whether I should do any more experiments before I leave UBC.<br />
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The simplest expectation is that once the cells have adjusted to the medium (after 'lag phase') they will grow at a constant rate until they run out of nutrients or experience other bad consequences of high cell density (little oxygen, accumulation of toxic byproducts). But all of these cultures instead exhibit 'diauxy', a mid-growth shift from one resource to another. We see this as a brief slowing or even cessation of growth at about OD=0.05 (orange shaded band), after which growth resumes, often at a different rate. The pause occurs because the cells need time to adjust their metabolism to a change they've caused in the medium, such as exhaustion of one nutrient or new availability of another. <br />
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I don't know enough about <i>R. capsulatus</i> metabolism to speculate about what the change might be, but it might affect production of Gene Transfer Agent particles. The pause isn't due to lysis of GTA-producing cells, because it's not changed in the ∆∆ strains, which have deletions of the GTA gene cluster and lysis gene.<br />
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SB1003, B10 and YW1 are all 'wildtype' strains, I think. Strain YW1 grows much slower than the others, although it still speeds up after the growth pause, and it reaches a slightly lower final density.<br />
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Strain DE442 carries a mutation that causes over-expression of the GTA genes and over-production of GTA particles. Growth curves in a 2013 paper found that this strain had a substantial drop in OD once growth ceased, thought to be due to lytic release of GTA particles, but no drop is seen in the Bioscreen culture. That work used a low-phosphate version of a different medium, RCV. But an earlier paper found strong lysis with the same complex medium I used (YPS), and low lysis with the high-phosphate (10 mM) standard RCV medium.<br />
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The lab upstairs has both low-phosphate and high-phosphate versions of the RCV medium, so I'm going to repeat the time course with both.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-66299073490386199322018-04-10T07:31:00.000-07:002018-04-10T07:31:55.049-07:00growth time coursesIn a few weeks I'll be headed for the Maritimes, for the final part of my sabbatical work on Gene Transfer Agent. But before I leave here I want to run some detailed growth time courses on GTA-producing strains, taking advantage of the BioScreen machine belonging to the lab next door.<br />
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I'll first do a trial run with all the strains I have, to check the basic growth kinetics under the Bioscreen growth conditions. Then I'll see if I can combine the growth measurements with testing for the amounts of GTA produced. Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-42156013718326767522018-03-06T16:42:00.001-08:002018-03-06T16:42:22.626-08:00Phage plaqueing still sucks - what to do now?I feel like I've been sucked down a hole of trying to get consistently countable plaques from the <i>Rhodobacter capsulatus</i> phage I'm testing. After seven weeks of plaqueing with various combinations of strains and agar concentrations and cell densities, I'm no closer to having a well-behaved phage I can use to test the GTA-as-vaccine hypothesis.<br />
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Along the way I've eliminated various sub-hypotheses:<br />
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<b>1. The plaques are tiny/faint/blurry/invisible because the phage capsids have long fibers that reduce diffusion through the top agar: </b> Test - use increasingly dilute top agar. Top agar us usually 0.75% agar; I've taken this down to 0.3% (the lowest concentration that's still stable enough to handle). The first time I got somewhat larger plaques, but this was not reproducible.<br />
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<b>2. The plaques are tiny/faint/blurry/</b><b>invisible</b><b> because GTA gene products contribute to phage production: </b> Test: Plaque phage on a GTA overproducer strain. Result: On the first try, plaques on the overproducer seemed larger. But this was not reproducible.<br />
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<b>3. The plaques are </b><b>tiny/faint/blurry/</b><b>invisible</b><b> because the GTA-as-vaccine hypothesis is true: </b> (Plaques can't grow because rapid diffusion of GTA particles allows surrounding cells to become CRISPR-resistant to the phage before the phage gets to them.) Tested by plaqueing the phage on cells deleted for the entire GTA operon and for the separate endolysin. Result: Plaques on these '∆∆' strains are just as lousy (maybe more lousy) than on the GTA-producer parents.<br />
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<b>4. Variant (large) plaques contain mutations that increase infectivity or diffusion: </b> I made new lysates from a couple of big plaques that spontaneously appeared among the tiny plaques, but these lysates still gave tiny or no plaques<br />
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I know that the phage lysates do infect and kill the cells, and do produce progeny phages. When I put a spot of sufficiently-concentrated phage onto a lawn, all the cells die, and when I make a lysate with this 'clear' top agar, I get way more phage then I put in. Can I use the lysate to test the GTA-as-vaccine hypothesis even though I don't have countable plaques?<br />
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What would I do? Here's an earlier blog post where I laid out a crude plan and a list of all the things I'd need to find out before actually doing the experiment that would test the hypothesis: <a href="http://rrresearch.fieldofscience.com/2018/01/questions-about-crispr-mediated-phage.html">http://rrresearch.fieldofscience.com/2018/01/questions-about-crispr-mediated-phage.html</a><br />
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Luckily, after I wrote the above I made another grand attempt at titering the phages on the various strains. Well, I made a sloppy attempt, learned from at and made a better attempt, which more-or-less worked. <br />
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<b>Basic test:</b> Pour lawns of the test strains, using cells concentrated from 400 µl of culture, in 1.5 ml of 0.4% top agar. Put 10 µl spots of different dilutions of phage lysates onto these lawns, let the liquid absorb, and check the next day. Yesterday I did this using photosynthetically grown cells (supposed to make better lawns) and today I've repeated it using cells grown aerobically in the dark. Here's yesterday's result for one of the two phage and one of the six strains:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT0RxIy0_nJJU8vyFH39zRIc4zYRflIoRNq8DcqfhZAXfLHLqSGIfOs5akUQvXUsh4Mj6ScoH6lff7vTjFRGqfSG9FTD3tPEXnr3cXB23HhL_qcHLBFj-tx2WXDAv22SYjHTwqgg/s1600/Plaques.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1000" data-original-width="1270" height="313" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT0RxIy0_nJJU8vyFH39zRIc4zYRflIoRNq8DcqfhZAXfLHLqSGIfOs5akUQvXUsh4Mj6ScoH6lff7vTjFRGqfSG9FTD3tPEXnr3cXB23HhL_qcHLBFj-tx2WXDAv22SYjHTwqgg/s400/Plaques.png" width="400" /></a></div>
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The central clear spot is undiluted lysate, and the other spots are 10-fold dilutions of that. For undiluted, 10^-1, 10^-2 and 1-^-3, the spot is clear (all the cells have been lysed). The 10^-4 spot still has patches of non-lysed lawn, and the 10^-5 and 10^-6 spots have distinguishable plaques. Two of the four healthy strains gave countable plaques (27 and 29), which is nicely consistent.</div>
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I'll wait for tomorrow's results before proceeding.</div>
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<br />Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-49416371802870658932018-02-22T13:34:00.003-08:002018-02-22T13:34:57.075-08:00Phage phrustrationAacckk! I've spent more than a month trying to get decent <i>R. capsulatus</i> phage plaques on <i>R. capsulatus</i> lawns. Still no consistent success. In one experiment I had much better plaques on cells of strain DE442 (a GTA overproducer), but that did not replicate. I suspect that non-tiny plaques depend on exactly the right balance of the cells' physiological state, their density, the agar concentration, the culture medium, and other factors I haven't attempted to vary.<br />
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Yesterday I was almost ready to do a UV-irradiation experiment to generate mutant phages that make larger plaques, starting with two lysates I'd grown up from single plaques that were much larger than the rest. But the dilution-series plates I was titering these lysates on grew up with very similar numbers of (mostly tiny) plaques, suggesting that phage contamination had crept into lysates with unexpectedly very low titers. <br />
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This week I've gotten a couple of good suggestions from visitors:<br />
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The first visitor suggested that I give up on the characterized/sequenced phages I've been working with and just isolate a better-behaved phage from R. capsulatus's natural environment. I'd have to learn how to do this (get water<br />
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Another visitor suggested that maybe the problem is the correctness of my hypothesis about GTA transduction of phage DNA leading to CRISPR-mediated phage immunity in the GTA recipient. That is, maybe the first cells to get infected in my lawns produce so many phage-DNA-carrying GTA particles that many of the neighbouring cells that would otherwise be lysed by the phage become immune to the phage before the plaque can form.<br />
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There's a simple way to test this - see if the phage form better plaques on a strain that doesn't produce GTA. So tomorrow I'm getting some GTA mutants from the guy upstairs.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-92040078836852905852018-01-24T16:06:00.003-08:002018-01-24T16:06:54.404-08:00Phage plans - let's put natural selection to work!I have a two-pronged plan to get a phage strain that gives good enough plaques for my GTA-as-vaccine experiments.<br />
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I obtained reasonable titers of two phages, 'Titan' and 'Saxon'. I'll invest a couple of weeks to see if I can get better and more reproducible plaques with either of these. The genome sequences of these phages are not closely related.<br />
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<b>First, improve the plaquing conditions: </b> The researcher who isolated the phages recommends using for the lawn cells that have been grown photosynthetically to a high density, He also suggested trying a lower top-agar concentration. I'll play around with these and other variables to see if I can get better plaques.<br />
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<b>Second, use artificial selection to get a better strain of phage:</b> I'll pick the few best-looking plaques of each of my two phages and plate the phage they contain in new lawns. From those new lawns I'll again pick the best-looking plaques, and plate their phage in new lawns. Etc. Maybe I'll introduce a bit of UV mutagenesis along the way.<br />
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The first step will be to make fresh lysates of these phages. The lawns I made before are too old, so I'll grow up some cells for lawns today and tomorrow I'll retiter the lysates. On Friday I can pick plaques from these lawns and make plate lysates. If there's a plate with near-confluent plaques I can use it directly to make a plate lysate. (10^7 or 10^8 pfu/ml, and I have maybe 5 µl so at best I can get plates with 5 x 10^4 or 5 x 10^5 plaques. The latter might be enough to get a good lysate. There are small volumes (50-100 µl?) of the original lysates in the lab upstairs, so maybe I'll sue these. Or Maybe I should save these until I've improved the plaquing conditions.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-49394222817783689262018-01-22T12:10:00.000-08:002018-01-22T12:10:10.851-08:00thin lawns, feeble or absent phageMy <a href="http://rrresearch.fieldofscience.com/2018/01/titering-my-lysates.html" target="_blank">phage titering</a> gave disappointing results. Three of the five lysates gave no plaques at all, and the other two gave small indistinct plaques that couldn't be accurately counted or characterized. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFMp00WyRcj2RzhugQj8ZUXzSKU76R8xfIH9cGXHYlfBLJaVDuOSxkAh26UKYWDUS0b3IMRMI4NL3LMJI1TAJOjPXAtPDnHZtAvFr3jyUaO_KtPHZJeFfGV4Xi2yECPj4Zzz_oJA/s1600/%25231427+titers.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="162" data-original-width="395" height="131" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFMp00WyRcj2RzhugQj8ZUXzSKU76R8xfIH9cGXHYlfBLJaVDuOSxkAh26UKYWDUS0b3IMRMI4NL3LMJI1TAJOjPXAtPDnHZtAvFr3jyUaO_KtPHZJeFfGV4Xi2yECPj4Zzz_oJA/s320/%25231427+titers.png" width="320" /></a></div>
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I took some photos of the plaques I did see. The top photo is a section of one lawn, with several thousand tiny indistinct plaques. (The blurry markings are the label on the bottom of the plate.) The second photo is a closeup of an area on another lawn where I had spotted more-dilute phage, taken with my iPhone's Olloclip zoom lens. A few tiny plaques are visible, maybe 3, maybe 5.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip3mk8XBrJ1ch3Zr7OgpVJ4AxOrl3kIfK1fYGrgnTQmu8XsP72lvV5T_Ko_SZsinKirJIHFTEVOFDwRu15DY7K2-dOYZSaQU2IYDHvgb1oDOWsWp3fLOF0NdQrK4luUBqi-Em84w/s1600/Titan+plaques.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="626" data-original-width="640" height="313" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip3mk8XBrJ1ch3Zr7OgpVJ4AxOrl3kIfK1fYGrgnTQmu8XsP72lvV5T_Ko_SZsinKirJIHFTEVOFDwRu15DY7K2-dOYZSaQU2IYDHvgb1oDOWsWp3fLOF0NdQrK4luUBqi-Em84w/s320/Titan+plaques.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi83_j3F9uEQFlZpy1bWSyzyhEZQ48Nbx_FUh4fWyOms4hU0vwj7e8bbLvavrHJFB7JDe5_4O2vS_vKQKTfoPzIm3kPs_OMVpZTj8nkT_TLV01mYF1Q3t_pJuFjTJhpUTYENh_BbQ/s1600/itan+plaques+closeup.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi83_j3F9uEQFlZpy1bWSyzyhEZQ48Nbx_FUh4fWyOms4hU0vwj7e8bbLvavrHJFB7JDe5_4O2vS_vKQKTfoPzIm3kPs_OMVpZTj8nkT_TLV01mYF1Q3t_pJuFjTJhpUTYENh_BbQ/s320/itan+plaques+closeup.png" width="320" /></a></div>
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For comparison, here's what nice plaques look like. These are plaques of the <i>E. coli</i> phage lambda (<a href="http://esciencecommons.blogspot.ca/2012/08/biophysicists-unravel-secrets-of.html" target="_blank">source</a>)</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMeo9R738XnMZnBSfgR5mumnj2H8Q2OoitLiuIIdGTBnSiPqp6G6gsYrq95VfIpKbBE1Tbl4Sj2RNGD-lBbAMfsjgABXbb1EDFq04I0BLa_-ifIRfeDG3cpyEtc55Ck24jTPkKbw/s1600/Lambda+plaques.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="222" data-original-width="400" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMeo9R738XnMZnBSfgR5mumnj2H8Q2OoitLiuIIdGTBnSiPqp6G6gsYrq95VfIpKbBE1Tbl4Sj2RNGD-lBbAMfsjgABXbb1EDFq04I0BLa_-ifIRfeDG3cpyEtc55Ck24jTPkKbw/s400/Lambda+plaques.png" width="400" /></a></div>
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I won't be able to use these <i>R. capsulatus</i> phage for my GTA-vaccine experiments unless I can get better plaques. I'll need to know whether the phage makes turbid or clear plaques, and I'll need to be able to count it accurately.</div>
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I can try using another strain as the host. These lawns were made with a culture of strain YW1, the strain that these phage were originally isolated on. I have several other strains, though I don't know if they are closely related.</div>
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I can also try changing the plating conditions. I followed the protocol that I obtained from people who have worked with these phage, but perhaps I could grow the cells to a different density, or incubate the plates at a different temperature. I'll ask the experts for advice.</div>
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<br />Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-85210266243296892742018-01-18T17:55:00.000-08:002018-01-18T17:55:29.328-08:00Titering my lysates<b>Planning today's work:</b><br />
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Titering the phage lysates should be a no-brainer, but it's been a long time since I worked with phage so I'd better think things through before I do it.<br />
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I have 15 µl of each of 5 phage stocks ('lysates'). The original titers (plaque-forming units/ml, pfu/ml) are written on the tubes - they range from 6x10^5 pfu/ml to 2x10^11 pfu/ml. But the lysates are probably quite old (maybe 2 years, maybe more), so their titers may have dropped a lot.<br />
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I think I'll do one poured-lawn plate of each, using an amount of lysate that should be about 1000 pfu according to the original titer. And I'll do a spotted-lawn plate for each phage, using undiluted lysate and a range of dilutions.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjVYaQ5PyP4LwK4fOLGztEcPYkn1a9o4guEv6C5I9JRc8kCJT8-TAuW-YPKxYGuRYXTsDl7ypQUZo9_ic3fNsDZPpgdDK5qcaOWwj_Q3X1EZsL-I28Dx6acO2NyEfTkQOcWxikZg/s1600/Titers.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="196" data-original-width="888" height="87" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjVYaQ5PyP4LwK4fOLGztEcPYkn1a9o4guEv6C5I9JRc8kCJT8-TAuW-YPKxYGuRYXTsDl7ypQUZo9_ic3fNsDZPpgdDK5qcaOWwj_Q3X1EZsL-I28Dx6acO2NyEfTkQOcWxikZg/s400/Titers.png" width="400" /></a></div>
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I'll dilute the lysates in the same YPS medium I've grown the cells in. It has calcium and magnesium added so should be fine for typical phage.Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-80516189515196284912018-01-18T14:20:00.003-08:002018-01-18T17:54:45.391-08:00About bacterial lawns and phage plaquesThis was going to be a post where I do the planning to titer my new lysates today, but it turned into an explanation of how microbiologists use plaques in lawns of bacteria to study phages.<br />
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<b>Wait, what's a 'lawn' and what's a 'plaque'? </b>A lawn is a thin layer of confluent bacterial growth, usually created by mixing a relatively large number of cells (≥10^6) with liquid agar solution ('top agar' or 'soft agar' and pouring the mixture onto the surface of a nutrient-containing agar plate. The top agar is usually at 0.5-0.75%, about half the concentration used for a normal solid plate. The cells can't move around in the agar, and they grow to high density using the nutrients that diffuse upward from the bottom layer.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMObcniGujq5RThKYuybzKPKTW9HePusP5-QiAg5SXXDCv_26xjah5AK5jpilodZng_bR5pkD8SzRkOJ0YMT8jFcUrhmyYIACWy8Scjo54mf2VaSuY4VY_fsDnWy2PjBiF8uhwIg/s1600/Lawn+no+plaques.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="195" data-original-width="933" height="82" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMObcniGujq5RThKYuybzKPKTW9HePusP5-QiAg5SXXDCv_26xjah5AK5jpilodZng_bR5pkD8SzRkOJ0YMT8jFcUrhmyYIACWy8Scjo54mf2VaSuY4VY_fsDnWy2PjBiF8uhwIg/s400/Lawn+no+plaques.png" width="400" /></a></div>
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If a few of the initial cells were infected with a phage, the phage they release when they die will infect neighbouring cells and kill them, creating a cell-free zone called a 'plaque'.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjlCKlXNhyq8NG8PamLDdtvwuMQ85LUhJYHN8BSpQVBhg5Vjdidh0MgA-nkO-rSY0ww6aTpSTCtEnFEjyICs88SPcHnIJTnyiMhqop7vpFA1fl3YGFIMQRC90SciG6_WBaQ5RWyg/s1600/lawn.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="195" data-original-width="933" height="82" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjlCKlXNhyq8NG8PamLDdtvwuMQ85LUhJYHN8BSpQVBhg5Vjdidh0MgA-nkO-rSY0ww6aTpSTCtEnFEjyICs88SPcHnIJTnyiMhqop7vpFA1fl3YGFIMQRC90SciG6_WBaQ5RWyg/s400/lawn.png" width="400" /></a></div>
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Here is a detailed drawing of what's happening as a plaque forms:<br />
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Initially there's just one infected cell, and sparse uninfected cells in its neighbourhood. When this cell lyses, the phages it releases can readily diffuse through the agar and infect nearby cells. While this is happening, the uninfected cells are growing and dividing. When the newly infected cells lyse, the phage they release add to the local population and infect more cells. The phage continue to diffuse away, but soon the neighbouring cells become so dense that they stop growing and the phage can no longer replicate in them. The cells are too big to diffuse through the agar like the phage, so lysis leaves a circular cell-free space called a plaque. Typical plaques are 1-2 mm across so easy to see with the naked eye.<br />
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By counting the number of plaques that form in a lawn of bacteria, we know how many infectious phages were present in the mixture we poured on the plate. This is the standard way to measure the number of phages (well, the number of 'plaque forming units', PFUs) in a preparation of phage (a 'lysate').<br />
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<b>Regular poured-lawn method: </b> Cells and diluted phage are incubated together in a small volume of liquid (broth or phage-dilution solution) for long enough that most of the phage have attached to the cells. Then hot liquid top agar is added to the tube and the contents are quickly mixed and poured onto an agar plate of whatever medium best supports lawn growth and plaque formation. (Quickly so the mixture cools before the cells are damaged.) The top agar quickly sets, and the plate is incubated overnight at an appropriate temperature for bacterial growth and phage plaque formation.<br />
<b><br /></b><b>Spot-titer method: </b> Cells are quickly mixed with hot top agar (no phage) and the mixture is poured onto agar plates and left to set. Sometimes the plates can be prepared days in advance, if the cells are happy sitting in the fridge. 10 µl dilutions of phage are then spotted onto the surface and the plates are incubated overnight as before. If you're gentle you can even streak a drop of lysate across the lawn as you would streak cells on a normal plate, allowing you to grow well-isolated plaques without the nuisance of diluting your lysate.<br />
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<b>Other ways we can use lawns and plaques:</b><br />
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<b>Isolating phage from a single plaque: </b> Often you want to start an experiment with a genetically pure phage lysate that you grew up from a single plaque. If plaques are well-separated (remember that the phage continue to diffuse out after the plaque forms and the lawn stops growing) you can use a Pasteur pipette to punch out the plaque away from the surrounding agar. If this plaque is put into a small volume of phage-dilution solution, the many thousands of phages it contains will diffuse out over a few hours (or less) and the phage-containing liquid can be used in your experiment, or to prepare a new lysate whose phage all derive from the one that originated the plaque.<br />
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<b>Plate lysates: </b> Lysates can be prepared in broth, by adding phage to growing cells, watching for the time when the culture clears because most of the cells have lysed, and pelleting out the cell debris. This is a bit fussy to do, since clearing depends on having the right proportions of phage and cells. A simpler method is to prepare a 'plate lysate', as follows. Mix the liquid from a picked plaque or a small amount of a lysate with cells and top agar, and pour a lawn. You want enough phage that the resulting plaques will be 'confluent' - will overlap just enough that very little intact lawn remains. Once the plaques have formed, overlay the top agar with 5 ml of phage-dilution solution and leave for a few hours or overnight. Half of the phage will diffuse into the liquid, and in the morning you just have to collect the liquid and add a few drops of chloroform to kill any cells. These lysates usually have very high titers, because the cells in a lawn can grow to much higher density than those in a liquid culture.<br />
<b><br class="Apple-interchange-newline" />Phage-resistant colonies: </b>Sometimes, the area around an initially infected cell includes a cell that is genetically resistant to the phage due to a new mutation that blocks phage attachment or reproduction. Such as cell (green in the diagram below) will be able to grow within the area of spreading phage, and its descendants will form a visible colony within the plaque.<br />
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<b>Turbid plaques: </b> One other phenomenon deserves mention, and that's the 'turbid' plaques formed when a 'temperate' phage infects a lawn. Temperate phages are those that have a mechanism to enter a dormant state in host cells, where the phage genome is passively replicated by the cellular machinery, usually because it is integrated into the cell's chromosome. Cells with such dormant phages ('lysogens', orange in the diagram below) are resistant to infection by external phages. When a temperate phage forms a plaque, most infected cells lyse and produce infectious phage, but some form lysogens that grow and divide within the plaque. Usually many such cells form causing the center of the plaque to appear cloudy ('turbid') rather than having visible colonies.<br />
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<br />Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com2tag:blogger.com,1999:blog-32079676.post-23055533556832073702018-01-16T13:34:00.004-08:002018-01-16T13:34:28.240-08:00Questions about CRISPR-mediated phage immunity<a href="http://rrresearch.fieldofscience.com/2018/01/might-gta-be-vaccination-system-for.html" target="_blank">Thursday's post</a> described the hypothesis that bacteria might use gene transfer agent particles to inoculate other cells in the population with fragments of phage DNA, and outlined an experiment to test this. Now I'm realizing that I need to know a lot more about the kind of immunity I should expect to see if this GTA-as-vaccine hypothesis is correct.<br />
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<b>Simplistic outline of the experiment:</b><br />
<ol>
<li>Infect GTA-producer strain of <i>R. capsulatus</i> with phage under conditions where the infection is inefficient and few cells lyse.</li>
<li>Remove cells and debris from the culture, to get a supernatant that will contain GTA particles and (unavoidably) some phage particles.</li>
<li>Expose a new culture to the supernatant so cells obtain DNA from the GTA particles, again under conditions where successful phage infection will be minimized.</li>
<li>Wash the surviving cells to remove phage (as much as possible). Allow time for CRISPR formation if needed.</li>
<li>Expose the cells to a titer of phage suitable for selecting resistant cells. As a control, also expose cells not treated with GTA. </li>
<li>Plate to isolate colonies from surviving cells.</li>
<li>Test the survivors for phage resistance.</li>
<li>Compare the frequency of resistance in treated and control cultures.</li>
<li>Test resistant colonies for CRISPR changes.</li>
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<b>Things I should find out before I do the experiment:</b><br />
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<b>1. How efficiently do introduced DNA fragments give rise to CRISPR spacers?</b> If this efficiency is too low relative to the background rate of phage resistance, I won't be able to detect an effect. This paper (<a href="https://www.nature.com/articles/ncomms5399" target="_blank">Hynes et al. 2014</a>, thanks to @AprilPawluk for pointing me to it) might let me estimate the efficiency. They exposed cells to a mixture of infectious and damaged phage (damaged by a restriction enzyme in the cell or by prior UV irradiation) at a multiplicity of infection (moi) of 0.1-0.2, and then examined the resulting confluently lysed lawns for phage-resistant colonies. Unfortunately they only report <b><i>relative</i></b> changes in frequency of resistant cells (maxima 16-fold and 6 fold for restriction and irradiation respectively), but in their Methods they mention that the highest frequencies of resistance they observed were about 10^-6. I don't know if this is for naive cells or pre-exposed cells, but even if it's for naive cells, the max frequency of CRISPR resistance I might expect is only about 10^-5. This would not pose a detection problem, but it would limit the population-level benefits of the proposed vaccine system.<br />
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<b>2. What fraction of the survivors of a phage infection are genetically resistant, and w</b><b>hat fraction of phage resistance arises by non-CRISPR mechanisms?</b><b> </b> If most survivors are just lucky, then it might be a lot of work to identify the genetically resistant ones. In the Hynes et al. experiments, all of the colonies were genetically resistant, and all had new CRISPR spacers. However this might be quite different for different phages. If most resistant cells have altered phage receptors rather than phage-specific CRISPR spacers, the effect of GTA-mediated CRISR resistance will be hard to detect.<br />
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<b>3. How quickly does CRISPR-mediated phage resistance arise after exposure to phage DNA? </b> I don't know. Cells in the Hynes experiment might have had one or two lytic-cycle durations between being infected by the damaged phage and being infected by an infectious phage.<br />
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<b>4. What fraction of phage infections are abortive and thus could lead to CRISPR immunity to subsequent infection? </b> Inspired by the Hynes experiment, I can increase abortive infections by UV-irradiating the phage lysate. (I know how to do this well from previous work.)<br />
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<b>5. How efficiently do phage spacers prevent phage infection?</b> April Pawluk (via Twitter) says they reduce infection by several orders of magnitude. In the Hynes work acquisition of a phage-derived CRISPR spacer enabled cells to form a colony in a sea of phage.<br />
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<b><span style="background-color: white; color: magenta; font-family: Trebuchet MS, sans-serif;">OK. I have lysates of five sequenced <i>R. capsulatus</i> phages (from Dave Bollivar via Tom Beatty), and I have the <i>R. capsulatus</i> strain these phages were isolated on, as well as GTA-producing and recipient strains. Time to get to work!</span></b>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-62743676615945367472018-01-11T16:47:00.002-08:002018-01-11T16:47:49.649-08:00Why GTA genes can't be maintained by 'selfish' transmissionBelow is the line of reasoning showing that the genes responsible for producing GTA particles cannot maintain themselves or spread into new populations by GTA-mediated transfer of themselves into new cells. I initially worked this out with a rigorous set of mathematical equations, but then realized that the problem was so glaringly obvious that math isn't needed.<br />
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The main GTA gene cluster is too big to fit inside a single GTA particle, so GTA particles can't transmit DNA that converts a GTA- cell into a GTA+ cell. Some genes outside the main cluster are also required for GTA production.<br />
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But GTA particles can (and do) contain one or more individual GTA genes. If a fragment containing a particular GTA gene is injected into a formerly-GTA+ cell that is now GTA- because it has a mutated version of this gene, the resulting recombination can restore the cell's original GTA+ genotype.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWcztuRUq-bALE3rL8tq6sOE2LQILYr-2lmj9DXlnc6HoCZR6bMTdv6c0YtbrC_EGlN1YeBh3XSFwf-EzaCz0KT_ycUHWoH1kxf6QE0yXyIZDkx3KnU4MalvjmTcE877KC6X-yjQ/s1600/GTA-selfish2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="241" data-original-width="1056" height="91" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWcztuRUq-bALE3rL8tq6sOE2LQILYr-2lmj9DXlnc6HoCZR6bMTdv6c0YtbrC_EGlN1YeBh3XSFwf-EzaCz0KT_ycUHWoH1kxf6QE0yXyIZDkx3KnU4MalvjmTcE877KC6X-yjQ/s400/GTA-selfish2.png" width="400" /></a></div>
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But these transfer events would not allow GTA+ cells to invade a GTA- population, or to maintain themselves in the face of loss of GTA function by mutation. That's true for all known GTA systems, even in the simplest (imaginary) case where production of GTA particles requires only a single gene that could easily fit into a GTA particle, as illustrated below. </div>
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Why? Three factors together require that production of GTA particles reduces the total number of GTA+ cells in the population:</div>
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<b>Problem 1: </b> GTA particles can only be released to the environment if the GTA+ producer cell lyses. So each production event removes one GTA+ cell from the population.</div>
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<b>Problem 2: </b> The GTA genes in the producer cell are not over-replicated as a phage genome would be, so each production event can produce at most one G+ particle (containing the GTA gene or cluster). </div>
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If all steps occurred with 100% efficiency, problems 1 and 2 would allow, at best, replacement of the lost GTA+ cell with a new one created by GTA-mediated recombination. But this would not maintain the numbers of GTA+ cells in the face of occasional loss of GTA genes by mutation or deletion. Nor would it allow GTA+ cells to invade a GTA- population.</div>
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<b>Problem 3: </b> Production of GTA particle production, transmission of their DNA to recipient cells, and recombination with the recipient genome are all likely to be at least moderately inefficient. Here's a partial list of expected inefficiencies:</div>
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<ol>
<li><b>Burst size:</b> Actual burst sizes are unknown, but packaging all the DNA in a <i style="font-size: 12pt;">R.capsulatus.</i><span style="font-size: 12pt;">
genome would need 841 particles, which is much larger than typical burst sizes for DNA phages.</span><span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">Capsid proteins may
be limiting, since they would be produced from single-copy GTA genes rather than replicated phage genomes.</span></li>
<li><b>Dispersion: </b> The GTA particles will disperse in the environment, and many will probably not find cells to attach to.</li>
<li><b>Stability:</b> Lab preps of GTA particles are
unstable in non-optimal storage conditions, so many particles will likely fall apart.</li>
<li><b>Recombination efficiency: </b> Only one DNA strand enters the cytoplasm, and some DNA degradation is likely.<span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">The highest observed transduction frequency is only ~4^-4, </span><span style="font-size: 12pt;">(theor. max: 1.2^-3)</span><span style="font-size: 12pt;"> so recombination
efficiency is probably only ~0.3. Recombining in a novel gene will be less efficient than simple strand replacement</span></li>
<li><b>Self-conversion:</b> Some G+ particles may attach to cells that are already GTA+.</li>
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</style>Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-16362168410151871402018-01-11T15:24:00.000-08:002018-01-11T15:42:33.153-08:00Might GTA be a vaccination system for infecting phages?My work at Dartmouth (to be described in upcoming posts) showed conclusively that genes encoding Gene Transfer Agents (such as the GTA system of <i>Rhodobacter capsulatus</i>) cannot be maintained by 'selfish' transfer of either whole GTA gene clusters or single GTA genes into GA- recipients. Neither can the GTA genes be maintained by general recombination benefits that can arise when fragments of chromosomal DNA are transferred into new cells. So, although 'gene transfer agent' does accurately describe one activity of these genes, it cannot be the activity for which they are selected.<br />
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The main obstacle to the maintenance of GTA genes, which applies to all the benefits is that any GTA+ cell that actively produces GTA particles cells must die, since cell lysis is needed to release their particles into the environment. Another obstacle, applying to selfish transfer, is that GTA genes are not over-replicated during GTA production (and are not preferentially packaged), so each cell death can produce only one GTA+ particle. <br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk2_hbZSrn13MfRc7u2O64DgJEUGVXXrAstxHJ9FqYiSokMu_tKatmIyJhtxhyphenhyphenMPUrqySuNMwVbKyzR4MSRy06b3x6EOAVGvrsLELbiT74OMadte-Yxj3OtV-EPKzFEPExsYYgvA/s1600/GTA-syringe.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="662" data-original-width="718" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk2_hbZSrn13MfRc7u2O64DgJEUGVXXrAstxHJ9FqYiSokMu_tKatmIyJhtxhyphenhyphenMPUrqySuNMwVbKyzR4MSRy06b3x6EOAVGvrsLELbiT74OMadte-Yxj3OtV-EPKzFEPExsYYgvA/s200/GTA-syringe.png" width="200" /></a><br />
I presented these results at the Analytical Genetics conference last week, and asked the other participants if they could think of alternative benefits of producing GTA particles. Sanna Koskiniemi from Uppsala University made the very interesting suggestion that GTA particles could serve as a syringe, packaging DNA fragments from a phage that's infecting the producer cell and transferring these fragments into other as-yet-uninfected cells, where they could trigger development of CRISPR immunity.<br />
<br />
I love this idea and want to test it. It doesn't overcome the cell-death obstacle, but it does overcome the selfish-transfer obstacle since a single producer cell could produce many particles of phage DNA from a single phage genome, and more if the phage genome is replicated.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxYT_kCHtHLFEYqmcVP8iiXPAX-Rry2f0ec6Xko_DuUdJUPkMlwM3wuw7pQn0TXLcd-_8egu1qKXT-5ntwQHWpCyprMWpGuBaJQEtdKJYJLGPgvmScnCCQTgT8H8Aod8KSJVX6Tw/s1600/GTA-CRISPR.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="254" data-original-width="1010" height="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxYT_kCHtHLFEYqmcVP8iiXPAX-Rry2f0ec6Xko_DuUdJUPkMlwM3wuw7pQn0TXLcd-_8egu1qKXT-5ntwQHWpCyprMWpGuBaJQEtdKJYJLGPgvmScnCCQTgT8H8Aod8KSJVX6Tw/s400/GTA-CRISPR.png" width="400" /></a></div>
<br />
One way to see if this could provide sufficient benefits to maintain the GTA genes is by simulation modeling like that I used to examine the recombination benefits. This could clairfy the important factors that would need to be examined.<br />
<br />
Here I want to start considering experimental tests of this hypothesis.<br />
<br />
The ideal test would be to infect the GTA-producing strain with a phage, preferably under low-growth conditions where phage infections are often abortive. (Luckily <i>R. capsulatus</i> produces most of its GTA under such conditions.) Then some recipient cultures would be exposed to the GTA-containing culture medium (and some not, as controls), and then all exposed to a lysate of the phage.<br />
<br />
"<i>But wait!</i>", you say. "<i>Won't the GTA-containing culture medium also contain some phage?</i>" Yes, probably. I don't think there's any way to inactivate the phage particles without also inactivating the GTA particles, or vice versa. We might be able to come up with either perfectly-abortive infection conditions (where infected cells don't produce any phage), or a cellular mutation that prevents phage production. If not, we might have to combine the GTA-exposure and phage-infection steps.<br />
<br />
"<i>And won't any phage lysate also contain some GTA particles?</i>" Yes, probably. But we could use a GTA- mutant as the host for lysate production. Not the mutant that can't lyse, but the one with the main GTA gene cluster completely deleted.<br />
<br />
What resources are available for this project? First I checked with my GTA colleagues, who confirm that <i>R. capsulatus</i> does have a CRISPR-Cas9 system. Then I asked if there were any well-characterized phage systems able to infect <i>R. capsulatus</i>. Until quite recently the answer would have been 'No', but a recent paper reported the isolation and sequences of 4 <i>R. capsulatus</i> phages. A Mu-like phage of <i>R. capsulatus</i> has also been characterized, but it did not form plaques on SB1003.<br />
<br />
The report about the 4 new phages used a different host strain (YW1-derived, not SB1003), so the first thing I'll need to do is check whether they form plaques on SB1003. Then I'll need to play around with infection and plating conditions... My idea of fun!Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-34893591996326851552017-10-16T13:23:00.003-07:002017-10-16T13:24:28.446-07:00Model of GTA evolution by infectious transfer<b>Here's the description of my model addressing Explanation 1 for GTA persistence. For now I've just pasted in the text of a Word file I prepared about 10 days ago.</b><br />
<br />
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 16.0pt;">A constant-population-size model of
large-head GTA transmission<o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<i style="mso-bidi-font-style: normal;">(Based
on Xin Chen’s model, but with stepwise generations and without logistic
growth.)<o:p></o:p></i></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Assumptions:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-top: 6.0pt; text-indent: .25in;">
<b style="mso-bidi-font-weight: normal;">The population:<o:p></o:p></b></div>
<div class="MsoListParagraphCxSpFirst" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->Population size is constant.<span style="mso-spacerun: yes;"> </span>Loss of GTA+ cells due to lysis during GTA
production is made up by growth of all cells after the transduction step.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->Dense, well-mixed culture in liquid medium (so
cells frequently encounter GTA particles)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">GTA
production:<o:p></o:p></b></div>
<div class="MsoListParagraphCxSpFirst" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->GTA particles come in two sizes.<span style="mso-spacerun: yes;"> </span>Small particles contain 4 kb DNA fragments.<span style="mso-spacerun: yes;"> </span>The hypothetical large particles contain
fragments that must be at least 14 kb (the size of the GTA gene cluster) but
could be as big as 50 kb.<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->The number of GTA particles a cell produces does
not depend on the proportion of small and large particles.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->DNA packaging by GTA is random; all parts of the
cell’s genome are equally represented.<span style="mso-spacerun: yes;">
</span>But in this model we only consider the particles containing the
full-length GTA cluster.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b style="mso-bidi-font-weight: normal;"><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="background: yellow; mso-highlight: yellow;">This is the killer: </span></b><span style="background: yellow; mso-highlight: yellow;"><span style="mso-spacerun: yes;"> </span>If the cell’s
chromosome is 5 MB and the large-particle capacity is 15 kb, only 2x10<sup>-4</sup>
of large particles will contain complete GTA gene clusters (will be G+
particles).<span style="mso-spacerun: yes;"> </span>If we change the
large-particle capacity to 20 kb, then about 1x10<sup>-3</sup> of large
particles will contain a complete cluster.<span style="mso-spacerun: yes;">
</span>A 50 kb capacity and a 3 MB chromosome would probably get it up to about
10<sup>-2</sup>.</span><span style="mso-spacerun: yes;"> </span>(And this
ignores the recombination machinery’s need for homologous DNA flanking the GTA
cluster to promote recombination.)<b style="mso-bidi-font-weight: normal;"><o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Transduction:<o:p></o:p></b></div>
<div class="MsoListParagraphCxSpFirst" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->GTA- cells completely lack the main GTA gene
cluster.<span style="mso-spacerun: yes;"> </span>They can only be converted to
GTA+ by homologous recombination with GTA-containing DNA from G+ particles.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->GTA particles cannot tell the difference between
GTA+ and GTA- recipients.<span style="mso-spacerun: yes;"> </span>Particles
capable of transducing GTA- cells to GTA+ can also ‘transduce’ GTA+ cells to
GTA+.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">9.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]-->All GTA particles produced in one cycle are
taken up by and transduce cells in that cycle.<span style="mso-spacerun: yes;">
</span>(The efficiency of infection and recombination is 1.)<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">10.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><!--[endif]-->The
model ignores large and small GTA particles that don’t transduce GTA+. <o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-top: 6.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-list: Ignore;">11.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><!--[endif]-->Each
cell takes up only one G+ particle (or none).<span style="mso-spacerun: yes;">
</span>This is reasonable, since the number of G+ particles is always going to
be much smaller than the number of cells.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.5in;">
<b style="mso-bidi-font-weight: normal;">Parameters:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">F</i></b><span style="mso-tab-count: 1;"> </span>Initial frequency of GTA+ cells (we want to consider a wide
range)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">c</i></b><span style="mso-tab-count: 1;"> </span>Fraction of GTA+ cells producing GTA particles (and consequently
lysing).<span style="mso-spacerun: yes;"> </span>(In wildtype lab cultures this
is <3 o:p=""></3></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">b</i></b><span style="mso-tab-count: 1;"> </span>Number of GTA particles produced by each burst.<span style="mso-spacerun: yes;"> </span>Default value is 100.<span style="mso-spacerun: yes;"> </span>(We have no actual measurements.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">µ</i></b><span style="mso-tab-count: 1;"> </span>Fraction of GTA particles that are large.<span style="mso-spacerun: yes;"> </span>(We expect this fraction to be small, since
large particles have not been observed.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">T</i></b><span style="mso-tab-count: 1;"> </span>Fraction of large GTA particles that are G+ particles (able to
transduce GTA).<span style="mso-spacerun: yes;"> </span>(This is limited by
genome size, GTA gene cluster size, and the DNA capacity of these hypothetical
particles.<span style="mso-spacerun: yes;"> </span>Plausible values are between
10<sup>-2</sup> and 10<sup>-4</sup>.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">G<span style="mso-tab-count: 1;"> </span>µ
* T</i></b> Fraction of GTA particles that contain complete GTA genes.<o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">What happens in one generation:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.5in;">
<b style="mso-bidi-font-weight: normal;">GTA production and cell lysis:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">N</i></b><span style="mso-tab-count: 1;"> </span>Proportion of GTA particles to cells remaining in the medium after
GTA+ cells have burst.<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="mso-tab-count: 1;"> </span>=
(Fcb)/(1 – Fc)</i></b><span style="mso-spacerun: yes;"> </span>(Note: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Fcb</i></b>
is the GTA production per original cell. <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="mso-spacerun: yes;"> </span>1 – Fc</i></b>
normalizes this to the number of cells remaining after lysis.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">N<sup>+</sup></i></b><span style="mso-tab-count: 1;"> </span>Proportion of GTA particles, per remaining cell,
that carry the complete GTA gene cluster (are ‘G+’ particles able to transduce
the GTA-production genotype to GTA- cells).<span style="mso-spacerun: yes;">
</span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
= <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">NµT</i></b><span style="mso-spacerun: yes;">
</span>=<span style="mso-spacerun: yes;"> </span><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">NG</i></b><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; text-indent: -.25in;">
Fraction of
surviving GTA+ cells per original cell (will be normalized to remaining cells
later):<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"> </i>=<i style="mso-bidi-font-style: normal;"> F(1 – c)</i></b><o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Transduction:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
Fraction of GTA- cells transduced to
GTA+: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">N<sup>+</sup>(1 – F)</i></b>.<span style="mso-spacerun: yes;">
</span>{Note: the <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">1 – F</i></b> corrects for the G+ particles that attach to and
‘transduce’ GTA+ cells.)<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
Fraction of GTA+ cells (per original
cell) after transduction: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="mso-spacerun: yes;"> </span>F(1 –
c) + N<sup>+</sup>(1 – F)</i></b>.<span style="mso-spacerun: yes;">
</span>(Note: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">F(1 – c) </i></b>removes cells killed by lysis, <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">N<sup>+</sup>(1 – F) </i></b>adds
cells gained by transduction.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
Fraction of GTA- cells (per original
cell) remaining after transduction:<span style="mso-spacerun: yes;"> </span>(<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">1 – F)
– N<sup>+</sup>(1 – F)</i></b>.<span style="mso-spacerun: yes;"> </span>(Note: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">1 – F
</i></b>is the original fraction of GTA- cells, <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">N<sup>+</sup>(1 – F) </i></b>removes
cells lost by transduction to GTA+.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Cell growth:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
Now we normalize the cell numbers to
‘per remaining cell’:<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
Total fraction of cells remaining
after GTA production and transduction:<o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<span style="mso-tab-count: 1;"> </span><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">1 – (Fc)
</i></b><span style="mso-spacerun: yes;"> </span>(Note: To normalize, divide the
above cell fractions by this value.)<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Fraction
of GTA+ cells after one complete cycle:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 1.0in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="background: aqua; font-size: 18.0pt; mso-highlight: aqua;">F’ = F(1 – c) + N<sup>+</sup>(1 – F) / 1 – Fc</span></i></b><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-size: 18.0pt;"><o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="color: #7030a0; font-size: 14.0pt;">How to evaluate the change
in the proportion of GTA+ cells?<o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">We
can expand <i style="mso-bidi-font-style: normal;">N<sup>+</sup></i> and pull out
the <i style="mso-bidi-font-style: normal;">F</i>, then look at the before/after
ratio:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; tab-stops: .75in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">F’ <span style="mso-tab-count: 1;"> </span>= F * (1 – c) + c * b * F * µ * T * (1 – F) / 1 – (F * c) <o:p></o:p></i></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt; tab-stops: .75in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="mso-tab-count: 1;"> </span>=
F * ((1 – c) + C * b * µ * T * (1 – F) / 1 – (F * c)<o:p></o:p></i></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<br /></div>
<div style="border: solid windowtext 1.0pt; margin-left: 31.5pt; margin-right: 112.5pt; mso-border-alt: solid windowtext .5pt; mso-element: para-border-div; padding: 1.0pt 4.0pt 1.0pt 4.0pt;">
<div class="MsoNormal" style="border: none; margin-top: 6.0pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 1.0pt 4.0pt 1.0pt 4.0pt; padding: 0in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-size: 16.0pt;">F’
/ F </span></i></b><span style="font-size: 16.0pt;">= <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">(1 – c) + c * b * µ * T * (1 – F)
/ 1 – (F * c)</i></b><o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
When the value of this expression is greater
than 1, GTA+ is increasing; when it is less than 1, GTA+ is decreasing.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
For simplicity, below I combine <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">b, µ
& T</i></b> as the compound variable <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b>.<o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">What happens if we vary <i style="mso-bidi-font-style: normal;">F</i>,
holding everything else constant?<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
Increase of GTA+ depends only on <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W.</i></b><span style="mso-spacerun: yes;"> </span>If <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b> is >1, GTA+ increases.<span style="mso-spacerun: yes;"> </span>If <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b> is <1 decreases.="" gta="" o:p=""></1></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
The rate of change is very slow when <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">F</i></b>
is close to 1 (when almost all cells are GTA+), and fast when <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">F</i></b>
is close to 0 (when almost all cells are GTA-).<o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">What happens if we vary <i style="mso-bidi-font-style: normal;">c</i>,
holding everything else constant?<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">C</i></b> affects how fast change happens,
but not its direction.<span style="mso-spacerun: yes;"> </span>If <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b>>1,
GTA+ still spreads; if <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b><1 decreases="" gta="" o:p="" still=""></1></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">What happens if we vary <i style="mso-bidi-font-style: normal;">W</i>,
holding everything else constant?<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
If <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b><1 always="" be="" denominator.="" numerator="" o:p="" smaller="" than="" the="" will=""></1></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
If <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b>>1, the numerator
will always be smaller than the denominator.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
In both cases., all the other
parameters cancel out.<span style="mso-spacerun: yes;"> </span>This confirms
that the direction of selection o GTA+ depends only on whether <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b>
is higher or lower than 1.<o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Would the result change if the population were growing? </b><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
I don’t think so, since GTA+ and GTA-
cells grow at the same rate. <o:p></o:p></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 14.0pt;">Since plausible values of <i style="mso-bidi-font-style: normal;">W</i> are all much lower than 1, I conclude
that GTA+ cells cannot increase by GTA-mediated transduction of GTA- cells to
GTA+.<o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 14.0pt;">GTA could spread by transduction if it did
preferentially package the GTA gene cluster into its particles.<span style="mso-spacerun: yes;"> </span>Of course, then it would be a phage.<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 14.0pt;">How the model’s assumptions affect this
outcome:<o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-top: 6.0pt;">
<i style="mso-bidi-font-style: normal;">Basically,
all the assumptions are either neutral or increase the chance that GTA+ will
spread. Making the simulation more realistic would just make things worse for
GTA+, not better.<o:p></o:p></i></div>
<div class="MsoNormal" style="margin-top: 6.0pt; text-indent: .25in;">
<b style="mso-bidi-font-weight: normal;">The population:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
1. <span style="mso-spacerun: yes;"> </span>Population size is constant.<span style="mso-spacerun: yes;"> </span>Loss of GTA+ cells due to lysis during GTA
production is made up by growth of all cells after the transduction step.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
I don’t think adding growth would
affect the outcome.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
2. <span style="mso-spacerun: yes;"> </span>Dense, well-mixed culture in liquid medium (so
cells frequently encounter GTA particles).<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
If the culture were more dilute or
poorly mixed, some GTA particles would not find new cells to attach to.<span style="mso-spacerun: yes;"> </span>This would reduce the amount of transduction
(effectively reducing <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">W</i></b>). <o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">GTA
production:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
3.<span style="mso-spacerun: yes;"> </span>GTA particles come in two sizes.<span style="mso-spacerun: yes;"> </span>Small particles contain 4 kb DNA fragments.<span style="mso-spacerun: yes;"> </span>The hypothetical large particles contain
fragments that must be at least 14 kb (the size of the GTA gene cluster) but
could be as big as 50 kb.<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
This is the central assumption of the
model.<span style="mso-spacerun: yes;"> </span>The size of the small particles
is known.<span style="mso-spacerun: yes;"> </span>The hypothesized large
particles could be as small as 15 kb (allows a bit of homologous sequence on
each side of the cluster to promote recombination).<span style="mso-spacerun: yes;"> </span>Phage capsids can in principle be very large,
but it’s parsimonious to assume a modest size.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
4.<span style="mso-spacerun: yes;"> </span>The number of GTA particles a cell produces
does not depend on the proportion of small and large particles.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt;">
Large capsids will require more
capsid protein molecules.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
5.<span style="mso-spacerun: yes;"> </span>DNA packaging by GTA is random; all parts of
the cell’s genome are equally represented.<span style="mso-spacerun: yes;">
</span>But in this model we only consider the particles containing the
full-length GTA cluster.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
Experimental results show slightly less
packaging of GTA sequences.<span style="mso-spacerun: yes;"> </span>If this
applies to the hypothetical large particles it would reduce production of G+
particles.<span style="mso-spacerun: yes;"> </span>If particles preferentially
package GTA, GTA would be a phage.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="background: yellow; mso-highlight: yellow;">6.<span style="mso-spacerun: yes;"> </span>This is the killer: </span></b><span style="background: yellow; mso-highlight: yellow;"><span style="mso-spacerun: yes;"> </span>If the cell’s chromosome is 5 MB and the
large-particle capacity is 15 kb, only 2x10<sup>-4</sup> of large particles
will contain complete GTA gene clusters (will be G+ particles).<span style="mso-spacerun: yes;"> </span>If we change the large-particle capacity to
20 kb, then about 1x10<sup>-3</sup> of large particles will contain a complete
cluster.<span style="mso-spacerun: yes;"> </span>A 50 kb capacity and a 3 MB
chromosome would probably get it up to about 10<sup>-2</sup>.</span><span style="mso-spacerun: yes;"> </span>(And this ignores the recombination
machinery’s need for homologous DNA flanking the GTA cluster to promote
recombination.)<b style="mso-bidi-font-weight: normal;"><o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
See point 3 above.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<b style="mso-bidi-font-weight: normal;">Transduction:<o:p></o:p></b></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
7.<span style="mso-spacerun: yes;"> </span>GTA- cells completely lack the main GTA gene
cluster.<span style="mso-spacerun: yes;"> </span>They can only be converted to
GTA+ by G+ particles.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
Transduction depends on homologous
recombination.<span style="mso-spacerun: yes;"> </span>Small GTA particles can
transduce functional alleles of individual GTA genes, replacing versions that
became mutated or even deleted in an ancestor of the recipient cell.<span style="mso-spacerun: yes;"> </span>But they cannot introduce GTA genes into
cells that completely lack the GTA cluster, because there will be no homologous
sequences to recombine with. <o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
8.<span style="mso-spacerun: yes;"> </span>GTA particles cannot tell the difference
between GTA+ and GTA- recipients.<span style="mso-spacerun: yes;">
</span>Particles capable of transducing GTA- cells to GTA+ can also ‘transduce’
GTA+ cells to GTA+.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
I think some phages and conjugative
plasmids may be able to detect whether potential hosts/recipients already have
the element, but we have no evidence that transduction frequencies differ
between GTA+ and GTA- recipients.<span style="mso-spacerun: yes;"> </span>Wall
et al (1975) surveyed 33 strains and found wide variation in both GA production
and transduction, but no correlation between these abilities.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 31.5pt; margin-right: 0in; margin-top: 6.0pt; text-indent: -13.5pt;">
9.<span style="mso-spacerun: yes;"> </span>All GTA particles produced in one cycle are
taken up by and transduce cells in that cycle.<span style="mso-spacerun: yes;">
</span>(The efficiency of infection and recombination is 1.)<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
This is unlikely to be true, but assuming
this increases the chance that each G+ particle successfully transduces a GTA-
cell to GTA+.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
If we were to relax this assumption the
model would need to include an explicit uptake process and to specify what
happens to particles that are not taken up.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
10. The model ignores large and small
GTA particles that don’t transduce GTA+.<span style="mso-spacerun: yes;">
</span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
This should be OK, since these should
not interfere with transduction by G+ particles, especially because their total
number per cell will be small. Removing this assumption would make GTA + spread
less likely.<o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
11. Each cell takes up only one G+
particle (or none).<span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 0in; margin-top: 6.0pt;">
This is a reasonable assumption, since
the number of G+ particles is always going to be much smaller than the number
of cells.<span style="mso-spacerun: yes;"> </span>If the number of G+ particles
were high, sometimes two G+ particles might inject their DNAs into the same
s=cell, which would reduce the efficiency of transduction.<o:p></o:p></div>
<div class="MsoListParagraph" style="margin-top: 6.0pt; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .25in; margin-right: 0in; margin-top: 6.0pt;">
<br /></div>
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="35" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
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<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
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<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
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<w:LsdException Locked="false" Priority="21" QFormat="true"
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<w:LsdException Locked="false" Priority="31" QFormat="true"
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<w:LsdException Locked="false" Priority="32" QFormat="true"
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<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
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Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-45966614169939590722017-10-16T13:23:00.001-07:002017-10-16T13:25:09.953-07:00Thinking about Gene Transfer AgentI'm at Dartmouth for three months, working with Olga Zhaxybayeva's group to improve our evolutionary understanding of Gene Transfer Agent. I'm writing an R-script simulation of the genetic exchange it causes (finally learning R), but my control runs with epistasis don't give the expected results. So I'm writing this post and creating a Powerpoint deck to clarify my thinking.<br />
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First, what's Gene Transfer Agent? A number of different kinds of bacteria produce 'transducing particles' called Gene Transfer Agents. These look line small phage capsids but they don't usually contain phage DNA; instead they contain random fragments of chromosomal DNA. In the best-characterized GTA ('RcGTA'), these are all 4.4 kb in length, which appears to be the DNA capacity of the tiny GTA heads. Like phage, GTA particles inject their DNA into recipient cells (usually of the same species), where it often recombines with the chromosome and can change the cell's genotype.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNnIs2EMztK5mU7MPpPNfWzEMkHpfRJxPbS_Xsa3MALmWBCwUR7yNWTflmsacXwevtLezAGmLdX_h2RAr2QQUUc_Gdr913P-R2CbpUTpbptmlJ70_cccfN1gwX0eghICiv2Caa-Q/s1600/GTA+vs+phage.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1139" data-original-width="1502" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNnIs2EMztK5mU7MPpPNfWzEMkHpfRJxPbS_Xsa3MALmWBCwUR7yNWTflmsacXwevtLezAGmLdX_h2RAr2QQUUc_Gdr913P-R2CbpUTpbptmlJ70_cccfN1gwX0eghICiv2Caa-Q/s400/GTA+vs+phage.png" width="400" /></a></div>
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GTA particles aren't infectious like phages are, both because they don't preferentially package the DNA that encodes them and because their heads are too small to contain this DNA. The RcGTA head and tail proteins are encoded by a 14 kb gene cluster. The sequences and organization of these genes strongly resemble that of homologous phage genes, so the known GTA systems are generally thought to have descended from what were integrated prophages. </div>
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In lab cultures of cells with the RcGTA genes (<i>Rhodobacter capsulatus</i> cells), GTA is produced mainly after exponential growth has ceased, and only produced by a small subset of cells. Like release of phage particles from infected cells, release of GTA requires lysis of the cell, and the genes for the holin and endolysin proteins are encoded separately from the main RcGTA cluster.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6WnvNY6y8FT3_gKchzE8_po62HUjoc1YdZuHeSoYXrq1PUyMJ8wNPVVwEa5RFejGroT2gd7Nnf2x7lQBeyzg9KKhyphenhyphenAdH_YFNdrCttY9xRcevxy6oA3iJQ_OgD1rBEoNJ1Ud0uBQ/s1600/GTA+slide+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1131" data-original-width="1504" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6WnvNY6y8FT3_gKchzE8_po62HUjoc1YdZuHeSoYXrq1PUyMJ8wNPVVwEa5RFejGroT2gd7Nnf2x7lQBeyzg9KKhyphenhyphenAdH_YFNdrCttY9xRcevxy6oA3iJQ_OgD1rBEoNJ1Ud0uBQ/s400/GTA+slide+1.png" width="400" /></a></div>
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There are good reasons to think that GTAs are not simply defective prophages that still can package small DNA fragments:<br />
<ol>
<li>The main RcGTA gene cluster has been somewhat stably
inherited over a very long time, maybe a more than a billion years. Some descendants have lost all the genes, but about 25% of the 225 alpha-proteobacterial genomes examined have retained versions of a single large cluster, typically containing 14-17 co-transcribed genes, most of which encode capsid head and tail proteins.</li>
<li><span style="font-family: "calibri";">Expression of this gene cluster is at least partly controlled by cellular regulatory mechanisms. </span></li>
<li><span style="font-family: "calibri";">Other genes, at other chromosomal locations, are also needed for efficient RcGTA production.</span></li>
</ol>
<div>
<span style="font-family: "calibri";">I just crunched some numbers from a detailed phylogenetic tree for the alpha-proteobacteria showing which taxa have GTA. The large GTA cluster is only found in a subclade (148 taxa, 109 distinct species names); the authors estimate that this subclade is 1.0 - 1.4 billion years old. 57% of the taxa in this subclade have the large GTA gene cluster.</span></div>
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My goal for these three months is to generate models of GTA evolution (probably computer simulations) that evaluate the following candidate explanations for its persistence:<br />
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<ol>
<li><b>Infectious spread</b> of GTA by rare large-head particles that package the 14 kb gene cluster.</li>
<li><b>Restoration</b> of mutated GTA genes by unidirectional recombination with functional alleles from GTA-producing cells.</li>
<li><b>Beneficial recombination</b> of chromosomal genes.</li>
</ol>
<div>
<b>Flawed model for Explanation 1: </b> Nobody has seen the large heads postulated by Explanation 1, but nobody has explicitly looked for them. The Zhaxybayeva lab already has an unpublished mathematical model that addresses this exp lanati on, created by a mathematically-inclined former post-doc. It asks how frequent such heads would need to be in order to maintain GTA-producing cells in a mixed population of GTA+ cells and GTA- cells lacking the gene cluster. The model assumes that large heads are produced at frequency µ, and that these inject the GTA gene cluster into GTA- cells, converting them into GTA+ cells. Only a small fraction of GTA+ cells are activated to produce GTA in any one generation, and these lyse after GTA production. </div>
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The conclusion from this model is that GTA+ cells can persist at high frequency even if they only make large particle for every 10^5 normal small particles. Because the model assumed a reasonable 'burst size' of 100 GTA particles per producer cell, this means that GTA+ can persist if only one cell in a thousand produces a single large particle. </div>
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But I didn't think this result could be correct. Since each cell lysis destroys a GTA+ cell and only one in a thousand creates a new GTA+ cell from a GTA- cell, the GTA+ population should be continually decreasing. Production of new GTA+ cells only compensates for 0.1% of the loss of GTA+ cells. </div>
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I initially had a hard time fully understanding the mathematics of this model. It included expressions for logistic growth, which complicated the math without adding anything to its utility. So I created my own version of this model, which gave a very different answer.<br />
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<div>
<b>New model for Explanation 1: </b> I'm going to put the description of this model into <a href="http://rrresearch.fieldofscience.com/2017/10/model-of-gta-evolution-by-infectious.html" target="_blank">another post</a>, because here I want to get on to my beneficial recombination model. <b>Bottom line:</b> the model's result is that transduction of the GTA gene cluster by large-head GTA particles can't come close to maintaining GTA+ cells in a mixed population even if every cell produces a large-head particle. This is because:<br />
<br />
<ol>
<li>All cells that produce GTA die; </li>
<li>Only a small fraction of large-head particles will contain a complete gene cluster (maybe 0.1 to 1%); </li>
<li>Except when GTA+ cells are rare, many particles will attach to GTA+ cells rather than to GTA- cells; </li>
<li>In a natural environment many GTA particles will fail to find recipients. (This issue isn't part of the model.)</li>
<li>To overcome these obstacles each GTA-producing cell would need to produce more than 1000 (10,000? 100,000?) large-head particles.</li>
</ol>
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<b>Finding the flaw in the lab's model: </b> Assuming that I understand the lab's model correctly, the main error is that it 'corrects' for the probability that a GTA particle will attach to a GTA+ cell rather than a GTA0- cell by multiplying by the <i><b>number</b></i> of GTA- cells rather than by their <b><i>frequency</i></b>. Since the model assumes populations of 10^7 to 10^9 cells, this overestimates the amount of transduction by orders of magnitude, leading to a comparable underestimate of the frequency of large heads needed to maintain GTA+.</div>
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<b>Model for Explanation 2: </b> I modified the basic structure of my Explanation 1 model to consider a related hypothesis. Defective alleles of GTA genes are expected to arise by random mutation. At least some of these will also prevent the cell from lysing when GTA production is induced. These cells can still receive functional alleles of their defective genes from GTA particles produced by 'wildtype' cells, but they can't transmit their defective alleles to the wildtype cells because they can't produce GTA. This asymmetry favours spread of functional alleles, and might be able to maintain GTA, although it wouldn't allow GTA+ to spread to cells that completely lack the GTA genes.</div>
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Like the model for Explanation 1, the result is a strong NO. Because the models are very similar, it's not surprising (in retrospect) that spread of functional alleles faces the same obstacles</div>
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<ol>
<li>All cells that produce GTA die; </li>
<li>Only a small fraction (about 0.1%) of particles will contain whatever GTA gene is mutated in a recipient cell; </li>
<li>Except when GTA+ cells are rare, many particles will attach to cells with the functional allele rather than to those with mutated allele; </li>
<li>In a natural environment many GTA particles will fail to find recipients. (This issue isn't part of the model.)</li>
<li>To overcome these obstacles each GTA-producing cell would need to produce more than 1000 (10,000? 100,000?) large-head particles.</li>
</ol>
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<b>Models for Explanation 3:</b> Most microbiologists assume that GTAs are maintained in their genomes by selection for presumed benefits of chromosomal recombination. They implicitly assume that randomizing the combinations of chromosomal alleles in a population creates a benefit strong enough to overcome the cost of the cell death associated with GTA production. They don't explicitly assume this, because they're not used to thinking rigorously about evolutionary processes. Instead their explanation usually relies on GTA-mediated recombination creating some specific beneficial new combination, and ignores the selective costs associated with other combinations.<br />
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In fact, many very smart people have spent many years looking for conditions where random chromosomal recombination creates benefits strong enough to maintain the genes that cause it. These 'evolution of sex' models have identified some conditions, but usually these benefits are small and occur only under special circumstances. Most of the time recombination appears to be a waste of time at best.<br />
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<b>Recombination Model 1: </b> Way back when I was a new post-doc spending a year in Dick Lewontin's lab, I developed a computer-simulation model of recombination by natural transformation (<a href="http://www.genetics.org/content/genetics/119/1/213.full" target="_blank">Redfield 1988, <i>Evolution of bacterrial transformaiton: Is sex with dead cells ever better than no sex at all?</i></a>). In this model I applied a relatively simple model of the evolution of sex to a population of naturally competent bacteria. My first goal for addressing Explanation 3 is to adapt this model so it applies to recombination caused b GTA rather than by natural transformation. I'll describe my progress (and current deadlock) in the next post.<br />
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<b>Recombination Model 2: </b> Model 1 is 'deterministic'; it ignores random ('stochastic') events, effectively assuming that the population is infinitely large. But the strongest benefits of recombination are now thought to arise from precisely the stochastic effects Model 1 ignores. So I also want to make a stochastic model that tracks individual cells, or at least a model that takes stochastic processes into account. I haven't started writing this model yet, but I might pattern it on the transformation model described by <a href="http://www.g3journal.org/content/4/2/325.short" target="_blank">Takeuchi et al, 2014</a>.</div>
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<!--EndFragment-->Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0tag:blogger.com,1999:blog-32079676.post-29078718412718000262017-08-18T16:34:00.001-07:002017-08-21T10:10:24.195-07:00What's noise, what's Illumina bias, and what's signal?The PhD student and I are trying to pin down the sources of variation in our sequencing coverage. It's critical that we understand this, because position-specific differences in coverage are how we are measuring differences in DNA uptake by competent bacteria.<br />
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<b><span style="color: purple; font-size: large;">Tl;dr: We see extensive and unexpected short-scale variation in coverage levels in both RNA-seq and DNA-based sequencing. Can anyone point us to resources that might explain this?</span></b><br />
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I'm going to start not with our DNA-uptake data but with some <i>H. influenzae</i> RNA-seq data. Each of the two graphs below shows the RNA-seq coverage and ordinary seq coverage of a 3 or 4 kb transcriptionally active segment.<br />
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Each coloured line shows the mean RNA-seq coverage for 2 or 3 biological replicates of a particular strain. The drab-green line is from the parental strain KW20 and the other two are from competence mutants. Since these genes are not competence genes the three strains have very similar expression levels. The replicates are not all from the same day, and were not all sequenced in the same batch. The coloured shading shows the standard errors for each strain. <br />
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<span class="s1">We were surprised by the degree of variation in coverage across each segment, and by the very strong agreement between replicates and between strains. Since each segment is from within an operon, its RNA-seq coverage arises from transcripts that all began at the same promoter (to the right of the segment shown). Yet the coverage varies dramatically. This variation can't be due to chance differences in the locations and endpoints of reads, since it's mirrored between replicates and between strains. So our initial conclusion was that it must be due to Illumina sequencing biases. </span><br />
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<span class="s1">But now</span> consider the black-line graphs inset below the RNA-seq lines. These are the normalized coverages produced by Illumina sequencing of genomic DNA from the same parental strain KW20. Here there's no sign of the dramatic variation seen in the RNA-seq data. So the RNA-seq variation must not be due to biases in the Illumina sequencing. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDYYYKFt-xR7KwNp0v849Hz631tjMB9dVspvApWompYYH69v0nU33L8W-FdjjnAjZPhwktmQErPw-eEIJ0vmq6eQHYXAB6XEv9Jemu5YtWKTrJPtGjljyHFn53ycqQWS7Xk8iRow/s1600/Rd+HI1667+coverage.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="737" data-original-width="1500" height="157" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDYYYKFt-xR7KwNp0v849Hz631tjMB9dVspvApWompYYH69v0nU33L8W-FdjjnAjZPhwktmQErPw-eEIJ0vmq6eQHYXAB6XEv9Jemu5YtWKTrJPtGjljyHFn53ycqQWS7Xk8iRow/s320/Rd+HI1667+coverage.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHluJVybKOq9iDF56FM96syQYj0Kgk9DqbNOjg1-Xg8EL9evVfkGXIoWtQB2WLNXvMo1t-9kKLMFeg-r6ZmtSYFrAdJoSIrhRZCx3D7r-eyBqr-SPhnu-CSpWl8ozxwf8vPkeVtA/s1600/Rd+oppABCDE+coverage.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="750" data-original-width="1500" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHluJVybKOq9iDF56FM96syQYj0Kgk9DqbNOjg1-Xg8EL9evVfkGXIoWtQB2WLNXvMo1t-9kKLMFeg-r6ZmtSYFrAdJoSIrhRZCx3D7r-eyBqr-SPhnu-CSpWl8ozxwf8vPkeVtA/s320/Rd+oppABCDE+coverage.png" width="320" /></a></div>
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<b>How else could the RNA-seq variation arise? </b><br />
<ul>
<li>Sequence-specific biases in RNA degradation during RNA isolation? If this were the cause I'd expect to see much more replicate-to-replicate variation, since our bulk measurements saw substantial variation in the integrity of the RNA preps.</li>
<li>Biases in reverse transcriptase? </li>
<li>Biases at the library construction steps? I think these should be the same in the genomic-DNA sequencing.</li>
</ul>
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<b>Now on to the control sequencing from our big DNA-uptake experiment.</b><br />
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In this experiment the PhD student mixed naturally competent cells with chromosomal DNA, and then recovered and sequenced the DNA that had been taken up. He sequenced three replicates with each of four different DNA preparations; 'large-' and 'short-' fragment preps from each of two different H. influenzae strains ('NP' and 'GG'). As controls he sequenced each of the four input samples. He then compared the mean sequencing coverage at each position in the genome to its coverage in the input DNA sample.<br />
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Here I just want to consider results of sequencing the control samples. We only have one replicate of each sample, but the 'large' (orange) and 'short' (blue) samples effectively serve as replicates. Here's the results for DNA from strain NP. Each strain's coverage has been normalized as reads per million mapped reads (long: 2.7e6 reads; short: 4.7e6 reads).<br />
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The top panel shows coverage of a 1 kb segment of the NP genome. Coverage is fairly even over this interval, and fairly similar between the two samples. Note how similar the small-scale variation is; at most positions the orange and blue samples go up and down roughly in unison. I presume that this variation is due to minor biases in the Illumina sequencing.<br />
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The middle panel is a 10 kb segment. The variation looks sharper only because the scale is compressed, but again the two traces are roughly mirroring each other,<br />
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The lower panel is a 100 kb segment. Again the variation looks sharper, and the traces roughly mirror each other. Overall the coverage is consistent, not varying more than two-fold.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTSnt6r_C5oGhbloEMqJ_RvFiPcStT1TjF3PCJuzHJ3AmSfB-K05uNb58ov3T3U5DieexKc_C_iQHlnbX_dpV9Y-TRmQ3NKfm4x8gZRQtGaDBgiEdP4udlTnyD-imo_YXjJoyCxQ/s1600/NP+coverage+variation.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1041" data-original-width="1425" height="466" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTSnt6r_C5oGhbloEMqJ_RvFiPcStT1TjF3PCJuzHJ3AmSfB-K05uNb58ov3T3U5DieexKc_C_iQHlnbX_dpV9Y-TRmQ3NKfm4x8gZRQtGaDBgiEdP4udlTnyD-imo_YXjJoyCxQ/s640/NP+coverage+variation.png" width="640" /></a></div>
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Now here's the corresponding analysis of variation in the GG control samples. In the 1 kb plot the very-small-scale position-to-position variation is similar to that of NP and is mirrored by both samples. But the blue line also has larger scale variation over hundreds of bp that isn't seen in the orange line. This '500-bp-scale' variation is seen more dramatically in the 10 kb view. We also see more variation in the orange line than was seen with NP. In the 100 kb view we also see extensive variation in coverage over intervals of 10 kb or larger, especially in the blue sample. It's especially disturbing that there are many regions where coverage is unexpectedly low.<br />
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The 500-bp-scale variation can't be due to the blue sample having more random noise in read locations, since it actually has four-fold higher absolute coverage than the orange sample. Here are coverage histograms for all four samples (note the extra peak of low coverage positions in the GG short histogram):</div>
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<b>If you've read all the way to here: </b>You no doubt have realized that we don't understand where most of this variation is coming from. We don't know why the RNA-seq coverage is so much more variable than the DNA-based coverage. We don't know how much of the variation we see between the NP samples is due to sequencing biases, or noise, or other factors. We don't know why the GG samples have so much more variation than the NP samples and so much unexpectedly low coverage. (The strains' sequences differ by only a few %.)</div>
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We will be grateful for any suggestions, especially for links to resources that might shed light on this. </div>
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Later: From the Twitterverse, a merenlab blog post about how strongly GC content can affect coverage: <span style="font-size: small;"><span style="font-weight: normal;"><a href="http://merenlab.org/2016/12/14/coverage-variation/" rel="bookmark" title="Wavy coverage patterns in mapping results">Wavy coverage patterns in mapping results</a>. This prompted me to check the %GC for the segment shown in the second RNA-seq plot above. Here it is, comparing regular sequencing coverage to %GC:</span></span></div>
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<span style="font-size: small;"><span style="font-weight: normal;"> I don't see any correlation, particularly not the expected correlation of high GC with low coverage. Nor is there any evident correlation with the RBNA-seq coverage for the same region.</span></span></div>
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Rosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.com0