tag:blogger.com,1999:blog-32079676.post2070590255581837936..comments2024-02-13T21:22:02.522-08:00Comments on RRResearch: Controlling mutagenesisRosie Redfieldhttp://www.blogger.com/profile/06807912674127645263noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-32079676.post-51688475723957621402007-11-08T04:15:00.000-08:002007-11-08T04:15:00.000-08:00Because our genomes are very big and only a small ...Because our genomes are very big and only a small fraction of bases mutate in any one cycle, the program won't scan every base and use the matrix to decide whether it stays the same or mutates. Instead it will first decide how many bases will mutate, randomly choose which positions in the genome these will be, and then use the matrix to decide which base each mutation changes to.<BR/><BR/>That's why the 'no change' cells of the matrix have values of 0. I'll let you know if the calculations don't give the desired base compositions.Rosie Redfieldhttps://www.blogger.com/profile/06807912674127645263noreply@blogger.comtag:blogger.com,1999:blog-32079676.post-5871180112572559622007-11-07T21:06:00.000-08:002007-11-07T21:06:00.000-08:00Hi Rosie,This looks fine to me with just some mino...Hi Rosie,<BR/><BR/>This looks fine to me with just some minor adjustments.<BR/><BR/>There are two types of matrices that are represented in the literature, depending on whether time is measured in discrete steps (like a year) or in continuous time.<BR/><BR/>In the first case (discrete time steps), you should have elements like 1-2gamma-alpha (first row, first column) along the diagonal in the matrix. For example, the probability that an A remains an A over one year would be 1-2gamma-alpha.<BR/><BR/>In the second case (continuous time), the matrix represents a rate per unit time of changing from state i to state j. In this case, the element in the first row and first column would be -2gamma-alpha. Then, the rate of change of the proportion of As per unit time could be written as a differential equation:<BR/><BR/>dA/dt = (-2gamma-alpha)*A+(delta)*T+(delta)*C+(beta)*G<BR/><BR/>The most likely type of simulation that you would want to run would run time in particular time units, with each loop corresponding to one time step (e.g., a cell replication, an hour, a year, or whatever). The first matrix would then tell you the fraction of As that stay the same (1-2gamma-alpha), the fraction that mutate to C (gamma), etc, within each loop.<BR/><BR/>Note that you don't have to normalize these rates by dividing by the sum. You would do that only if you wanted to say that the probability that A mutates to something is 2gamma+alpha, after which point you could say that the fraction of the mutations going to C is gamma/(2gamma+alpha), the fraction going to T is gamma/(2gamma+alpha), and the fraction going to G is alpha/(2gamma+alpha). But this normalization isn't necessary if you just run your simulations using the matrix to give the probability of moving from state i to j in a loop.<BR/><BR/>Let me know if it converges to the right equilibrium!<BR/><BR/>Cheers,<BR/>SallyAnonymousnoreply@blogger.com