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Lecture 18 : Mutation October 30, 2015 Last Time u Exam to be returned Monday. Answer key is posted u Effects of population structure, admixture, selection, and mutation on LD u Admixture calculation u Selective sweeps Today Mutation introduction Mutation-reversion equilibrium Mutation and selection What Controls Genetic Diversity Within Populations? 4 major evolutionary forces Mutation Drift + - Diversity +/Selection + Migration Mutation Primary driver of genetic diversity Main source of new variants within a reproductively isolated species Mutation often ignored because rates assumed to be extremely low relative to magnitude of other effects Accumulation of mutations in population primarily a function of drift and selection PLUS rate of backmutation Mutation rates are tough to estimate! Spontaneous mutation rates Schlager and Dickie (1967) tracked spontaneous mutation at 5 loci controlling coat color in 17 million house mice Forward > Backward mutation http://jaxmice.jax.org http://www.gsc.riken.go.jp Mutation Rates can Vary Tremendously Among Loci Length mutations occur much more frequently than point mutations in repetitive regions Microsatellite mutation rates as high as 10-2 Source: SilkSatDB Reverse Mutations Most mutations are “reversible” such that original allele can be reconstituted Probability of reversion is generally lower than probability of mutation to a new state Possible States for Second Mutation at a Locus Thr Tyr Leu Leu ACC TAT TTG CTG Reversion A C ACC TCT TTG CTG Thr Ser Leu Leu C T ACC TTT TTG CTG Thr Cys Leu Leu ACC TGT TTG CTG Thr C G Phe Leu Leu Allele Frequency Change Through Time With no back-mutation: p1 p0 p0 (1 ) p0 pt (1 ) p0 t How long would it take to reduce A1 allele frequency by 50% if μ=10-5? Two-Allele System with Forward and Reverse Mutation A1 µ ν A2 where μ is forward mutation rate, and ν is reverse mutation rate Expected change in mutant allele: q p q Allele Frequency Change Driven By Mutation q p q q q( ) Equilibrium between forward and reverse mutations: qe ( ) pe ( ) Allele Frequency Change Through Time with Reverse mutation Allele Frequency (p) Reverse Mutation (ν) Forward Mutation (µ) Mutant Alleles (q) Equilibrium Occurs between Forward and Reverse Mutation Is this equilibrium stable or unstable? qe ( ) μ=10-5 Forward mutation 10-5 Lower rate of reverse mutation means higher qeq Mutation-Reversion Equilibrium pe ( ) where µ=forward mutation rate (0.00001) and ν is reverse mutation rate (0.000005) What if the population is not infinite? Fate of Alleles in Mutation-Drift Balance p=frequency of new mutant allele in small population Time to fixation of a new mutation is much longer than time to loss 1 u ( p) 2N An equilibrium occurs between creation of new mutants, and loss by drift 1 u (q) 1 2N u(p) is probability of fixation u(q) is probability of loss Infinite Alleles Model (Crow and Kimura Model) Each mutation creates a completely new allele Alleles are lost by drift and gained by mutation: a balance occurs Is this realistic? Average human protein contains about 300 amino acids (900 nucleotides) Number of possible mutant forms of a gene: n4 900 7.14 x10 542 If all mutations are equally probable, what is the chance of getting same mutation twice? Fate of Alleles in Mutation-Drift Balance p=frequency of new mutant allele in small population Time to fixation of a new mutation is much longer than time to loss 1 u ( p) 2N An equilibrium occurs between creation of new mutants, and loss by drift 1 u (q) 1 2N u(p) is probability of fixation u(q) is probability of loss Mutation & Mating Simulation 1. Select two gametes from the gamete pool (brown is wild=type, green=mutant 2. Find a mate using the Excel sheet (e.g., see below) 3. Pass a random allele down to each of 2 offspring. One of these offspring will become you for the next generation. 4. Mutate an offspring allele if indicated by the Excel sheet by choosing a new random allele from the pool (cup of candy) (rate = 1x10-2) 5. Repeat for the next generation. Apoorva Margo x Results of Mutation & Mating Simulation The forward mutation rate was quite high (1x10-2), and the reverse mutation rate was at least an order of magnitude lower (based on the freqency of brown M&M’s in the mutant pool), so the frequency of mutant alleles increased fairly dramatically even with substantial potential for genetic drift.