HIV and population genetics 2. Please sit in row K or forward

Transcription

1 HIV and population genetics 2 Please sit in row K or forward

2 Random biological fact of the day: a giant wall of... myovirus P-SSM4 100 nm >10 8 viruses / ml in seawater Sullivan MB et al. PLoS Biology Vol. 3, No. 5, e144 doi: /journal.pbio

3 Topics for today HIV evolution inside a patient (the four forces continued) Measures of genetic variation in a population: heterozygosity

4 Where we left off last time Mutation Genetic drift Natural selection Migration

5 A simple model of allele frequency changes due to genetic drift 1 2 Two alleles Fixed population size Organisms have only one copy of each sequence Asexual reproduction Make next generation by sampling with replacement No new mutation

6 Generation 1 2

7 Generation 1 2 Repeatedly sample until next generation is same size as first.

8 Generation 1 2 3

9 Genetic Drift allele fixed Frequency of allele Generations allele lost

10 In a population of size 50, the allele is present in a single copy. What is the probability that is lost in the next generation?

11 Relating the model to the real scenario of HIV in a patient Viral population Key similarity: random effects exert strong influence over how much a given viral particle is able to reproduce.

12 Four forces that can change allele frequencies in populations Mutation Genetic drift Natural selection Migration

13 HIV must struggle against the patient s immune system Viral population SEM of blood cells Bruce and Harry Schaefer, National Cancer Institute

14 A definition of selection: Natural selection is the differential survival and/or reproduction of individuals in a population due to differences in their physical characteristics.

15 A population genetic model with natural selection w 1 = 1 w 2 = 0.5 Fitness: Metric of an individual organism s ability to survive and reproduce In our model, the probability that an individual survives to reproduction

16 1

17 1 Natural selection

18 1 2 Natural selection

19 1 2 Natural selection In addition to natural selection, which of the four forces is present in this model?

20 Natural selection: alleles which lead to better survival become more numerous over time Frequency of allele Generations

21 Natural selection within an HIV patient: measuring relative fitness Strain 1 Allow strains to compete with each other over time. Measure amount of each at end: Cell culture dish with helper T cells from a person without HIV Strain 2 Strain 1 Strain 2 Troyer et al. J Virol. 2005;79(14):

22 Natural selection within an HIV patient: relative fitness over time Freeman and Heron 4 th ed. Troyer et al. J Virol. 2005;79(14):

23 Four forces that can change allele frequencies in populations Mutation Genetic drift Natural selection Migration

24 Migration (gene flow) Frequency of allele Before migration Migration can Introduce new alleles Alter freq of existing alleles After migration

25 Topics for today HIV evolution inside a patient (the four forces continued) Measures of genetic variation in a population: heterozygosity

26 Population genetic simulations with ongoing mutation GGC Sampling with replacement Replication with possible mutation GGC 1 2 Generation

27 GGC TGG 1 2 Generation

28 GGC GGC TGG GGA GGC 1 2 Generation 3

29 Measuring genetic variation in a population: heterozygosity Heterozygosity: the probability two alleles sampled randomly (with replacement) from the gene pool are different. GGC GGA GGC Site 1 Site 3 Site 2 Heterozygosity, site 1 Heterozygosity, site 2 Heterozygosity, site 3

30 Measuring genetic variation in a population: heterozygosity Heterozygosity: the probability two alleles sampled randomly (with replacement) from the gene pool are different. GGC GGA GGC Site 1 Site 3 Site 2 Heterozygosity, site 1 Heterozygosity, site 2 Heterozygosity, site 3 0 0

31 Calculating heterozygosity Alleles at site 3 G C G A C count frequency A C G T Probability of pulling 2 A alleles Probability of pulling 2 C alleles Probability of pulling 2 G alleles Probability of pulling 2 T alleles Heterozygosity at site 3 (probability of pulling two different alleles) If you have a little extra time: what is the theoretically maximum possible value for heterozygosity in nucleotide sequences?

32 Calculating heterozygosity Alleles at site 3 G C G A C A C G T count frequency Probability of pulling 2 A alleles 0.04 Probability of pulling 2 C alleles 0.16 Probability of pulling 2 G alleles 0.16 Probability of pulling 2 T alleles 0 Heterozygosity at site 3 (probability of pulling two different alleles) = 0.64 If you have a little extra time: what is the theoretically maximum possible value for heterozygosity in nucleotide sequences? (1 -.25^2 -.25^2 -.25^2 -.25^2) = 0.75

33 Measuring genetic variation in a population: heterozygosity Heterozygosity, site 1 Heterozygosity, site 2 Heterozygosity, site GGC GGA GGC 0.64 Average heterozygosity over all three sites: 0.213

34 Plot of heterozygosity in a drift simulation with ongoing mutation Starting allele: AAA Mutation probability: mutations per nucleotide Heterozygosity averaged over three nucleotide sites Heterozygosity Assymptote less that 0.75 Generations

35 Worksheet (Rip it off from the back of your packet) Name: Mutation probability = mutations per nucleotide Heterozygosity Assymptote less that 0.75 Generations 1. Why does this plot of heterozygosity vs. generations have an asymptote less than 0.75? 2. What would you expect to happen if we increased the mutation probability? Decreased it? (you can draw this)

36 Worksheet (Rip it off from the back of your packet) Name: Mutation probability = mutations per nucleotide (RED) Mutation probability = mutations per nucleotide (BLUE) Mutation probability = mutations per nucleotide (BLACK) Heterozygosity Generations 1. Why does this plot of heterozygosity vs. generations have an asymptote less than 0.75? Genetic drift is removing variation in these simulations. The more variation there is, the more drift removes. Once the amount of variation becomes large enough, the variation added by mutation is balanced by that removed by drift. 2. What would you expect to happen if we increased the mutation probability? Decreased it? (you can draw this)

37 Question: why has HIV killed so many people? Defeating the immune system Attacks the immune system itself Rapid evolution Helper T-cell count (cells per mm3) Acute Asymptomatic AIDS Weeks Years Based on Maartens, Gary, Connie Celum, and Sharon R. Lewin. "HIV infection: epidemiology, pathogenesis, treatment, and prevention." The Lancet (2014):

38 Hand in your worksheets please! (and be sure you put your full name on it)