Hierarchical Bayesian Modeling of the HIV Response to Therapy

Transcription

1 Hierarchical Bayesian Modeling of the HIV Response to Therapy Shane T. Jensen Department of Statistics, The Wharton School, University of Pennsylvania March 23, 2010 Joint Work with Alex Braunstein and Jon McAuliffe

2 Therapy: Disrupting the HIV infection cycle Drugs are a popular medical strategies for keep viral load down by disrupting infection cycle of HIV Drug therapies: drugs designed to bind to surface of HIV and prevent it from attaching to target cells We will model a promising new type of treatment Antisense gene therapy: allow HIV to bind to target cell and release viral RNA, but then attack viral RNA directly before it can be integrated into target cell genome HIV will try to evolve (change either protein or RNA) to escape this therapy

3 Drug Therapy versus Gene Therapy Illustration +',-$%&"'()*$!"#"$%&"'()*$ HIV Drug Therapy HIV Virion HIV viral RNA HIV Gene Therapy cytosol nucleus

4 Mutation and Recombination Primary mechanisms for evolution: Mutation: change of identity of a single RNA nucleotide. Can also delete nucleotides Recombination: two viral RNA sequences are spliced to produce a hybrid sequence.!"#$"#"%!"#$"#"%!"$$"#"%!"$$"#"% HIV has one of the highest rates of mutation/recombination of any organism ever seen

5 Population Genetics Due to high mutation and recombination rates, individuals infected with HIV can have several distinct HIV strains Need to model HIV as a population of sequences, not a specific sequence, that evolves in response to therapy

6 Issues with Evolutionary Response Goal is to model the evolutionary response (through mutation and recombination) of HIV to therapy Three crucial components of problem must be addressed: Mutation vs. recombination Rates for both processes of sequence change must be modeled simultaneously Spatial heterogeneity Therapies target specific regions of HIV genome and so evolution could also be in specific locations Two sample comparison Real interest is differences in mutation and recombination rates between treatment and control sequences

7 Overview of our Approach The coalescent with recombination: a population genetics model we build upon to model mutation and recombination rates for a population of sequences We expand previous coalescent-based approaches to allow changes at nucleotide level (instead of protein level) Blocking structure for mutation and recombination rates Allows for spatial heterogeneity while still sharing information between neighboring sequence regions Hierarchical prior distribution handles two sample structure Allows for differential treatment effect while pooling information between treatment and control sequences

8 Notation Data are aligned nucleotide sequences H = (H C, H T ) H C = (h C 1,..., hc n ) are control sequences of length L H T = (h T 1,..., ht m) are treatment sequences of length L Parameters of interest are Θ = (ρ C, ρ T, µ C, µ T ) ρ are recombination rates (treatment and control) µ are mutation rates (treatment and control) All rates also vary spatially along length of sequences Ancestry G relates all sequences to each other Need model that relates data H to unknowns G and Θ

9 Coalescent model for sequence history G Coalescent: sequences coalesce into common lineages back to their most recent common ancestor '()(*+,-)".3$" '()(*+,-)".3#" '()(*+,-)".3!" '()(*+,-)"."/01**().2"!" #" $" %" &" Mutation rates µ easy to build into coalescent model G Recombination can also be included in coalescent G

10 Estimation with Coalescent Sequence ancestry G is not of direct interest: goal is mutation and recombination rates Θ Maximum likelihood estimation sup Θ,G p(h Θ, G) or integration over all possible ancestries G p(h Θ) = G p(h Θ, G) p(g) are both very difficult tasks given the large space of G Even for a relatively small number of sequences, such as 100, the space of possible G is huge.

11 Product of Approximate Conditionals Marginal likelihood p(h Θ) intractable over all G PAC (Product of approximate conditionals) likelihood p(h Θ) = p(h 1 Θ) p(h 2 h 1, Θ)p(h 3 h 2, h 1, Θ) ˆp(h 1 Θ) ˆp(h 2 h 1, Θ)ˆp(h 3 h 2, h 1, Θ) Approximate sequence h k+1 as a mosaic of sequences (h 1,..., h k ) generated by a hidden Markov model ˆp(h k+1 h 1:k, Θ) calculated using forward summing algorithm for HMMs. Depends on ordering of sequences so average calculation over several different orderings

12 Structure on Mutation and Recombination PAC likelihood allows us to more easily integrate out ancestry G so we can focus on modeling of parameters Θ Θ includes mutation rates µ and recombination rates ρ Now need additional structure in our model to address: Spatial heterogeneity: different rates for mutation and recombination in different sequence regions Two-samples comparison: want to estimate differential rates between treatment vs. control populations Should allow us to estimate differential evolution response to therapy

13 Hierarchical Blocking Structure Hierarchical prior on mutation µ and recombination ρ Rates vary along sequence in piece-wise constant way e.g. B µ contiguous blocks (µ 1,..., µ Bµ ) of mutation rates Treatment µ T j vs. control µ C j vary around block-specific µ j

14 Blocking Structure Example Grand central mutation and recombination rates (gray) Central mutation/recombination rate for each block (blue) Treatment and control rates around central rate (black)

15 Model Implementation PAC likelihood ˆp(H Θ) gives sequences H as function of mutation and recombination rates Θ Hierarchical prior distribution P(Θ) for spatial heterogeneity and two sample comparison Focus on posterior distribution for inference: p(θ H) ˆp(H Θ) p(θ) MCMC implementation: Gibbs and Metropolis-Hastings moves for most parameters as well as reversible jump moves for the blocking structure

16 MCMC moves 1 Reversible jump moves for blocking structure: 1 Choose block uniformly to split or merge with a neighbor 2 Move block boundary to the left or right 2 Gibbs moves for rate parameters 1 Sample treatment vs control rates (µ T j, µ C j ) for each block 2 Sample central mutation rate µ j for each block 3 Sample grand central mutation rate µ 0 4 Sample variance of treatment and control mutation rates σ 2 µ 5 Sample variance of central mutation rates σ 2 µ 0 3 Same set of blocking and rate moves for recombination 4 MH move for transition/transversion ratio κ

17 Application to Antisense Gene Therapy VIRxSYS gene therapy: data generated in vitro from a sample of wt-hiv that were exposed to VIRxSYS gene therapy and a control sample Focus on treatment effects: differential mutation rate µ T µ C and recombination rate ρ T ρ C for each location along the sequence

18 Mutation Treatment Effect of Antisense Gene Therapy The large increase in mutation overlaps with the antisense target region. Increases in mutation to the left of antisense target region are consistent with other gene therapy studies.

19 Recombination Treatment Effect of Antisense Gene Therapy The area of decreased recombination corresponds to the area of increased mutation, but it is not significant. Wide posterior intervals in part because recombination does not seem to have a strong spatial signal

20 Simpler Approaches for Mutation Simplest approach would just be to examine mutation directly through segregating sites Segregating sites are nucleotide locations where at least one sequence in the sample differs from the others. A!GATTACA!CAT!ATTACC A!GATTACA!CAT!ATTGCC A!GATTACA!CAT!ATTACC A!GACTACAGCAT!ATTACC A!GATTACA!CAT!ATTAAC

21 Comparison to Segregating Sites Compare segregating sites (blue = treatment, red = control) to posterior differential mutation rate µ T µ C Higher density of segregating sites around elevated mutation area, but our model allows sharing of information between closely located sites

22 Summary Our sophisticated model allows us to measure viral evolutionary change through spatially-varying recombination and mutation at the nucleotide level. Our model measures pairwise differences in mutation and recombination between treatment and control groups, allowing estimation of spatially varying treatment effects. Our methodology able to detect biologically relevant signal in two HIV applications: Identified drug-resistant mutations in Enfuvirtide drug therapy Detect elevated mutation rates that overlap with antisense target in VIRxSYS gene therapy