Mutation rate, selection, and epistasis inferred from RNA virus haplotypes via neural posterior estimation

RNA viruses are particularly notorious for their high levels of genetic diversity, which is generated through the forces of mutation and natural selection. However, disentangling these two forces is a considerable challenge, and this may lead to widely divergent estimates of viral mutation rates, as well as difficulties in inferring the fitness effects of mutations. Here, we develop, test, and apply an approach aimed at inferring the mutation rate and key parameters that govern natural selection, from haplotype sequences covering full-length genomes of an evolving virus population. Our approach employs neural posterior estimation, a computational technique that applies simulation-based inference with neural networks to jointly infer multiple model parameters. We first tested our approach on synthetic data simulated using different mutation rates and selection parameters while accounting for sequencing errors. Reassuringly, the inferred parameter estimates were accurate and unbiased. We then applied our approach to haplotype sequencing data from a serial passaging experiment with the MS2 bacteriophage, a virus that parasites Escherichia coli. We estimated that the mutation rate of this phage is around 0.2 mutations per genome per replication cycle (95% highest density interval: 0.051-0.56). We validated this finding with two different approaches based on single-locus models that gave similar estimates but with much broader posterior distributions. Furthermore, we found evidence for reciprocal sign epistasis between four strongly beneficial mutations that all reside in an RNA stem loop that controls the expression of the viral lysis protein, responsible for lysing host cells and viral egress. We surmise that there is a fine balance between over- and underexpression of lysis that leads to this pattern of epistasis. To recap, we have developed an approach for joint inference of the mutation rate and selection parameters from full haplotype data with sequencing errors and used it to reveal features governing MS2 evolution.