Faithful Models of Viral Fitness can be Inferred from Mutation Patterns in Viral DNA Sequences Sampled from a Population

Abstract

A detailed understanding of fitness landscapes of viruses can be exploited to computationally screen candidate vaccines and therapeutic drugs. Inverse Ising models inferred using techniques rooted in entropy maximization have recently been proposed as accurate fitness landscapes for certain proteins of HIV. Such landscapes are parameterized based on statistical quantities measured from population sequence ensembles, like the average probabilities of mutation at single amino acid sites, pairs of sites etc. Since individual sequences in the ensemble have evolved under diverse immune responses, patterns of mutation in such data can reflect systematic biases arising from immune escape rather than intrinsic fitness requirements. Therefore, delineating the role of immune pressure in shaping mutational patterns in the population and understanding how intrinsic fitness can be faithfully inferred from sequence data is important. We performed simulations of a discrete molecular quasispecies model that reveals the essential role of immune pressure in driving viral evolution on its intrinsic fitness landscape. Our simulations show that in the absence of immune pressure the virus remains frozen in its ground state and mutations that reflect the correlation structure of its fitness landscape are not selected at the population level. In the presence of immune pressure, there is an intermediate mutation rate per site per generation that favors viral adaptation and selects mutations. We studied an analytical mapping our quasispecies model to an equilibrium 2-D Ising system. Analyzing the resulting Hamiltonian using variational mean field theory enabled us to derive analytical expressions for the “effective fitness” of an arbitrary viral strain evolving under immune pressure in a population. A spearman rank correlation analysis shows that the effective fitness is extremely well correlated with the intrinsic fitness, thus enabling robust inference.