Spin models inferred from patient-derived viral sequence data faithfully describe HIV fitness landscapes

Abstract

Mutational escape from vaccine-induced immune responses has thwarted the development of a successful vaccine against AIDS, whose causative agent is HIV, a highly mutable virus. Knowing the virus’ fitness as a function of its proteomic sequence can enable rational design of potent vaccines, as this information can focus vaccine-induced immune responses to target mutational vulnerabilities of the virus. Spin models have been proposed as a means to infer intrinsic fitness landscapes of HIV proteins from patient-derived viral protein sequences. These sequences are the product of nonequilibrium viral evolution driven by patient-specific immune responses and are subject to phylogenetic constraints. How can such sequence data allow inference of intrinsic fitness landscapes? We combined computer simulations and variational theory á la Feynman to show that, in most circumstances, spin models inferred from patient-derived viral sequences reflect the correct rank order of the fitness of mutant viral strains. Our findings are relevant for diverse viruses.

Inference of epistatic effects leading to entrenchment and drug resistance in HIV-1 protease

“…This process is then repeated for each position by selecting the merger of characters which minimizes the RMSD in MI between all pairs of positions ij with the original alphabet size Q ¼ 21 and reduced alphabet size Q ¼ Q 0 , and is stopped once Q ¼ 2. Due to residue conservation at many loci in the HIV-1 protease genome, the average number of characters per position is 2, and several previous studies of HIV-1 have used a binary alphabet to extract meaningful information from sequences (Wu et al 2003;Ferguson et al 2013;Shekhar et al 2013;Flynn et al 2015). However, using a binary alphabet (wildtype, mutant) marginalizes potentially informative distinctions between amino acids at certain positions, especially PI-associated sites, that acquire multiple mutations from the wildtype.…”

“…Recently, probabilistic models, called Potts models, have been used to assign scores to individual protein sequences which correlate with experimental measures of fitness (Haq et al 2012;Ferguson et al 2013;Mann et al 2014;Figliuzzi et al 2015;Hopf et al 2017). These advances build upon previous and ongoing work in which Potts models have been used to extract information from sequence data regarding tertiary and quaternary structure of protein families (Weigt et al 2009;Morcos et al 2011Morcos et al , 2014Marks et al 2012;Sulkowska et al 2012;Sutto et al 2015;Barton et al 2016a;Haldane et al 2016;Jacquin et al 2016) and sequencespecific quantitative predictions of viral protein stability and fitness (Haq et al 2012;Shekhar et al 2013;Barton et al 2016b;Butler et al 2016).…”

“…Protein contacts derived from Potts models have been used for several innovative purposes; for example, for ab-initio structure predictions (Tang et al 2015), to bias molecular dynamics simulations to reveal metastable conformations (Morcos et al 2013), and to distinguish sequence-specific interactions which contribute to the stability of alternate functional conformations (Haldane et al 2016). More recently, these models have been used to probe protein fitness landscapes as the Potts Hamiltonian provides a mapping from protein sequences to statistical energy scores in which sequences with lower scores are more probable (Shekhar et al 2013;Figliuzzi et al 2015;Hopf et al 2017). We make use of this property of Potts statistical models in this work.…”

“…Several schemes have been developed to solve the Inverse Ising problem, from very fast but very approximate mean field solutions and messagepassing algorithms (Mézard and Mora 2009;Weigt et al 2009;Morcos et al 2011), fast and less approximate pseudolikelihood maximization solutions (Ekeberg et al 2013), to computationally demanding Monte Carlo algorithms (Mora and Bialek 2011;Shekhar et al 2013;Sutto et al 2015;Haldane et al 2016) and cluster expansion methods (Barton et al 2016a). More information regarding specifics of different inference methodologies can be found in the following reviews and the references within (Marks et al 2012;Levy et al 2017).…”

Optimal Design of Experiments by Combining Coarse and Fine Measurements

“…In contrast, experimentally measuring the phenotypic change is much more difficult. A related problem is to predict the viral fitness landscape given HIV sequences obtained from patients; again collecting patient samples is much easier than measuring fitness directly [9,10]. In singlecell RNA sequencing, decomposition methods that extract the correlation structure of shallow gene expression measurements is an ongoing challenge [11,12].…”