An inference model gives insights into innate immune adaptation and repertoire diversity.

The innate immune system is the body's first line of defense against infection. Natural killer (NK) cells, a vital part of the innate immune system, help to control infection and eliminate cancer. Studies have identified a vast array of receptors that NK cells use to discriminate between healthy and unhealthy cells. However, at present, it is difficult to explain how NK cells will respond to novel stimuli in different environments. In addition, the expression of different receptors on individual NK cells is highly stochastic, but the reason for these variegated expression patterns is unclear. Here, we studied the recognition of unhealthy target cells as an inference problem, where NK cells must distinguish between healthy targets with normal variability in ligand expression and ones that are clear "outliers." Our mathematical model fits well with experimental data, including NK cells' adaptation to changing environments and responses to different target cells. Furthermore, we find that stochastic, "sparse" receptor expression profiles are best able to detect a variety of possible threats, in agreement with experimental studies of the NK cell repertoire. While our study was specifically motivated by NK cells, our model is general and could also apply more broadly to explain principles of target recognition for other immune cell types.

Correlated Allele Frequency Changes Reveal Clonal Structure and Selection in Temporal Genetic Data.

In evolving populations where the rate of beneficial mutations is large, subpopulations of individuals with competing beneficial mutations can be maintained over long times. Evolution with this kind of clonal structure is commonly observed in a wide range of microbial and viral populations. However, it can be difficult to completely resolve clonal dynamics in data. This is due to limited read lengths in high-throughput sequencing methods, which are often insufficient to directly measure linkage disequilibrium or determine clonal structure. Here, we develop a method to infer clonal structure using correlated allele frequency changes in time-series sequence data. Simulations show that our method recovers true, underlying clonal structures when they are known and accurately estimate linkage disequilibrium. This information can then be combined with other inference methods to improve estimates of the fitness effects of individual mutations. Applications to data suggest novel clonal structures in an E. coli long-term evolution experiment, and yield improved predictions of the effects of mutations on bacterial fitness and antibiotic resistance. Moreover, our method is computationally efficient, requiring orders of magnitude less run time for large data sets than existing methods. Overall, our method provides a powerful tool to infer clonal structures from data sets where only allele frequencies are available, which can also improve downstream analyses.

Adenovirus-vectored vaccine containing multidimensionally conserved parts of the HIV proteome is immunogenic in rhesus macaques.

An effective vaccine that can protect against HIV infection does not exist. A major reason why a vaccine is not available is the high mutability of the virus, which enables it to evolve mutations that can evade human immune responses. This challenge is exacerbated by the ability of the virus to evolve compensatory mutations that can partially restore the fitness cost of immune-evading mutations. Based on the fitness landscapes of HIV proteins that account for the effects of coupled mutations, we designed a single long peptide immunogen comprising parts of the HIV proteome wherein mutations are likely to be deleterious regardless of the sequence of the rest of the viral protein. This immunogen was then stably expressed in adenovirus vectors that are currently in clinical development. Macaques immunized with these vaccine constructs exhibited T-cell responses that were comparable in magnitude to animals immunized with adenovirus vectors with whole HIV protein inserts. Moreover, the T-cell responses in immunized macaques strongly targeted regions contained in our immunogen. These results suggest that further studies aimed toward using our vaccine construct for HIV prophylaxis and cure are warranted.

Inferring Epistasis from Genetic Time-series Data.

Epistasis refers to fitness or functional effects of mutations that depend on the sequence background in which these mutations arise. Epistasis is prevalent in nature, including populations of viruses, bacteria, and cancers, and can contribute to the evolution of drug resistance and immune escape. However, it is difficult to directly estimate epistatic effects from sampled observations of a population. At present, there are very few methods that can disentangle the effects of selection (including epistasis), mutation, recombination, genetic drift, and genetic linkage in evolving populations. Here we develop a method to infer epistasis, along with the fitness effects of individual mutations, from observed evolutionary histories. Simulations show that we can accurately infer pairwise epistatic interactions provided that there is sufficient genetic diversity in the data. Our method also allows us to identify which fitness parameters can be reliably inferred from a particular data set and which ones are unidentifiable. Our approach therefore allows for the inference of more complex models of selection from time-series genetic data, while also quantifying uncertainty in the inferred parameters.

Predominance of positive epistasis among drug resistance-associated mutations in HIV-1 protease.

Drug-resistant mutations often have deleterious impacts on replication fitness, posing a fitness cost that can only be overcome by compensatory mutations. However, the role of fitness cost in the evolution of drug resistance has often been overlooked in clinical studies or in vitro selection experiments, as these observations only capture the outcome of drug selection. In this study, we systematically profile the fitness landscape of resistance-associated sites in HIV-1 protease using deep mutational scanning. We construct a mutant library covering combinations of mutations at 11 sites in HIV-1 protease, all of which are associated with resistance to protease inhibitors in clinic. Using deep sequencing, we quantify the fitness of thousands of HIV-1 protease mutants after multiple cycles of replication in human T cells. Although the majority of resistance-associated mutations have deleterious effects on viral replication, we find that epistasis among resistance-associated mutations is predominantly positive. Furthermore, our fitness data are consistent with genetic interactions inferred directly from HIV sequence data of patients. Fitness valleys formed by strong positive epistasis reduce the likelihood of reversal of drug resistance mutations. Overall, our results support the view that strong compensatory effects are involved in the emergence of clinically observed resistance mutations and provide insights to understanding fitness barriers in the evolution and reversion of drug resistance.

MPF-BML: a standalone GUI-based package for maximum entropy model inference.

SUMMARY: Learning underlying correlation patterns in data is a central problem across scientific fields. Maximum entropy models present an important class of statistical approaches for addressing this problem. However, accurately and efficiently inferring model parameters are a major challenge, particularly for modern high-dimensional applications such as in biology, for which the number of parameters is enormous. Previously, we developed a statistical method, minimum probability flow-Boltzmann Machine Learning (MPF-BML), for performing fast and accurate inference of maximum entropy model parameters, which was applied to genetic sequence data to estimate the fitness landscape for the surface proteins of human immunodeficiency virus and hepatitis C virus. To facilitate seamless use of MPF-BML and encourage more widespread application to data in diverse fields, we present a standalone cross-platform package of MPF-BML which features an easy-to-use graphical user interface. The package only requires the input data (protein sequence data or data of multiple configurations of a complex system with large number of variables) and returns the maximum entropy model parameters. AVAILABILITY AND IMPLEMENTATION: The MPF-BML software is publicly available under the MIT License at https://github.com/ahmedaq/MPF-BML-GUI. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Fitness landscape of the human immunodeficiency virus envelope protein that is targeted by antibodies.

HIV is a highly mutable virus, and over 30 years after its discovery, a vaccine or cure is still not available. The isolation of broadly neutralizing antibodies (bnAbs) from HIV-infected patients has led to renewed hope for a prophylactic vaccine capable of combating the scourge of HIV. A major challenge is the design of immunogens and vaccination protocols that can elicit bnAbs that target regions of the virus's spike proteins where the likelihood of mutational escape is low due to the high fitness cost of mutations. Related challenges include the choice of combinations of bnAbs for therapy. An accurate representation of viral fitness as a function of its protein sequences (a fitness landscape), with explicit accounting of the effects of coupling between mutations, could help address these challenges. We describe a computational approach that has allowed us to infer a fitness landscape for gp160, the HIV polyprotein that comprises the viral spike that is targeted by antibodies. We validate the inferred landscape through comparisons with experimental fitness measurements, and various other metrics. We show that an effective antibody that prevents immune escape must selectively bind to high escape cost residues that are surrounded by those where mutations incur a low fitness cost, motivating future applications of our landscape for immunogen design.

Characterization of Intact Proviruses in Blood and Lymph Node from HIV-Infected Individuals Undergoing Analytical Treatment Interruption.

The role of lymphoid tissue as a potential source of HIV-1 rebound following interruption of antiretroviral therapy (ART) is uncertain. To address this issue, we compared the latent viruses obtained from CD4+ T cells in peripheral blood and lymph nodes to viruses emerging during treatment interruption. Latent viruses were characterized by sequencing near-full-length (NFL) proviral DNA and env from viral outgrowth assays (VOAs). Five HIV-1-infected individuals on ART were studied, four of whom participated in a clinical trial of a TLR9 agonist that included an analytical treatment interruption. We found that 98% of intact or replication-competent clonal sequences overlapped between blood and lymph node. In contrast, there was no overlap between 205 latent reservoir and 125 rebound sequences in the four individuals who underwent treatment interruption. However, rebound viruses could be accounted for by recombination. The data suggest that CD4+ T cells carrying latent viruses circulate between blood and lymphoid tissues in individuals on ART and support the idea that recombination may play a role in the emergence of rebound viremia.IMPORTANCE HIV-1 persists as a latent infection in CD4+ T cells that can be found in lymphoid tissues in infected individuals during ART. However, the importance of this tissue reservoir and its contribution to viral rebound upon ART interruption are not clear. In this study, we sought to compare latent HIV-1 from blood and lymph node CD4+ T cells from five HIV-1-infected individuals. Further, we analyzed the contribution of lymph node viruses to viral rebound. We observed that the frequencies of intact proviruses were the same in blood and lymph node. Moreover, expanded clones of T cells bearing identical proviruses were found in blood and lymph node. These latent reservoir sequences did not appear to be the direct origin of rebound virus. Instead, latent proviruses were found to contribute to the rebound compartment by recombination.

Paired quantitative and qualitative assessment of the replication-competent HIV-1 reservoir and comparison with integrated proviral DNA.

HIV-1-infected individuals harbor a latent reservoir of infected CD4+ T cells that is not eradicated by antiretroviral therapy (ART). This reservoir presents the greatest barrier to an HIV-1 cure and has remained difficult to characterize, in part, because the vast majority of integrated sequences are defective and incapable of reactivation. To characterize the replication-competent reservoir, we have combined two techniques, quantitative viral outgrowth and qualitative sequence analysis of clonal outgrowth viruses. Leukapheresis samples from four fully ART-suppressed, chronically infected individuals were assayed at two time points separated by a 4- to 6-mo interval. Overall, 54% of the viruses emerging from the latent reservoir showed gp160 env sequences that were identical to at least one other virus. Moreover, 43% of the env sequences from viruses emerging from the reservoir were part of identical groups at the two time points. Groups of identical expanded sequences made up 54% of proviral DNA, and, as might be expected, the sequences of replication-competent viruses in the active reservoir showed limited overlap with integrated proviral DNA, most of which is known to represent defective viruses. Finally, there was an inverse correlation between proviral DNA clone size and the probability of reactivation, suggesting that replication-competent viruses are less likely to be found among highly expanded provirus-containing cell clones.

Scaling laws describe memories of host-pathogen riposte in the HIV population.

The enormous genetic diversity and mutability of HIV has prevented effective control of this virus by natural immune responses or vaccination. Evolution of the circulating HIV population has thus occurred in response to diverse, ultimately ineffective, immune selection pressures that randomly change from host to host. We show that the interplay between the diversity of human immune responses and the ways that HIV mutates to evade them results in distinct sets of sequences defined by similar collectively coupled mutations. Scaling laws that relate these sets of sequences resemble those observed in linguistics and other branches of inquiry, and dynamics reminiscent of neural networks are observed. Like neural networks that store memories of past stimulation, the circulating HIV population stores memories of host-pathogen combat won by the virus. We describe an exactly solvable model that captures the main qualitative features of the sets of sequences and a simple mechanistic model for the origin of the observed scaling laws. Our results define collective mutational pathways used by HIV to evade human immune responses, which could guide vaccine design.

Rational design of vaccine targets and strategies for HIV: a crossroad of statistical physics, biology, and medicine.

Vaccination has saved more lives than any other medical procedure. Pathogens have now evolved that have not succumbed to vaccination using the empirical paradigms pioneered by Pasteur and Jenner. Vaccine design strategies that are based on a mechanistic understanding of the pertinent immunology and virology are required to confront and eliminate these scourges. In this perspective, we describe just a few examples of work aimed to achieve this goal by bringing together approaches from statistical physics with biology and clinical research.

The fitness landscape of HIV-1 gag: advanced modeling approaches and validation of model predictions by in vitro testing.

Viral immune evasion by sequence variation is a major hindrance to HIV-1 vaccine design. To address this challenge, our group has developed a computational model, rooted in physics, that aims to predict the fitness landscape of HIV-1 proteins in order to design vaccine immunogens that lead to impaired viral fitness, thus blocking viable escape routes. Here, we advance the computational models to address previous limitations, and directly test model predictions against in vitro fitness measurements of HIV-1 strains containing multiple Gag mutations. We incorporated regularization into the model fitting procedure to address finite sampling. Further, we developed a model that accounts for the specific identity of mutant amino acids (Potts model), generalizing our previous approach (Ising model) that is unable to distinguish between different mutant amino acids. Gag mutation combinations (17 pairs, 1 triple and 25 single mutations within these) predicted to be either harmful to HIV-1 viability or fitness-neutral were introduced into HIV-1 NL4-3 by site-directed mutagenesis and replication capacities of these mutants were assayed in vitro. The predicted and measured fitness of the corresponding mutants for the original Ising model (r = -0.74, p = 3.6×10-6) are strongly correlated, and this was further strengthened in the regularized Ising model (r = -0.83, p = 3.7×10-12). Performance of the Potts model (r = -0.73, p = 9.7×10-9) was similar to that of the Ising model, indicating that the binary approximation is sufficient for capturing fitness effects of common mutants at sites of low amino acid diversity. However, we show that the Potts model is expected to improve predictive power for more variable proteins. Overall, our results support the ability of the computational models to robustly predict the relative fitness of mutant viral strains, and indicate the potential value of this approach for understanding viral immune evasion, and harnessing this knowledge for immunogen design.

A binary trait model reveals the fitness effects of HIV-1 escape from T cell responses.

Natural selection often acts on multiple traits simultaneously. For example, the virus HIV-1 faces pressure to evade host immunity while also preserving replicative fitness. While past work has studied selection during HIV-1 evolution, it is challenging to quantitatively separate different contributions to fitness. This task is made more difficult because a single mutation can affect both immune escape and replication. Here, we develop an evolutionary model that disentangles the effects of escaping CD8+ T cell-mediated immunity, which we model as a binary trait, from other contributions to fitness. After validation in simulations, we applied this model to study within-host HIV-1 evolution in a clinical data set. We observed strong selection for immune escape, sometimes greatly exceeding past estimates, especially early in infection. Conservative estimates suggest that roughly half of HIV-1 fitness gains during the first months to years of infection can be attributed to T cell escape. Our approach is not limited to HIV-1 or viruses, and could be adapted to study the evolution of quantitative traits in other contexts.

popDMS infers mutation effects from deep mutational scanning data.

Deep mutational scanning (DMS) experiments provide a powerful method to measure the functional effects of genetic mutations at massive scales. However, the data generated from these experiments can be difficult to analyze, with significant variation between experimental replicates. To overcome this challenge, we developed popDMS, a computational method based on population genetics theory, to infer the functional effects of mutations from DMS data. Through extensive tests, we found that the functional effects of single mutations and epistasis inferred by popDMS are highly consistent across replicates, comparing favorably with existing methods. Our approach is flexible and can be widely applied to DMS data that includes multiple time points, multiple replicates, and different experimental conditions.

Parallel HIV-1 evolutionary dynamics in humans and rhesus macaques who develop broadly neutralizing antibodies.

Human immunodeficiency virus (HIV)-1 exhibits remarkable genetic diversity. For this reason, an effective HIV-1 vaccine must elicit antibodies that can neutralize many variants of the virus. While broadly neutralizing antibodies (bnAbs) have been isolated from HIV-1 infected individuals, a general understanding of the virus-antibody coevolutionary processes that lead to their development remains incomplete. We performed a quantitative study of HIV-1 evolution in two individuals who developed bnAbs. We observed strong selection early in infection for mutations affecting HIV-1 envelope glycosylation and escape from autologous strain-specific antibodies, followed by weaker selection for bnAb resistance later in infection. To confirm our findings, we analyzed data from rhesus macaques infected with viruses derived from the same two individuals. We inferred remarkably similar fitness effects of HIV-1 mutations in humans and macaques. Moreover, we observed a striking pattern of rapid HIV-1 evolution, consistent in both humans and macaques, that precedes the development of bnAbs. Our work highlights strong parallels between infection in rhesus macaques and humans, and it reveals a quantitative evolutionary signature of bnAb development.

The energy costs of insulators in biochemical networks.

Complex networks of biochemical reactions, such as intracellular protein signaling pathways and genetic networks, are often conceptualized in terms of modules--semiindependent collections of components that perform a well-defined function and which may be incorporated in multiple pathways. However, due to sequestration of molecular messengers during interactions and other effects, collectively referred to as retroactivity, real biochemical systems do not exhibit perfect modularity. Biochemical signaling pathways can be insulated from impedance and competition effects, which inhibit modularity, through enzymatic futile cycles that consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption. We test this hypothesis through a combined theoretical and computational analysis of a simplified physical model of covalent cycles, using two innovative measures of insulation, as well as a possible new way to characterize optimal insulation through the balancing of these two measures in a Pareto sense. Our results indicate that indeed better insulation requires more energy. While insulation may facilitate evolution by enabling a modular plug-and-play interconnection architecture, allowing for the creation of new behaviors by adding targets to existing pathways, our work suggests that this potential benefit must be balanced against the metabolic costs of insulation necessarily incurred in not affecting the behavior of existing processes.

Estimating linkage disequilibrium and selection from allele frequency trajectories.

Genetic sequences collected over time provide an exciting opportunity to study natural selection. In such studies, it is important to account for linkage disequilibrium to accurately measure selection and to distinguish between selection and other effects that can cause changes in allele frequencies, such as genetic hitchhiking or clonal interference. However, most high-throughput sequencing methods cannot directly measure linkage due to short-read lengths. Here we develop a simple method to estimate linkage disequilibrium from time-series allele frequencies. This reconstructed linkage information can then be combined with other inference methods to infer the fitness effects of individual mutations. Simulations show that our approach reliably outperforms inference that ignores linkage disequilibrium and, with sufficient sampling, performs similarly to inference using the true linkage information. We also introduce two regularization methods derived from random matrix theory that help to preserve its performance under limited sampling effects. Overall, our method enables the use of linkage-aware inference methods even for data sets where only allele frequency time series are available.

Bézier interpolation improves the inference of dynamical models from data.

Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using Bézier interpolation. We applied our approach to two dynamical inference problems: Determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that Bézier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.

Small RNA sequencing of field Culex mosquitoes identifies patterns of viral infection and the mosquito immune response.

Mosquito-borne disease remains a significant burden on global health. In the United States, the major threat posed by mosquitoes is transmission of arboviruses, including West Nile virus by mosquitoes of the Culex genus. Virus metagenomic analysis of mosquito small RNA using deep sequencing and advanced bioinformatic tools enables the rapid detection of viruses and other infecting organisms, both pathogenic and non-pathogenic to humans, without any precedent knowledge. In this study, we sequenced small RNA samples from over 60 pools of Culex mosquitoes from two major areas of Southern California from 2017 to 2019 to elucidate the virome and immune responses of Culex. Our results demonstrated that small RNAs not only allowed the detection of viruses but also revealed distinct patterns of viral infection based on location, Culex species, and time. We also identified miRNAs that are most likely involved in Culex immune responses to viruses and Wolbachia bacteria, and show the utility of using small RNA to detect antiviral immune pathways including piRNAs against some pathogens. Collectively, these findings show that deep sequencing of small RNA can be used for virus discovery and surveillance. One could also conceive that such work could be accomplished in various locations across the world and over time to better understand patterns of mosquito infection and immune response to many vector-borne diseases in field samples.

MPL resolves genetic linkage in fitness inference from complex evolutionary histories.

Genetic linkage causes the fate of new mutations in a population to be contingent on the genetic background on which they appear. This makes it challenging to identify how individual mutations affect fitness. To overcome this challenge, we developed marginal path likelihood (MPL), a method to infer selection from evolutionary histories that resolves genetic linkage. Validation on real and simulated data sets shows that MPL is fast and accurate, outperforming existing inference approaches. We found that resolving linkage is crucial for accurately quantifying selection in complex evolving populations, which we demonstrate through a quantitative analysis of intrahost HIV-1 evolution using multiple patient data sets. Linkage effects generated by variants that sweep rapidly through the population are particularly strong, extending far across the genome. Taken together, our results argue for the importance of resolving linkage in studies of natural selection.