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Human immunodeficiency virus (HIV)-1 exhibits remarkable genetic diversity. An effective HIV-1 vaccine must therefore 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 humans and rhesus macaques, including 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. The inferred fitness effects of HIV-1 mutations in humans and macaques were remarkably similar. Moreover, we observed a striking pattern of rapid HIV-1 fitness gains 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.

Epistasis can profoundly influence evolutionary dynamics. Temporal genetic data, consisting of sequences sampled repeatedly from a population over time, provides a unique resource to understand how epistasis shapes evolution. However, detecting epistatic interactions from sequence data is technically challenging. Existing methods for identifying epistasis are computationally demanding, limiting their applicability to real-world data. Here, we present a novel computational method for inferring epistasis that significantly reduces computational costs without sacrificing accuracy. We validated our approach in simulations and applied it to study HIV-1 evolution over multiple years in a data set of 16 individuals. There we observed a strong excess of negative epistatic interactions between beneficial mutations, especially mutations involved in immune escape. Our method is general and could be used to characterize epistasis in other large data sets.

Multiple SARS-CoV-2 variants have arisen during the first years of the pandemic, often bearing many new mutations. Several explanations have been offered for the surprisingly sudden emergence of multiple mutations that enhance viral fitness, including cryptic transmission, spillover from animal reservoirs, epistasis between mutations, and chronic infections. Here, we simulated pathogen evolution combining within-host replication and between-host transmission. We found that, under certain conditions, chronic infections can lead to SARS-CoV-2-like bursts of mutations even without epistasis. Chronic infections can also increase the global evolutionary rate of a pathogen even in the absence of clear mutational bursts. Overall, our study supports chronic infections as a plausible origin for highly mutated SARS-CoV-2 variants. More generally, we also describe how chronic infections can influence pathogen evolution under different scenarios.

Summary: 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., Availability and Implementation: popDMS is implemented in Python and Julia, and is freely available on GitHub at https://github.com/bartonlab/popDMS., (© The Author(s) 2024. Published by Oxford University Press.)

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., Competing Interests: Conflict of interest None declared., (© The Author(s) 2024. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)

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.

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., (© 2023. The Author(s).)

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., (© The Author(s) 2023. Published by Oxford University Press on behalf of the Genetics Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

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.

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., (© The Author(s) 2022. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)

The novel coronavirus SARS-CoV-2, which emerged in late 2019, has since spread around the world and infected hundreds of millions of people with coronavirus disease 2019 (COVID-19). While this viral species was unknown prior to January 2020, its similarity to other coronaviruses that infect humans has allowed for rapid insight into the mechanisms that it uses to infect human hosts, as well as the ways in which the human immune system can respond. Here, we contextualize SARS-CoV-2 among other coronaviruses and identify what is known and what can be inferred about its behavior once inside a human host. Because the genomic content of coronaviruses, which specifies the virus's structure, is highly conserved, early genomic analysis provided a significant head start in predicting viral pathogenesis and in understanding potential differences among variants. The pathogenesis of the virus offers insights into symptomatology, transmission, and individual susceptibility. Additionally, prior research into interactions between the human immune system and coronaviruses has identified how these viruses can evade the immune system's protective mechanisms. We also explore systems-level research into the regulatory and proteomic effects of SARS-CoV-2 infection and the immune response. Understanding the structure and behavior of the virus serves to contextualize the many facets of the COVID-19 pandemic and can influence efforts to control the virus and treat the disease. IMPORTANCE COVID-19 involves a number of organ systems and can present with a wide range of symptoms. From how the virus infects cells to how it spreads between people, the available research suggests that these patterns are very similar to those seen in the closely related viruses SARS-CoV-1 and possibly Middle East respiratory syndrome-related CoV (MERS-CoV). Understanding the pathogenesis of the SARS-CoV-2 virus also contextualizes how the different biological systems affected by COVID-19 connect. Exploring the structure, phylogeny, and pathogenesis of the virus therefore helps to guide interpretation of the broader impacts of the virus on the human body and on human populations. For this reason, an in-depth exploration of viral mechanisms is critical to a robust understanding of SARS-CoV-2 and, potentially, future emergent human CoVs (HCoVs).

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.

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., Competing Interests: Competing interest statement: The authors have filed an application for a patent on the immunogen.

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., Competing Interests: The authors have declared that no competing interests exist.

Dengue virus (DENV)-associated disease is a growing threat to public health across the globe. Co-circulating as four different serotypes, DENV poses a unique challenge for vaccine design as immunity to one serotype predisposes a person to severe and potentially lethal disease upon infection from other serotypes. Recent experimental studies suggest that an effective vaccine against DENV should elicit a strong T cell response against all serotypes, which could be achieved by directing T cell responses toward cross-serotypically conserved epitopes while avoiding serotype-specific ones. Here, we used experimentally-determined DENV T cell epitopes and patient-derived DENV sequences to assess the cross-serotypic variability of the epitopes. We reveal a distinct near-binary pattern of epitope conservation across serotypes for a large number of DENV epitopes. Based on the conservation profile, we identify a set of 55 epitopes that are highly conserved in at least 3 serotypes. Most of the highly conserved epitopes lie in functionally important regions of DENV non-structural proteins. By considering the global distribution of human leukocyte antigen (HLA) alleles associated with these DENV epitopes, we identify a potentially robust subset of HLA class I and class II restricted epitopes that can serve as targets for a universal T cell-based vaccine against DENV while covering ~99% of the global population., Competing Interests: The authors have declared that no competing interests exist.

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., (© The Author(s) 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Vaccination has essentially eradicated poliovirus. Yet, its mutation rate is higher than that of viruses like HIV, for which no effective vaccine exists. To investigate this, we infer a fitness model for the poliovirus viral protein 1 (vp1), which successfully predicts in vitro fitness measurements. This is achieved by first developing a probabilistic model for the prevalence of vp1 sequences that enables us to isolate and remove data that are subject to strong vaccine-derived biases. The intrinsic fitness constraints derived for vp1, a capsid protein subject to antibody responses, are compared with those of analogous HIV proteins. We find that vp1 evolution is subject to tighter constraints, limiting its ability to evade vaccine-induced immune responses. Our analysis also indicates that circulating poliovirus strains in unimmunized populations serve as a reservoir that can seed outbreaks in spatio-temporally localized sub-optimally immunized populations.

We consider the problem of inferring a graphical Potts model on a population of variables. This inverse Potts problem generally involves the inference of a large number of parameters, often larger than the number of available data, and, hence, requires the introduction of regularization. We study here a double regularization scheme, in which the number of Potts states (colors) available to each variable is reduced and interaction networks are made sparse. To achieve the color compression, only Potts states with large empirical frequency (exceeding some threshold) are explicitly modeled on each site, while the others are grouped into a single state. We benchmark the performances of this mixed regularization approach, with two inference algorithms, adaptive cluster expansion (ACE) and pseudolikelihood maximization (PLM), on synthetic data obtained by sampling disordered Potts models on Erdős-Rényi random graphs. We show in particular that color compression does not affect the quality of reconstruction of the parameters corresponding to high-frequency symbols, while drastically reducing the number of the other parameters and thus the computational time. Our procedure is also applied to multisequence alignments of protein families, with similar results.

An effective vaccine is urgently required to curb the HIV-1 epidemic. We have previously described an approach to model the fitness landscape of several HIV-1 proteins, and have validated the results against experimental and clinical data. The fitness landscape may be used to identify mutation patterns harmful to virus viability, and consequently inform the design of immunogens that can target such regions for immunological control. Here we apply such an analysis and complementary experiments to HIV-1 Nef, a multifunctional protein which plays a key role in HIV-1 pathogenesis. We measured Nef-driven replication capacities as well as Nef-mediated CD4 and HLA-I down-modulation capacities of thirty-two different Nef mutants, and tested model predictions against these results. Furthermore, we evaluated the models using 448 patient-derived Nef sequences for which several Nef activities were previously measured. Model predictions correlated significantly with Nef-driven replication and CD4 down-modulation capacities, but not HLA-I down-modulation capacities, of the various Nef mutants. Similarly, in our analysis of patient-derived Nef sequences, CD4 down-modulation capacity correlated the most significantly with model predictions, suggesting that of the tested Nef functions, this is the most important in vivo . Overall, our results highlight how the fitness landscape inferred from patient-derived sequences captures, at least in part, the in vivo functional effects of mutations to Nef. However, the correlation between predictions of the fitness landscape and measured parameters of Nef function is not as accurate as the correlation observed in past studies for other proteins. This may be because of the additional complexity associated with inferring the cost of mutations on the diverse functions of Nef.

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., (Copyright © 2019 Vibholm et al.)

A clinical trial was performed to evaluate 3BNC117, a potent anti-HIV-1 antibody, in infected individuals during suppressive antiretroviral therapy and subsequent analytical treatment interruption (ATI). The circulating reservoir was evaluated by quantitative and qualitative viral outgrowth assay (Q 2 VOA) at entry and after 6 mo. There were no significant quantitative changes in the size of the reservoir before ATI, and the composition of circulating reservoir clones varied in a manner that did not correlate with 3BNC117 sensitivity. 3BNC117 binding site amino acid variants found in rebound viruses preexisted in the latent reservoir. However, only 3 of 217 rebound viruses were identical to 868 latent viruses isolated by Q 2 VOA and near full-length sequencing. Instead, 63% of the rebound viruses appeared to be recombinants, even in individuals with 3BNC117-resistant reservoir viruses. In conclusion, viruses emerging during ATI in individuals treated with 3BNC117 are not the dominant species found in the circulating latent reservoir, but frequently appear to represent recombinants of latent viruses., (© 2018 Cohen et al.)

Eliciting antibodies that are cross reactive with surface proteins of diverse strains of highly mutable pathogens (e.g., HIV, influenza) could be key for developing effective universal vaccines. Mutations in the framework regions of such broadly neutralizing antibodies (bnAbs) have been reported to play a role in determining their properties. We used molecular dynamics simulations and models of affinity maturation to study specific bnAbs against HIV. Our results suggest that there are different classes of evolutionary lineages for the bnAbs. If germline B cells that initiate affinity maturation have high affinity for the conserved residues of the targeted epitope, framework mutations increase antibody rigidity as affinity maturation progresses to evolve bnAbs. If the germline B cells exhibit weak/moderate affinity for conserved residues, an initial increase in flexibility via framework mutations may be required for the evolution of bnAbs. Subsequent mutations that increase rigidity result in highly potent bnAbs. Implications of our results for immunogen design are discussed., Competing Interests: VO, JL, JB, MK No competing interests declared, AC Senior editor, eLife, (© 2018, Ovchinnikov et al.)

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., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

Ras proteins are highly conserved signaling molecules that exhibit regulated, nucleotide-dependent switching between active and inactive states. The high conservation of Ras requires mechanistic explanation, especially given the general mutational tolerance of proteins. Here, we use deep mutational scanning, biochemical analysis and molecular simulations to understand constraints on Ras sequence. Ras exhibits global sensitivity to mutation when regulated by a GTPase activating protein and a nucleotide exchange factor. Removing the regulators shifts the distribution of mutational effects to be largely neutral, and reveals hotspots of activating mutations in residues that restrain Ras dynamics and promote the inactive state. Evolutionary analysis, combined with structural and mutational data, argue that Ras has co-evolved with its regulators in the vertebrate lineage. Overall, our results show that sequence conservation in Ras depends strongly on the biochemical network in which it operates, providing a framework for understanding the origin of global selection pressures on proteins.

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.

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., Competing Interests: The authors declare no conflict of interest.

Motivation: Graphical models are often employed to interpret patterns of correlations observed in data through a network of interactions between the variables. Recently, Ising/Potts models, also known as Markov random fields, have been productively applied to diverse problems in biology, including the prediction of structural contacts from protein sequence data and the description of neural activity patterns. However, inference of such models is a challenging computational problem that cannot be solved exactly. Here, we describe the adaptive cluster expansion (ACE) method to quickly and accurately infer Ising or Potts models based on correlation data. ACE avoids overfitting by constructing a sparse network of interactions sufficient to reproduce the observed correlation data within the statistical error expected due to finite sampling. When convergence of the ACE algorithm is slow, we combine it with a Boltzmann Machine Learning algorithm (BML). We illustrate this method on a variety of biological and artificial datasets and compare it to state-of-the-art approximate methods such as Gaussian and pseudo-likelihood inference., Results: We show that ACE accurately reproduces the true parameters of the underlying model when they are known, and yields accurate statistical descriptions of both biological and artificial data. Models inferred by ACE more accurately describe the statistics of the data, including both the constrained low-order correlations and unconstrained higher-order correlations, compared to those obtained by faster Gaussian and pseudo-likelihood methods. These alternative approaches can recover the structure of the interaction network but typically not the correct strength of interactions, resulting in less accurate generative models., Availability and Implementation: The ACE source code, user manual and tutorials with the example data and filtered correlations described herein are freely available on GitHub at https://github.com/johnbarton/ACE CONTACTS: jpbarton@mit.edu, cocco@lps.ens.frSupplementary information: Supplementary data are available at Bioinformatics online., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

Human immunodeficiency virus (HIV) evolves within infected persons to escape being destroyed by the host immune system, thereby preventing effective immune control of infection. Here, we combine methods from evolutionary dynamics and statistical physics to simulate in vivo HIV sequence evolution, predicting the relative rate of escape and the location of escape mutations in response to T-cell-mediated immune pressure in a cohort of 17 persons with acute HIV infection. Predicted and clinically observed times to escape immune responses agree well, and we show that the mutational pathways to escape depend on the viral sequence background due to epistatic interactions. The ability to predict escape pathways and the duration over which control is maintained by specific immune responses open the door to rational design of immunotherapeutic strategies that might enable long-term control of HIV infection. Our approach enables intra-host evolution of a human pathogen to be predicted in a probabilistic framework.

Human immunodeficiency virus (HIV) evolves with extraordinary rapidity. However, its evolution is constrained by interactions between mutations in its fitness landscape. Here we show that an Ising model describing these interactions, inferred from sequence data obtained prior to the use of antiretroviral drugs, can be used to identify clinically significant sites of resistance mutations. Successful predictions of the resistance sites indicate progress in the development of successful models of real viral evolution at the single residue level and suggest that our approach may be applied to help design new therapies that are less prone to failure even where resistance data are not yet available.

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.

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.

The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L(2)-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L(2)-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.

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.

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., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The actual focal length of a three-dimensional continuous profile symmetric biconvex microlens with normal monochromatic plane wave illumination is theoretically determined using a full-field separation of variables method in the oblate spheroidal coordinate system. The investigations are performed for microlenses of 5, 10, and 20 wavelength diameters by calculating the electromagnetic field distributions inside of and adjacent to the microlenses. The importance and potential application of the microlens actual focal length in the design of microlens optical systems are demonstrated by showing that for normal monochromatic TEM00 mode Gaussian beam illumination, the transmitted beam waist position through a single microlens, calculated using Self's beam waist position transformation formula [Appl. Opt.22, 658 (1983)] with the microlens actual focal length, closely matches the exact value given by the separation of variables method.

A solution procedure is developed for the determination of the electromagnetic field that results from the interaction of a tightly focused beam with a plane surface with and without a layer. The effects of angle of incidence, relative index of refraction, polarization, layer thickness, and incident beam profile on the resulting electromagnetic field distribution are demonstrated.

A solution procedure is developed for the determination of the electromagnetic field that results from the interaction of a focused light sheet with a plane surface. The effects of angle of incidence, relative index of refraction, polarization, and incident light sheet profile on the resulting electromagnetic field distribution are demonstrated.

A general spheroidal coordinate separation-of-variables solution is developed for the determination of the acoustic pressure distribution near the surface of a rigid spheroid for a monofrequency incident acoustic field of arbitrary character. Calculations are presented, for both the prolate and oblate geometries, demonstrating the effects of incident field orientation and character (plane-wave, spherical wave, cylindrical wave, and focused beam) on the resultant acoustic pressure distribution.

A spheroidal coordinate separation-of-variables solution has been developed for the determination of the internal, near-surface, and far-scattered electromagnetic fields for irregularly shaped elongated (prolatelike) and irregularly shaped flattened (oblatelike) particles with arbitrary monochromatic illumination. Calculated results are presented, for both plane-wave and focused-Gaussian-beam illumination, which demonstrate the effects of particle geometry on the internal, near-surface, and far-scattered-field distributions.

A spheroidal coordinate separation-of-variables solution has been developed for the determination of internal, near-surface, and scattered electromagnetic fields of a layered spheroid (either prolate or oblate) with arbitrary monochromatic illumination (e.g., plane wave or focused Gaussian beam). Calculated results are presented for layered 2:1 axis ratio prolate and oblate spheroids with an equivalent sphere size parameter of 20.

A spheroidal coordinate separation-of-variables solution has been developed for the determination of the internal, near-surface, and scattered fields of a spheroid (either prolate or oblate) with an embedded source of arbitrary type, location, and orientation. Presented results for (1,0) and (1,1) electric multipoles embedded in 2:1 axis ratio prolate and oblate spheroids (equal volume sphere size parameter equal to 20) illustrate that the presence of the spheroid interface can have a profound effect on the corresponding far-field scattering pattern. The calculation procedure could be used, for example, to model the emission of inelastic scattered light (Raman, fluorescence, etc.) from biological particles of appreciably elongated (prolatelike) or appreciably flattened (oblatelike) geometries.

Van de Hulst's localization principle relates the principal mode number to the external beam position that maximizes energy coupling to a spherical cavity mode. Our experiments in lasing microdroplets verify localization but only for low- Q modes, when the cavity may be considered to be a nearly perfect homogeneous sphere. The principle fails in the perturbation-dominated high- Q limit. Surprisingly, near-surface resonances are still efficiently excited in these cases but require impact parameters slightly smaller than the sphere radius. Numerical modeling suggests that this new input channel depends on surface scattering.

A previously developed theoretical procedure for determination of electromagnetic fields associated with the interaction of a higher-order Gaussian beam with a homogeneous spherical particle is used to investigate the effects of incident beam type on far-field scattering. Far-field scattering patterns are calculated for (0,0), (0,1), and (1,1) mode Hermite-Gaussian beams and for the helix doughnut mode beam. The effects of incident beam type on the angular distribution of far-field scattering, for both on-sphere-center and off-sphere-center focusing, are examined.