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.

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.

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.

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.

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.

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.

Pathogenesis, Symptomatology, and Transmission of SARS-CoV-2 through Analysis of Viral Genomics and Structure

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).

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.

Pathogenesis, Symptomatology, and Transmission of SARS-CoV-2 through Analysis of Viral Genomics and Structure

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.

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.

Cross-serotypically conserved epitope recommendations for a universal T cell-based dengue vaccine

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.

The rise in global incidence of DENV and the resulting rise in mortality rate necessitates an effective universal vaccine against it. Since infection from one DENV serotype makes a person vulnerable to severe disease upon infection from another serotype, an effective vaccine should protect against all DENV serotypes. Increasing experimental evidence suggests that T cells are important for protecting against DENV. In this work, we comprehensively analyzed the extensive publicly-available data on DENV and revealed a distinct pattern of epitope conservation for several of the DENV T cell epitopes. Importantly, we identified a set of epitopes that are highly conserved across at least three DENV serotypes. Incorporating information about the HLA alleles associated with these epitopes, we identified a potentially robust set of epitopes as targets for a prospective universal T cell-based vaccine that maximizes global population coverage. By training the immune system to target specific regions of DENV proteins which are likely to protect against multiple serotypes, a T cell-based vaccine might be effective in circumventing progression to severe dengue infection.

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.

Inference of compressed Potts graphical models

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.

Modelling and in vitro testing of the HIV-1 Nef fitness landscape

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.

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.

Relationship between latent and rebound viruses in a clinical trial of anti-HIV-1 antibody 3BNC117

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 (Q²VOA) 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 Q²VOA 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.

Role of framework mutations and antibody flexibility in the evolution of broadly neutralizing antibodies

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.

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.

Deconstruction of the Ras switching cycle through saturation mutagenesis

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.

ACE: adaptive cluster expansion for maximum entropy graphical model inference

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.

Relative rate and location of intra-host HIV evolution to evade cellular immunity are predictable

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.

Identification of drug resistance mutations in HIV from constraints on natural evolution

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 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.

At least 70 million people have been infected with HIV since the beginning of the epidemic and an effective vaccine remains elusive. The high mutation rate and diversity of HIV strains enables the virus to effectively evade host immune responses, presenting a significant challenge for HIV vaccine design. We have developed an approach to translate clinical databases of HIV sequences into mathematical models quantifying the capacity of the virus to replicate as a function of mutations within its genome. We have previously shown how such “fitness landscapes” can be used to guide the design of vaccines to attack vulnerable regions from which it is difficult for the virus to escape by mutation. Here, using new modeling approaches, we have improved on our previous models of HIV fitness landscape by accounting for undersampling of HIV sequences and the specific identity of mutant amino acids. We experimentally tested the accuracy of the improved models to predict the fitness of HIV with multiple mutations in the Gag protein. The experimental data are in strong agreement with model predictions, supporting the value of these models as a novel approach for determining mutational vulnerabilities of HIV-1, which, in turn, can inform vaccine design.

Large pseudocounts and L2-norm penalties are necessary for the mean-field inference of Ising and Potts models

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.

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

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.

Actual focal length of a symmetric biconvex microlens and its application in determining the transmitted beam waist position

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.

Electromagnetic field for a tightly focused beam incident upon ordinary and layered plane surfaces

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.

Electromagnetic field for a focused light sheet incident on a plane surface

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.

Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field

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.

Electromagnetic field calculations for an irregularly shaped, near-spheroidal particle with arbitrary illumination

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.

Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination

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.

Electromagnetic fields for a spheroidal particle with an arbitrary embedded source

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.

Excitation localization principle for spherical microcavities

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.

Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field 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.

Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects

A theoretical procedure has been developed for the determination of internal and external electromagnetic fields that result from the interaction of a higher-order Gaussian beam with a homogeneous sphere. Specific calculations are performed for (1, 0), (0, 1), and (1, 1) mode Hermite-Gaussian beams and for doughnut mode beams of four different polarizations (radial, angular, arced, and helix). The effects of incident beam type on resonance excitation, and on the spatial distribution of the internal and near-surface electromagnetic fields, are examined.

Electromagnetic-field calculations for irregularly shaped, layered cylindrical particles with focused illumination

Theoretical procedures are presented for the determination of internal and external electromagnetic fields for the plane two-dimensional problem of an arbitrary monochromatic field (e.g., a focused laser light sheet) incident upon an irregularly shaped, layered cylindrical particle. Equations for the arbitrary illumination of a layered circular cylindrical particle are also given as a special case of the general solution.

Electromagnetic-field calculations for irregularly shaped, axisymmetric layered particles with focused illumination

Theoretical procedures are presented for the determination of the internal and the near-surface electromagnetic fields for an arbitrary monochromatic field (e.g., a focused laser beam) incident upon an irregulary shaped, axisymmetric layered particle. The layered spherical particle solution is also given as a special case of the general solution. Systematic calculations are presented that demonstrate the effects of particle shape and incident focused-beam orientation on the electromagnetic-field distributions.

Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination

A previously developed [Appl. Opt. 34, 5542 (1995)] theoretical procedure for the calculation of the internal and the near-surface electromagnetic fields for nonabsorbing spheroidal particles with arbitrary monochromatic illumination has been generalized to permit solutions for absorbing (i.e., complex relative index of refraction) spheroidal particles. Calculations are presented that demonstrate the general effects of absorption on the internal and near-surface electromagnetic-field distributions for the particular case of a plane wave that is incident upon a 2:1-axis-ratio oblate spheroidal particle.

Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination

A theoretical procedure in which a spheroidal coordinate separation-of-variables solution is used is developed for the determination of the internal and the near-surface electromagnetic fields for an arbitrary monochromatic field that is incident upon a homogeneous spheroidal particle. Calculations are presented for both the prolate and the oblate geometries, demonstrating the effects of particle size, particle axis ratio, and the orientation and character (plane-wave and focused Gaussian beam) of the incident field on the resultant internal and near-surface electromagnetic-field distributions.

Theoretical analysis of the effects of particle trajectory and structural resonances on the performance of a phase-Doppler particle analyzer

<p>A generalized theoretical model for the response of a phase-Doppler particle analyzer (PDPA) to homogeneous, spherical particles passing at arbitrary locations through a crossed beam measurement volume is presented. The model is based on the arbitrary beam theory [J. Appl. Phys. 64, 1632 (19$8)] and is valid for arbitrary particle size and complex refractive index. In contrast to classical Lorenz-Mie theory, the arbitrary beam approach has the added capability of accounting for effects that are due to the presence of the finite-size crossed incident beams that are used in the PDPA measurement technique.</p><p>The theoretical model is used to compute phase shift as a function of both the particle position within the measurement volume and particle diameter (1.0 µm < diameter water droplets < 10.0 µm for both resonant and nonresonant sizes) for 30° off-axis receiver configuration. Results indicate that trajectory effects are most pronounced for particle trajectories through the edge of the crossed beam measurement volume on the side opposite the detector. Trajectories through the center of the probe volume gave phase shifts that are nearly identical to those obtained with Lorenz-Mie plane-wave theory. Phase shifts calculated for particle diameters corresponding to electric-wave resonances showed the largest deviation from the corresponding nonresonance diameter phase shifts. Phase shifts for droplets at magnetic wave resonance conditions showed smaller effects, closely following. the behavior of nonresonant particle sizes. The major influence of aerosol trajectory on actual particle size determination (for both resonant and nonresonant particle sizes) is that the measured aerosol size distributions will appear broader than the actual size distribution that exists within a spray.</p>

Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing

A theoretical model is presented for the formation of small-particle shadow images in a single-lens laser-imaging system. The model uses a modification of classical Lorenz-Mie theory, presented by the authors in an earlier paper, to calculate the external electromagnetic fields resulting from the interaction of a Gaussian laser beam with a finite absorbing spherical particle. Propagation of the electric field through the imaging system components is developed from a scalar viewpoint using the thin-lens transformation and the Fresnel approximation to the Huygens-Fresnel propagation equation. The theoretical model is valid for either transparent or absorbing spheres and has no restrictions on the allowable degree or direction of aerosol defocus. Direct comparisons between theoretical calculations and experimental observations are reported for 53-microm-diameter transparent water droplets and 66-microm-diameter absorbing nickel spheres for defocus ranging from -2 mm (toward the lens) to +2 mm (away from the lens). Theory and experiment showed good agreement in the boundary edge gradient and the location of the external peaks, while observable differences existed in the magnitude of the central spots. Theoretical results, comparing water and nickel aerosols, showed observable differences in the calculated average internal intensity (AII). In contrast, the boundary edge gradient showed less dependence on changes in the optical properties of the particle. These results indicate that criteria, such as the AII, used in focus determination must be reevaluated when applying in-focus sizing algorithms to aerosols with significantly different optical properties.

Electromagnetic field for a beam incident on two adjacent spherical particles

Through an application of our previously derived single spherical particle-arbitrary beam interaction theory, an iterative procedure has been developed for the determination of the electromagnetic field for a beam incident on two adjacent spherical particles. The two particles can differ in size and composition and can have any positioning relative to each other and relative to the focal point and propagation direction of the incident beam. Example calculations of internal and near-field normalized source function ( approximately |E|(2)) distributions are presented. Also presented are calculations demonstrating the effect of the relative positioning of the second adjacent particle on far-field scattering patterns.