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The competition for resources is a defining feature of microbial communities. In many contexts, from soils to host-associated communities, highly diverse microbes are organized into metabolic groups or guilds with similar resource preferences. The resource preferences of individual taxa that give rise to these guilds are critical for understanding fluxes of resources through the community and the structure of diversity in the system. However, inferring the metabolic capabilities of individual taxa, and their competition with other taxa, within a community is challenging and unresolved. Here we address this gap in knowledge by leveraging dynamic measurements of abundances in communities. We show that simple correlations are often misleading in predicting resource competition. We show that spectral methods such as the cross-power spectral density (CPSD) and coherence that account for time-delayed effects are superior metrics for inferring the structure of resource competition in communities. We first demonstrate this fact on synthetic data generated from consumer-resource models with time-dependent resource availability, where taxa are organized into groups or guilds with similar resource preferences. By applying spectral methods to oceanic plankton time-series data, we demonstrate that these methods detect interaction structures among species with similar genomic sequences. Our results indicate that analyzing temporal data across multiple timescales can reveal the underlying structure of resource competition within communities.

Since the approval of the first antibody drug in 1986, a total of 162 antibodies have been approved for a wide range of therapeutic areas, including cancer, autoimmune, infectious, or cardiovascular diseases. Despite advances in biotechnology that accelerated the development of antibody drugs, the drug discovery process for this modality remains lengthy and costly, requiring multiple rounds of optimizations before a drug candidate can progress to preclinical and clinical trials. This multi-optimization problem involves increasing the affinity of the antibody to the target antigen while refining additional biophysical properties that are essential to drug development such as solubility, thermostability or aggregation propensity. Additionally, antibodies that resemble natural human antibodies are particularly desirable, as they are likely to offer improved profiles in terms of safety, efficacy, and reduced immunogenicity, further supporting their therapeutic potential. In this article, we explore the use of energy-based generative models to optimize a candidate monoclonal antibody. We identify tradeoffs when optimizing for multiple properties, concentrating on solubility, humanness and affinity and use the generative model we develop to generate candidate antibodies that lie on an optimal Pareto front that satisfies these constraints.

Cells use signalling pathways as windows into the environment to gather information, transduce it into their interior, and use it to drive behaviours. MAPK (ERK) is a highly conserved signalling pathway in eukaryotes, directing multiple fundamental cellular behaviours such as proliferation, migration, and differentiation, making it of few central hubs in the signalling circuitry of cells. Despite this versatility of behaviors, population-level measurements have reported low information content (\textless 1 bit) relayed through the ERK pathway, rendering the population barely able to distinguish the presence or absence of stimuli. Here, we contrast the information transmitted by a single cell and a population of cells. Using a combination of optogenetic experiments, data analysis based on information theory framework, and numerical simulations we quantify the amount of information transduced from the receptor to ERK, from responses to singular, brief and sparse input pulses. We show that single cells are indeed able to resolve between graded stimuli, yielding over 2 bit of information, however showing a large population heterogeneity., Comment: 13 pages, 5 figures, 10 pages of supplemental material

The onset of neural induction in the anterior ectoderm of ascidian embryos is regulated at the extracellular level by FGF signaling molecules, which control the acquisition of neural fate through the activation of the ERK pathway. Among the anterior ectoderm cells exposed to FGF, only a fraction will acquire neural fate. The selection of neural precursors depends on the quasi-invariant geometry of the embryo, which imposes upon each ectoderm cell a precise area of cell surface contact with underlying FGF-expressing (mesendoderm) cells. Here, we investigate information transmission between FGF and activated ERK and how this depends on the geometry of the system. Optimizing information transmission with the constraint that the total FGF-emitting surface area is restricted, as in the embryo, we find that the surface contacts with FGF that maximize information transmission are close to those observed experimentally. This information optimal solution is compatible with the anterior ectoderm cells having different areas of cell surface exposure to FGF, allowing the embryo to use cell surface areas as a regulatory mechanism for differentiating the outcome of cells that sense a constant FGF concentration.

Viruses like influenza have long coevolved with host immune systems, gradually shaping the evolutionary trajectory of these pathogens. Host immune systems develop immunity against circulating strains, which in turn avoid extinction by exploiting antigenic escape mutations that render new strains immune from existing antibodies in the host population. Infected hosts are also mobile, which can spread the virus to regions without developed host immunity, offering additional reservoirs for viral growth. While the effects of migration on long term stability have been investigated, we know little about how antigenic escape coupled with migration changes the survival and spread of emerging viruses. By considering the two processes on equal footing, we show that on short timescales an intermediate host mobility rate increases the survival probability of the virus through antigenic escape. We show that more strongly connected migratory networks decrease the survival probability of the virus. Using data from high traffic airports we argue that current human migration rates are beneficial for viral survival.

B cell receptors (BCRs) play a crucial role in recognizing and fighting foreign antigens. High-throughput sequencing enables in-depth sampling of the BCRs repertoire after immunization. However, only a minor fraction of BCRs actively participate in any given infection. To what extent can we accurately identify antigen-specific sequences directly from BCRs repertoires? We present a computational method grounded on sequence similarity, aimed at identifying statistically significant responsive BCRs. This method leverages well-known characteristics of affinity maturation and expected diversity. We validate its effectiveness using longitudinally sampled human immune repertoire data following influenza vaccination and Sars-CoV-2 infections. We show that different lineages converge to the same responding CDR3, demonstrating convergent selection within an individual. The outcomes of this method hold promise for application in vaccine development, personalized medicine, and antibody-derived therapeutics.

The adaptive immune response relies on T cells that combine phenotypic specialization with diversity of T cell receptors (TCRs) to recognize a wide range of pathogens. TCRs are acquired and selected during T cell maturation in the thymus. Characterizing TCR repertoires across individuals and T cell maturation stages is important for better understanding adaptive immune responses and for developing new diagnostics and therapies. Analyzing a dataset of human TCR repertoires from thymocyte subsets, we find that the variability between individuals generated during the TCR V(D)J recombination is maintained through all stages of T cell maturation and differentiation. The inter-individual variability of repertoires of the same cell type is of comparable magnitude to the variability across cell types within the same individual. To zoom in on smaller scales than whole repertoires, we defined a distance measuring the relative overlap of locally similar sequences in repertoires. We find that the whole repertoire models correctly predict local similarity networks, suggesting a lack of forbidden T cell receptor sequences. The local measure correlates well with distances calculated using whole repertoire traits and carries information about cell types.

In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical divergences quantify the difference between two distributions. However, their estimation is very difficult and empirical methods often fail, especially when the samples are small. We develop a Bayesian estimator of the Kullback-Leibler divergence between two probability distributions that makes use of a mixture of Dirichlet priors on the distributions being compared. We study the properties of the estimator on two examples: probabilities drawn from Dirichlet distributions, and random strings of letters drawn from Markov chains. We extend the approach to the squared Hellinger divergence. Both estimators outperform other estimation techniques, with better results for data with a large number of categories and for higher values of divergences.

Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the co-evolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other non-antigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of non-antigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

A cornerstone of the classical view of tolerance is the elimination of self-reactive T cells during negative selection in the thymus. However, high-throughput T-cell receptor sequencing data has so far failed to detect substantial signatures of negative selection in the observed repertoires. In addition, quantitative estimates as well as recent experiments suggest that the elimination of self-reactive T cells is at best incomplete. We discuss several recent theoretical ideas that can explain tolerance while being consistent with these observations, including collective decision making through quorum sensing, and sensitivity to change through dynamic tuning and adaptation. We propose that a unified quantitative theory of tolerance should combine these elements to explain the plasticity of the immune system and its robustness to autoimmunity.

Biological cells encode information about their environment through biochemical signaling networks that control their internal state and response. This information is often encoded in the dynamical patterns of the signaling molecules, rather than just their instantaneous concentrations. Here, we analytically calculate the information contained in these dynamics for a number of paradigmatic cases in the linear regime, for both static and time-dependent input signals. When considering oscillatory output dynamics, we report the emergence of synergy between successive measurements, meaning that the joint information in two measurements exceeds the sum of the individual information. We extend our analysis numerically beyond the scope of linear input encoding to reveal synergetic effects in the cases of frequency or damping modulation, both of which are relevant to classical biochemical signaling systems.

B-cell repertoires are characterized by a diverse set of receptors of distinct specificities generated through two processes of somatic diversification: V(D)J recombination and somatic hypermutations. B cell clonal families stem from the same V(D)J recombination event, but differ in their hypermutations. Clonal families identification is key to understanding B-cell repertoire function, evolution and dynamics. We present HILARy (High-precision Inference of Lineages in Antibody Repertoires), an efficient, fast and precise method to identify clonal families from single- or paired-chain repertoire sequencing datasets. HILARy combines probabilistic models that capture the receptor generation and selection statistics with adapted clustering methods to achieve consistently high inference accuracy. It automatically leverages the phylogenetic signal of shared mutations in difficult repertoire subsets. Exploiting the high sensitivity of the method, we find the statistics of evolutionary properties such as the site frequency spectrum and dN/dS ratio do not depend on the junction length. We also identify a broad range of selection pressures spanning two orders of magnitude.

Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum entropy models, reproduce the empirical steady state distributions, it remains challenging to learn dynamical models. We present a novel inference method, called generalized Glauber dynamics. Constructed through a non-Markovian fluctuation dissipation theorem, generalized Glauber dynamics tunes the dynamics of an interacting system, while keeping the steady state distribution fixed. We motivate the need for the method on real data from Eco-HAB, an automated habitat for testing behavior in groups of mice under semi-naturalistic conditions, and present it on simple Ising spin systems. We show its applicability for experimental data, by inferring dynamical models of social interactions in a group of mice that reproduce both its collective behavior and the long tails observed in individual dynamics.

Chronic infections of the human immunodeficiency virus (HIV) create a very complex co-evolutionary process, where the virus tries to escape the continuously adapting host immune system. Quantitative details of this process are largely unknown and could help in disease treatment and vaccine development. Here we study a longitudinal dataset of ten HIV-infected people, where both the B-cell receptors and the virus are deeply sequenced. We focus on simple measures of turnover, which quantify how much the composition of the viral strains and the immune repertoire change between time points. At the single-patient level, the viral-host turnover rates do not show any statistically significant correlation, however they correlate if the information is aggregated across patients. In particular, we identify an anti-correlation: large changes in the viral pool composition come with small changes in the B-cell receptor repertoire. This result seems to contradict the naive expectation that when the virus mutates quickly, the immune repertoire needs to change to keep up. However, we show that the observed anti-correlation naturally emerges and can be understood in terms of simple population-genetics models.

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Due to their symmetry, these proteins constitute excellent model systems to investigate how evolution relates to structure, folding and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat-proteins. We model the energetics by a combination of an inverse Potts model scheme with an explicit mechanistic model of duplications and deletions of repeats to calculate the evolutionary parameters of the system at single residue level. This is used to inform an Ising-like model that allows for the generation of folding curves, apparent domain emergence and occupation of intermediate states that are highly compatible with experimental data in specific case studies. We analyzed the folding of thousands of natural Ankyrin-repeat proteins and found that a multiplicity of folding mechanisms are possible. Fully cooperative all-or-none transition are obtained for arrays with enough sequence-similar elements and strong interactions between them, while non-cooperative element-by-element intermittent folding arose if the elements are dissimilar and the interactions between them are energetically weak. In between, we characterised nucleation-propagation and multi-domain folding mechanisms. Finally, we showed that stability and cooperativity of a repeat-array can be quantitatively predicted from a simple energy score, paving the way for guiding protein folding design with a co-evolutionary model., Comment: 8 pages, 5 figures plus Supplementary text and Figures

Affinity maturation is crucial for improving the binding affinity of antibodies to antigens. This process is mainly driven by point substitutions caused by somatic hypermutations of the immunoglobulin gene. It also includes deletions and insertions of genomic material known as indels. While the landscape of point substitutions has been extensively studied, a detailed statistical description of indels is still lacking. Here we present a probabilistic inference tool to learn the statistics of indels from repertoire sequencing data, which overcomes the pitfalls and biases of standard annotation methods. The model includes antibody-specific maturation ages to account for variable mutational loads in the repertoire. After validation on synthetic data, we applied our tool to a large dataset of human immunoglobulin heavy chains. The inferred model allows us to identify universal statistical features of indels in heavy chains. We report distinct insertion and deletion hotspots, and show that the distribution of lengths of indels follows a geometric distribution, which puts constraints on future mechanistic models of the hypermutation process.

In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its lymphocyte repertoire. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the encountered strain. This process of affinity maturation generates a memory pool whose diversity and size remain difficult to predict. We assume that the immune system follows a strategy that maximizes the long-term immune coverage and minimizes the short-term metabolic costs associated with affinity maturation. This strategy is defined as an optimal decision process on a finite dimensional phenotypic space, where a pre-existing population of naive cells is sequentially challenged with a neutrally evolving strain. We unveil a trade-off between immune protection against future strains and the necessary reorganization of the repertoire. This plasticity of the repertoire drives the emergence of distinct regimes for the size and diversity of the memory pool, depending on the density of naive cells and on the mutation rate of the strain. The model predicts power-law distributions of clonotype sizes observed in data, and rationalizes antigenic imprinting as a strategy to minimize metabolic costs while keeping good immune protection against future strains.

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence ratio, or equivalently the posterior function. Here we frame the inference task as an estimation of an energy function parametrized with an artificial neural network. We present an intuitive approach where the optimal model of the likelihood-to-evidence ratio is found by maximizing the likelihood of simulated data. Within this framework, the connection between the task of simulation-based inference and mutual information maximization is clear, and we show how several known methods of posterior estimation relate to alternative lower bounds to mutual information. These distinct objective functions aim at the same optimal energy form and therefore can be directly benchmarked. We compare their accuracy in the inference of model parameters, focusing on four dynamical systems that encompass common challenges in time series analysis: dynamics driven by multiplicative noise, nonlinear interactions, chaotic behavior, and high-dimensional parameter space.

The spatial organization of complex biochemical reactions is essential for the regulation of cellular processes. Membrane-less structures called foci containing high concentrations of specific proteins have been reported in a variety of contexts, but the mechanism of their formation is not fully understood. Several competing mechanisms exist that are difficult to distinguish empirically, including liquid-liquid phase separation, and the trapping of molecules by multiple binding sites. Here we propose a theoretical framework and outline observables to differentiate between these scenarios from single molecule tracking experiments. In the binding site model, we derive relations between the distribution of proteins, their diffusion properties, and their radial displacement. We predict that protein search times can be reduced for targets inside a liquid droplet, but not in an aggregate of slowly moving binding sites. These results are applicable to future experiments and suggest different biological roles for liquid droplet and binding site foci.

The evolution of many microbes and pathogens, including circulating viruses such as seasonal influenza, is driven by immune pressure from the host population. In turn, the immune systems of infected populations get updated, chasing viruses even further away. Quantitatively understanding how these dynamics result in observed patterns of rapid pathogen and immune adaptation is instrumental to epidemiological and evolutionary forecasting. Here we present a mathematical theory of co-evolution between immune systems and viruses in a finite-dimensional antigenic space, which describes the cross-reactivity of viral strains and immune systems primed by previous infections. We show the emergence of an antigenic wave that is pushed forward and canalized by cross-reactivity. We obtain analytical results for shape, speed, and angular diffusion of the wave. In particular, we show that viral-immune co-evolution generates a new emergent timescale, the persistence time of the wave's direction in antigenic space, which can be much longer than the coalescence time of the viral population. We compare these dynamics to the observed antigenic turnover of influenza strains, and we discuss how the dimensionality of antigenic space impacts on the predictability of the evolutionary dynamics. Our results provide a concrete and tractable framework to describe pathogen-host co-evolution.

High-throughput sequencing of T- and B-cell receptors makes it possible to track immune repertoires across time, in different tissues, in acute and chronic diseases and in healthy individuals. However quantitative comparison between repertoires is confounded by variability in the read count of each receptor clonotype due to sampling, library preparation, and expression noise. We review methods for accounting for both biological and experimental noise and present an easy-to-use python package NoisET that implements and generalizes a previously developed Bayesian method. It can be used to learn experimental noise models for repertoire sequencing from replicates, and to detect responding clones following a stimulus. We test the package on different repertoire sequencing technologies and datasets. We review how such approaches have been used to identify responding clonotypes in vaccination and disease data. Availability: NoisET is freely available to use with source code at github.com/statbiophys/NoisET.

Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate enough, may perform very differently for the two tasks. Exact discretizations, which work equally well at any scale, are characterized by the property of invariance under coarse-graining. Motivated by this observation, we build an explicit Renormalization Group approach for Gaussian time series generated by auto-regressive models. We show that the RG fixed points correspond to discretizations of linear SDEs, and only come in the form of first order Markov processes or non-Markovian ones. This fact provides an alternative explanation of why standard delay-vector embedding procedures fail in reconstructing partially observed noise-driven systems. We also suggest a possible effective Markovian discretization for the inference of partially observed underdamped equilibrium processes based on the exploitation of the Einstein relation., Comment: 13 pages, 3 figures, 1 table

Subclasses of lymphocytes carry different functional roles to work together to produce an immune response and lasting immunity. Additionally to these functional roles, T and B-cell lymphocytes rely on the diversity of their receptor chains to recognize different pathogens. The lymphocyte subclasses emerge from common ancestors generated with the same diversity of receptors during selection processes. Here we leverage biophysical models of receptor generation with machine learning models of selection to identify specific sequence features characteristic of functional lymphocyte repertoires and subrepertoires. Specifically using only repertoire level sequence information, we classify CD4$^+$ and CD8$^+$ T-cells, find correlations between receptor chains arising during selection and identify T-cells subsets that are targets of pathogenic epitopes. We also show examples of when simple linear classifiers do as well as more complex machine learning methods.

Somatic hypermutations of immunoglobulin (Ig) genes occuring during affinity maturation drive B-cell receptors' ability to evolve strong binding to their antigenic targets. The landscape of these mutations is highly heterogeneous, with certain regions of the Ig gene being preferentially targeted. However, a rigorous quantification of this bias has been difficult because of phylogenetic correlations between sequences and the interference of selective forces. Here, we present an approach that corrects for these issues, and use it to learn a model of hypermutation preferences from a recently published large IgH repertoire dataset. The obtained model predicts mutation profiles accurately and in a reproducible way, including in the previously uncharacterized Complementarity Determining Region 3, revealing that both the sequence context of the mutation and its absolute position along the gene are important. In addition, we show that hypermutations occurring concomittantly along B-cell lineages tend to co-localize, suggesting a possible mechanism for accelerating affinity maturation.

Immune repertoires provide a unique fingerprint reflecting the immune history of individuals, with potential applications in precision medicine. However, the question of how personal that information is and how it can be used to identify individuals has not been explored. Here, we show that individuals can be uniquely identified from repertoires of just a few thousands lymphocytes. We present "Immprint," a classifier using an information-theoretic measure of repertoire similarity to distinguish pairs of repertoire samples coming from the same versus different individuals. Using published T-cell receptor repertoires and statistical modeling, we tested its ability to identify individuals with great accuracy, including identical twins, by computing false positive and false negative rates $< 10^{-6}$ from samples composed of 10,000 T-cells. We verified through longitudinal datasets and simulations that the method is robust to acute infections and the passage of time. These results emphasize the private and personal nature of repertoire data.

COVID-19 is a global pandemic caused by the SARS-CoV-2 coronavirus. T cells play a key role in the adaptive antiviral immune response by killing infected cells and facilitating the selection of virus-specific antibodies. However neither the dynamics and cross-reactivity of the SARS-CoV-2-specific T cell response nor the diversity of resulting immune memory are well understood. In this study we use longitudinal high-throughput T cell receptor (TCR) sequencing to track changes in the T cell repertoire following two mild cases of COVID-19. In both donors we identified CD4+ and CD8+ T cell clones with transient clonal expansion after infection. The antigen specificity of CD8+ TCR sequences to SARS-CoV-2 epitopes was confirmed by both MHC tetramer binding and presence in large database of SARS-CoV-2 epitope-specific TCRs. We describe characteristic motifs in TCR sequences of COVID-19-reactive clones and show preferential occurence of these motifs in publicly available large dataset of repertoires from COVID-19 patients. We show that in both donors the majority of infection-reactive clonotypes acquire memory phenotypes. Certain T cell clones were detected in the memory fraction at the pre-infection timepoint, suggesting participation of pre-existing cross-reactive memory T cells in the immune response to SARS-CoV-2.

Recent advances in modelling VDJ recombination and subsequent selection of T and B cell receptors provide useful tools to analyze and compare immune repertoires across time, individuals, and tissues. A suite of tools--IGoR [1], OLGA [2] and SONIA [3]--have been publicly released to the community that allow for the inference of generative and selection models from high-throughput sequencing data. However using these tools requires some scripting or command-line skills and familiarity with complex datasets. As a result the application of the above models has not been available to a broad audience. In this application note we fill this gap by presenting Simple OLGA & SONIA (SOS), a web-based interface where users with no coding skills can compute the generation and post-selection probabilities of their sequences, as well as generate batches of synthetic sequences. The application also functions on mobile phones.

The diversity of T-cell receptor (TCR) repertoires is achieved by a combination of two intrinsically stochastic steps: random receptor generation by VDJ recombination, and selection based on the recognition of random self-peptides presented on the major histocompatibility complex. These processes lead to a large receptor variability within and between individuals. However, the characterization of the variability is hampered by the limited size of the sampled repertoires. We introduce a new software tool SONIA to facilitate inference of individual-specific computational models for the generation and selection of the TCR beta chain (TRB) from sequenced repertoires of 651 individuals, separating and quantifying the variability of the two processes of generation and selection in the population. We find not only that most of the variability is driven by the VDJ generation process, but there is a large degree of consistency between individuals with the inter-individual variance of repertoires being about 2% of the intra-individual variance. Known viral-specific TCRs follow the same generation and selection statistics as all TCRs., Comment: 13 pages, 7 figure, 2 tables

Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in the quantitative reconstruction of the model from experimental data, even in the simple case of equilibrium Langevin dynamics of Hamiltonian systems. We develop a novel Bayesian inference approach to learn the parameters of such stochastic effective models from discrete finite length trajectories. We first discuss the failure of naive inference approaches based on the estimation of derivatives through finite differences, regardless of the time resolution and the length of the sampled trajectories. We then derive, adopting higher order discretization schemes, maximum likelihood estimators for the model parameters that provide excellent results even with moderately long trajectories. We apply our method to second order models of collective motion and show that our results also hold in the presence of interactions., Comment: we correct previous inaccuracy about a reference; 29 pages, 9 figures

High-throughput sequencing of B- and T-cell receptors makes it possible to track immune repertoires across time, in different tissues, and in acute and chronic diseases or in healthy individuals. However, quantitative comparison between repertoires is confounded by variability in the read count of each receptor clonotype due to sampling, library preparation, and expression noise. Here, we present a general Bayesian approach to disentangle repertoire variations from these stochastic effects. Using replicate experiments, we first show how to learn the natural variability of read counts by inferring the distributions of clone sizes as well as an explicit noise model relating true frequencies of clones to their read count. We then use that null model as a baseline to infer a model of clonal expansion from two repertoire time points taken before and after an immune challenge. Applying our approach to yellow fever vaccination as a model of acute infection in humans, we identify candidate clones participating in the response.

T-cell receptors (TCR) are key proteins of the adaptive immune system, generated randomly in each individual, whose diversity underlies our ability to recognize infections and malignancies. Modeling the distribution of TCR sequences is of key importance for immunology and medical applications. Here, we compare two inference methods trained on high-throughput sequencing data: a knowledge-guided approach, which accounts for the details of sequence generation, supplemented by a physics-inspired model of selection; and a knowledge-free Variational Auto-Encoder based on deep artificial neural networks. We show that the knowledge-guided model outperforms the deep network approach at predicting TCR probabilities, while being more interpretable, at a lower computational cost.

The diverse repertoire of T-cell receptors (TCR) plays a key role in the adaptive immune response to infections. Previous studies show that secondary responses to the yellow fever vaccine - the model for acute infection in humans - are weaker than primary ones, but only quantitative measurements can describe the concentration changes and lineage fates for distinct T-cell clones in vivo over time. Using TCR alpha and beta repertoire sequencing for T-cell subsets, as well as single-cell RNAseq and TCRseq, we track the concentrations and phenotypes of individual T-cell clones in response to primary and secondary yellow fever immunization showing their large diversity. We confirm the secondary response is an order of magnitude weaker, albeit $\sim10$ days faster than the primary one. Estimating the fraction of the T-cell response directed against the single immunodominant epitope, we identify the sequence features of TCRs that define the high precursor frequency of the two major TCR motifs specific for this particular epitope. We also show the consistency of clonal expansion dynamics between bulk alpha and beta repertoires, using a new methodology to reconstruct alpha-beta pairings from clonal trajectories.

Immune repertoires rely on diversity of T-cell and B-cell receptors to protect us against foreign threats. The ability to recognize a wide variety of pathogens is linked to the number of different clonotypes expressed by an individual. Out of the estimated $\sim 10^{12}$ different B and T cells in humans, how many of them express distinct receptors? We review current and past estimates for these numbers. We point out a fundamental limitation of current methods, which ignore the tail of small clones in the distribution of clone sizes. We show that this tail strongly affects the total number of clones, but it is impractical to access experimentally. We propose that combining statistical models with mechanistic models of lymphocyte clonal dynamics offers possible new strategies for estimating the number of clones.

The adaptive immune system is a dynamical, self-organized multiscale system that protects vertebrates from both pathogens and internal irregularities, such as tumours. For these reason it fascinates physicists, yet the multitude of different cells, molecules and sub-systems is often also petrifying. Despite this complexity, as experiments on different scales of the adaptive immune system become more quantitative, many physicists have made both theoretical and experimental contributions that help predict the behaviour of ensembles of cells and molecules that participate in an immune response. Here we review some recent contributions with an emphasis on quantitative questions and methodologies. We also provide a more general methods section that presents some of the wide array of theoretical tools used in the field., Comment: 78 page review

The first cell fate decisions in the developing fly embryo are made very rapidly : hunchback genes decide in a few minutes whether a given nucleus follows the anterior or the posterior developmental blueprint by reading out the positional information encoded in the Bicoid morphogen. This developmental system constitutes a prototypical instance of the broad spectrum of regulatory decision processes that combine speed and accuracy. Traditional arguments based on fixed-time sampling of Bicoid concentration indicate that an accurate readout is not possible within the short times observed experimentally. This raises the general issue of how speed-accuracy tradeoffs are achieved. Here, we compare fixed-time sampling strategies to decisions made on-the-fly, which are based on updating and comparing the likelihoods of being at an anterior or a posterior location. We found that these more efficient schemes can complete reliable cell fate decisions even within the very short embryological timescales. We discuss the influence of promoter architectures on the mean decision time and decision error rate and present concrete promoter architectures that allow for the fast readout of the morphogen. Lastly, we formulate explicit predictions for new experiments involving Bicoid mutants.

Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature include the effectively one-dimensional escape characteristic of influenza A and the prolonged coexistence of lineages in influenza B. Here we use an evolutionary model for viruses in the presence of immune host systems with finite memory to delineate parameter regimes of these patterns in a in two-dimensional antigenic space. We find that for small effective mutation rates and mutation jump ranges, a single lineage is the only stable solution. Large effective mutation rates combined with large mutational jumps in antigenic space lead to multiple stably co-existing lineages over prolonged evolutionary periods. These results combined with observations from data constrain the parameter regimes for the adaptation of viruses, including influenza.

The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family--the total number of sequences in that family--can be estimated using models of maximum entropy trained on multiple sequence alignments of naturally occuring amino acid sequences. We analyzed and calculated the size of three abundant repeat proteins families, whose members are large proteins made of many repetitions of conserved portions of ~ 30 amino acids. While amino acid conservation at each position of the alignment explains most of the reduction of diversity relative to completely random sequences, we found that correlations between amino acid usage at different positions significantly impact that diversity. We quantified the impact of different types of correlations, functional and evolutionary, on sequence diversity. Analysis of the detailed structure of the coding space of the families revealed a rugged landscape, with many local energy minima of varying sizes with a hierarchical structure, reminiscent of fustrated energy landscapes of spin glass in physics. This clustered structure indicates a multiplicity of subtypes within each family, and suggests new strategies for protein design.

CRISPR-Cas mediated immunity in bacteria allows bacterial populations to protect themselves against pathogens. However, it also exposes them to the dangers of auto-immunity by developing protection that targets its own genome. Using a simple model of the coupled dynamics of phage and bacterial populations, we explore how acquisition rates affect the survival rate of the bacterial colony. We find that the optimal strategy depends on the initial population sizes of both viruses and bacteria. Additionally, certain combinations of acquisition and dynamical rates and initial population sizes guarantee protection, due to a dynamical balance between the evolving population sizes, without relying on acquisition of viral spacers. Outside this regime, the high cost of auto-immunity limits the acquisition rate. We discuss these optimal survival strategies in terms of recent experiments., Comment: 5 figures, 10 pages

Hypervariable T-cell receptors (TCR) play a key role in adaptive immunity, recognising a vast diversity of pathogen-derived antigens. High throughput sequencing of TCR repertoires (RepSeq) produces huge datasets of T-cell receptor sequences from blood and tissue samples. However, our ability to extract clinically relevant information from RepSeq data is limited, mainly because little is known about TCR-disease associations. Here we present a statistical approach called ALICE (Antigen-specific Lymphocyte Identification by Clustering of Expanded sequences) that identifies TCR sequences that are actively involved in the current immune response from a single RepSeq sample, and apply it to repertoires of patients with a variety of disorders - autoimmune disease (ankylosing spondylitis), patients under cancer immunotherapy, or subject to an acute infection (live yellow fever vaccine). The method's robustness is demonstrated by the agreement of its predictions with independent assays, and is supported by its ability to selectively detect responding TCR in the memory but not in the naive subset. ALICE requires no longitudinal data collection nor large cohorts, and is thus directly applicable to most RepSeq datasets. Its results facilitate the identification of TCR variants associated with a wide variety of diseases and conditions, which can be used for diagnostics, rational vaccine design and evaluation of the adaptive immune system state.

Motivation: High-throughput sequencing of large immune repertoires has enabled the development of methods to predict the probability of generation by V(D)J recombination of T- and B-cell receptors of any specific nucleotide sequence. These generation probabilities are very non-homogeneous, ranging over 20 orders of magnitude in real repertoires. Since the function of a receptor really depends on its protein sequence, it is important to be able to predict this probability of generation at the amino acid level. However, brute-force summation over all the nucleotide sequences with the correct amino acid translation is computationally intractable. The purpose of this paper is to present a solution to this problem. Results: We use dynamic programming to construct an efficient and flexible algorithm, called OLGA (Optimized Likelihood estimate of immunoGlobulin Amino-acid sequences), for calculating the probability of generating a given CDR3 amino acid sequence or motif, with or without V/J restriction, as a result of V(D)J recombination in B or T cells. We apply it to databases of epitope-specific T-cell receptors to evaluate the probability that a typical human subject will possess T cells responsive to specific disease-associated epitopes. The model prediction shows an excellent agreement with published data. We suggest that OLGA may be a useful tool to guide vaccine design. Availability: Source code is available at https://github.com/zsethna/OLGA

The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called $\alpha$ and $\beta$, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the $\alpha\beta$ generation process. We estimate the probabilities of a rescue recombination of the $\beta$ chain on the second chromosome upon failure or success on the first chromosome. Unlike $\beta$ chains, $\alpha$ chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that $\sim 28 \%$ of cells express both $\alpha$ chains. We report that clones sharing the same $\beta$ chain but different $\alpha$ chains are overrepresented, suggesting that they respond to common immune challenges. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCR$\alpha\beta$ is lower than $10^{-12}$ and estimate the generation diversity and sharing properties of the $\alpha\beta$ TCR repertoire.

An adaptive agent predicting the future state of an environment must weigh trust in new observations against prior experiences. In this light, we propose a view of the adaptive immune system as a dynamic Bayesian machinery that updates its memory repertoire by balancing evidence from new pathogen encounters against past experience of infection to predict and prepare for future threats. This framework links the observed initial rapid increase of the memory pool early in life followed by a mid-life plateau to the ease of learning salient features of sparse environments. We also derive a modulated memory pool update rule in agreement with current vaccine response experiments. Our results suggest that pathogenic environments are sparse and that memory repertoires significantly decrease infection costs even with moderate sampling. The predicted optimal update scheme maps onto commonly considered competitive dynamics for antigen receptors.

Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution? Are there quantitative laws that govern and constrain evolution? Is evolution repeatable or predictable? Historically, the study of evolution involved classifying and comparing species, typically based on morphology. In addition to phenotypes on the organismal and molecular scales, we now use whole-genome sequencing to uncover not only the differences between species but also to characterize genetic diversity within-species in unprecedented detail. This diversity can be compared to predictions of quantitative models of evolutionary dynamics. Here, we review key theoretical models of population genetics and evolution along with examples of data from lab evolution experiments, longitudinal sampling of viral populations, microbial communities and the studies of immune repertoires. In all these systems, evolution is shaped by often variable biological and physical environments. While these variable environments can be modeled implicitly in cases such as host-pathogen co-evolution, the dynamic environment, and emerging ecology often cannot be ignored. Integrating dynamics on different scales, both in terms of observation and theoretical models, remains a major challenge towards a better understanding of evolution., Comment: Rapporteur report for the proceedings of the 2017 Solvay Conference

T-cell receptor (TCR) repertoire data contain information about infections that could be used in disease diagnostics and vaccine development, but extracting that information remains a major challenge. Here we developed a statistical framework to detect TCR clone proliferation and contraction from longitudinal repertoire data. We applied this framework to data from three pairs of identical twins immunized with the yellow fever vaccine. We identified 500-1500 responding TCRs in each donor and validated them using three independent assays. While the responding TCRs were mostly private, albeit with higher overlap between twins, they could be well predicted using a classifier based on sequence similarity. Our method can also be applied to samples obtained post-infection, making it suitable for systematic discovery of new infection-specific TCRs in the clinic.