arXiv subjects

Aleksandra M. Walczak

Publications and source records attributed to Aleksandra M. Walczak.

At least 37 records · Page 2Linked to original sources

arXiv2023

Bayesian estimation of the Kullback-Leibler divergence for categorical sytems using mixtures of Dirichlet priors

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.

stat.ME↗

arXiv2023

Dynamical information synergy in biochemical signaling networks

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.

q-bio.MN↗

arXiv2023

Towards a quantitative theory of tolerance

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.

q-bio.PE↗

arXiv2022

NoisET: Noise learning and Expansion detection of T-cell receptors

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.

q-bio.GN↗

arXiv2022

MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories

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.

cs.LG↗

arXiv2022

Learning the statistics and landscape of somatic mutation-induced insertions and deletions in antibodies

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.

q-bio.GN↗

arXiv2022

From evolution to folding of repeat proteins

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.

q-bio.BM↗

arXiv2021

Affinity maturation for an optimal balance between long-term immune coverage and short-term resource constraints

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.

q-bio.PE↗

arXiv2021

Antigenic waves of virus-immune co-evolution

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.

q-bio.PE↗

arXiv2021

Physical observables to determine the nature of membrane-less cellular sub-compartments

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.

physics.bio-ph↗

arXiv2020

Immune Fingerprinting through Repertoire Similarity

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.

q-bio.GN↗

arXiv2020

Longitudinal high-throughput TCR repertoire profiling reveals the dynamics of T cell memory formation after mild COVID-19 infection

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.

q-bio.GN↗

arXiv2020

Learning the heterogeneous hypermutation landscape of immunoglobulins from high-throughput repertoire data

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.

q-bio.GN↗

arXiv2020

Building general Langevin models from discrete data sets

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.

q-bio.QM↗

arXiv2020

Inferring the immune response from repertoire sequencing

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.

q-bio.QM↗

arXiv2020

SOS: Online probability estimation and generation of T and B cell receptors

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.

q-bio.GN↗

arXiv2020

On generative models of T-cell receptor sequences

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.

q-bio.QM↗

arXiv2020

Primary and secondary anti-viral response captured by the dynamics and phenotype of individual T cell clones

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.

q-bio.GN↗