arXiv subjects

Aleksandra M. Walczak

Publications and source records attributed to Aleksandra M. Walczak.

At least 55 records · Page 3Linked to original sources

arXiv2020

Population variability in the generation and thymic selection of T-cell repertoires

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.

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arXiv2019

Quantitative Immunology for Physicists

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.

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arXiv2019

How many different clonotypes do immune repertoires contain?

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.

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arXiv2019

Size and structure of the sequence space of repeat proteins

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.

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arXiv2019

Hunchback promoters can readout morphogenetic positional information in less than a minute

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.

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arXiv2019

Multi-lineage evolution in viral populations driven by host immune systems

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.

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arXiv2018

Genesis of the alpha beta T-cell receptor

The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called $α$ and $β$, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the $αβ$ generation process. We estimate the probabilities of a rescue recombination of the $β$ chain on the second chromosome upon failure or success on the first chromosome. Unlike $β$ chains, $α$ 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 $α$ chains. We report that clones sharing the same $β$ chain but different $α$ 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$αβ$ is lower than $10^{-12}$ and estimate the generation diversity and sharing properties of the $αβ$ TCR repertoire.

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arXiv2018

How a well-adapting immune system remembers

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.

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arXiv2018

OLGA: fast computation of generation probabilities of B- and T-cell receptor amino acid sequences and motifs

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

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arXiv2018

Cost and benefits of CRISPR spacer acquisition

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.

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arXiv2018

Progress and open problems in evolutionary dynamics

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.

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arXiv2018

Precise tracking of vaccine-responding T-cell clones reveals convergent and personalized response in identical twins

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.

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arXiv2018

Predicting the spectrum of TCR repertoire sharing with a data-driven model of recombination

Despite the extreme diversity of T cell repertoires, many identical T-cell receptor (TCR) sequences are found in a large number of individual mice and humans. These widely-shared sequences, often referred to as `public', have been suggested to be over-represented due to their potential immune functionality or their ease of generation by V(D)J recombination. Here we show that even for large cohorts the observed degree of sharing of TCR sequences between individuals is well predicted by a model accounting for by the known quantitative statistical biases in the generation process, together with a simple model of thymic selection. Whether a sequence is shared by many individuals is predicted to depend on the number of queried individuals and the sampling depth, as well as on the sequence itself, in agreement with the data. We introduce the degree of publicness conditional on the queried cohort size and the size of the sampled repertoires. Based on these observations we propose a public/private sequence classifier, `PUBLIC' (Public Universal Binary Likelihood Inference Classifier), based on the generation probability, which performs very well even for small cohort sizes.

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arXiv2017

Physical epistatic landscape of antibody binding affinity

Affinity maturation produces antibodies that bind antigens with high specificity by accumulating mutations in the antibody sequence. Mapping out the antibody-antigen affinity landscape can give us insight into the accessible paths during this rapid evolutionary process. By developing a carefully controlled null model for noninteracting mutations, we characterized epistasis in affinity measurements of a large library of antibody variants obtained by Tite-Seq, a recently introduced Deep Mutational Scan method yielding physical values of the binding constant. We show that representing affinity as the binding free energy minimizes epistasis. Yet, we find that epistatically interacting sites contribute substantially to binding. In addition to negative epistasis, we report a large amount of beneficial epistasis, enlarging the space of high-affinity antibodies as well as their mutational accessibility. These properties suggest that the degeneracy of antibody sequences that can bind a given antigen is enhanced by epistasis - an important property for vaccine design.

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arXiv2017

Method for identification of condition-associated public antigen receptor sequences

Diverse repertoires of hypervariable immunoglobulin receptors (TCR and BCR) recognize antigens in the adaptive immune system. The development of immunoglobulin receptor repertoire sequencing methods makes it possible to perform repertoire-wide disease association studies of antigen receptor sequences. We developed a statistical framework for associating receptors to disease from only a small cohort of patients, with no need for a control cohort. Our method successfully identifies previously validated Cytomegalovirus and type 1 diabetes responsive receptors.

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arXiv2017

Transitions in optimal adaptive strategies for populations in fluctuating environments

Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist phenotype that compromise between conditions, or population-wise diversification (bet-hedging). Which strategy provides the largest selective advantage in the long run depends on the range of accessible phenotypes and the statistics of the environmental fluctuations. Here, we analyze this problem in a simple mathematical model of population growth. First, we review and extend a graphical method to identify the nature of the optimal strategy when the environmental fluctuations are uncorrelated. Temporal correlations in environmental fluctuations open up new strategies that rely on memory but are mathematically challenging to study: we present here new analytical results to address this challenge. We illustrate our general approach by analyzing optimal adaptive strategies in the presence of trade-offs that constrain the range of accessible phenotypes. Our results extend several previous studies and have applications to a variety of biological phenomena, from antibiotic resistance in bacteria to immune responses in vertebrates.

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arXiv2017

Inferring repeat protein energetics from evolutionary information

Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing covariations in extant sequences. Still, many natural proteins that fold into the same structural topology show different stabilization energies, and these are often related to their physiological behavior. We propose a description for the energetic variation given by sequence modifications in repeat proteins, systems for which the overall problem is simplified by their inherent symmetry. We explicitly account for single amino acid and pair-wise interactions and treat higher order correlations with a single term. We show that the resulting force field can be interpreted with structural detail. We trace the variations in the energetic scores of natural proteins and relate them to their experimental characterization. The resulting energetic force field allows the prediction of the folding free energy change for several mutants, and can be used to generate synthetic sequences that are statistically indistinguishable from the natural counterparts.

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arXiv2017

Population dynamics of immune repertoires

The evolution of the adaptive immune system is characterized by changes in the relative abundances of the B- and T-cell clones that make up its repertoires. To fully capture this evolution, we need to describe the complex dynamics of the response to pathogenic and self-antigenic stimulations, as well as the statistics of novel lymphocyte receptors introduced throughout life. Recent experiments, ranging from high-throughput immune repertoire sequencing to quantification of the response to specific antigens, can help us characterize the effective dynamics of the immune response. Here we describe mathematical models informed by experiments that lead to a picture of clonal competition in a highly stochastic context. We discuss how different types of competition, noise and selection shape the observed clone-size distributions, and contrast them with predictions of a neutral theory of clonal evolution. These mathematical models show that memory and effector immune repertoire evolution is far from neutral, and is driven by the history of the pathogenic environment, while naive repertoire dynamics are consistent with neutral theory and competition in a fixed antigenic environment. Lastly, we investigate the effect of long-term clonal selection on repertoire aging.

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