laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
 
2016
Fluctuating fitness shapes the clone-size distribution of immune repertoires - Desponds, Jonathan and Mora, Thierry and Walczak, Aleksandra M.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 113274-279 (2016) 
LPS


Abstract : The adaptive immune system relies on the diversity of receptors expressed on the surface of B-and T cells to protect the organism from a vast amount of pathogenic threats. The proliferation and degradation dynamics of different cell types (B cells, T cells, naive, memory) is governed by a variety of antigenic and environmental signals, yet the observed clone sizes follow a universal power-law distribution. Guided by this reproducibility we propose effective models of somatic evolution where cell fate depends on an effective fitness. This fitness is determined by growth factors acting either on clones of cells with the same receptor responding to specific antigens, or directly on single cells with no regard for clones. We identify fluctuations in the fitness acting specifically on clones as the essential ingredient leading to the observed distributions. Combining our models with experiments, we characterize the scale of fluctuations in antigenic environments and we provide tools to identify the relevant growth signals in different tissues and organisms. Our results generalize to any evolving population in a fluctuating environment.
JSP Special Issue on Information Processing in Living Systems - Mora, Thierry and Peliti, Luca and Rivoire, Olivier
JOURNAL OF STATISTICAL PHYSICS 1621085-1087 (2016) 
LPS
Renyi entropy, abundance distribution, and the equivalence of ensembles - Mora, Thierry and Walczak, Aleksandra M.
PHYSICAL REVIEW E 93 (2016) 
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Abstract : Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the Renyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation between the abundance distribution and the Renyi entropy, by analogy with the equivalence of ensembles in thermodynamics. The abundance distribution is mapped onto the density of states, and the Renyi entropy to the free energy. The two quantities are related in the thermodynamic limit by a Legendre transform, by virtue of the equivalence between the micro-canonical and canonical ensembles. In this limit, we show how the Renyi entropy can be constructed geometrically from rank-frequency plots. This mapping predicts that non-concave regions of the rank-frequency curve should result in kinks in the Renyi entropy as a function of its order. We illustrate our results on simple examples, and emphasize the limitations of the equivalence of ensembles when a thermodynamic limit is not well defined. Our results help choose reliable diversity measures based on the experimental accuracy of the abundance distributions in particular frequency ranges.
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Comparison of clonal complexity of primary and secondary trout IGM and IGT response using deep sequencing - Magadan, Susana and Jouneau, Luc and Chara, Wahiba and Lunazzi, Aurelie and Walzcak, Alexandra and Mora, Thierry and Quillet, Edwige and Ovensen, Oystein and Six, Adrien and Sunyer, Oriol and Boudinot, Pierre
FISH \& SHELLFISH IMMUNOLOGY 5385 (2016) 
LPS
repgenHMM: a dynamic programming tool to infer the rules of immune receptor generation from sequence data - Elhanati, Yuval and Marcou, Quentin and Mora, Thierry and Walczak, Aleksandra M.
BIOINFORMATICS 321943-1951 (2016) 
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Abstract : Motivation: The diversity of the immune repertoire is initially generated by random rearrangements of the receptor gene during early T and B cell development. Rearrangement scenarios are composed of random events-choices of gene templates, base pair deletions and insertions-described by probability distributions. Not all scenarios are equally likely, and the same receptor sequence may be obtained in several different ways. Quantifying the distribution of these rearrangements is an essential baseline for studying the immune system diversity. Inferring the properties of the distributions from receptor sequences is a computationally hard problem, requiring enumerating every possible scenario for every sampled receptor sequence. Results: We present a Hidden Markov model, which accounts for all plausible scenarios that can generate the receptor sequences. We developed and implemented a method based on the Baum-Welch algorithm that can efficiently infer the parameters for the different events of the rearrangement process. We tested our software tool on sequence data for both the alpha and beta chains of the T cell receptor. To test the validity of our algorithm, we also generated synthetic sequences produced by a known model, and confirmed that its parameters could be accurately inferred back from the sequences. The inferred model can be used to generate synthetic sequences, to calculate the probability of generation of any receptor sequence, as well as the theoretical diversity of the repertoire. We estimate this diversity to be approximate to 10(23) for human T cells. The model gives a baseline to investigate the selection and dynamics of immune repertoires.
A Tractable Method for Describing Complex Couplings between Neurons and Population Rate - Gardella, Christophe and Marre, Olivier and Mora, Thierry
ENEURO 3 (2016) 
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Abstract : Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the summed activity of all neurons in the population. However, an explicit, tractable model for these interactions is still lacking. Here we build a probabilistic model of population activity that reproduces the firing rate of each cell, the distribution of the population rate, and the linear coupling between them. This model is tractable, meaning that its parameters can be learned in a few seconds on a standard computer even for large population recordings. We inferred our model for a population of 160 neurons in the salamander retina. In this population, single-cell firing rates depended in unexpected ways on the population rate. In particular, some cells had a preferred population rate at which they were most likely to fire. These complex dependencies could not be explained by a linear coupling between the cell and the population rate. We designed a more general, still tractable model that could fully account for these nonlinear dependencies. We thus provide a simple and computationally tractable way to learn models that reproduce the dependence of each neuron on the population rate.
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Persisting fetal clonotypes influence the structure and overlap of adult human TCR repertoires - Pogorelyy, M. and Elhanati, Y. and Marcou, Q. and Sycheva, A. and Komech, E. and Britanova, O. and Chudakov, D. and Mamedov, I and Lebedev, Y. and Mora, T. and Walczak, A.
EUROPEAN JOURNAL OF IMMUNOLOGY 4652 (2016) 
LPS
Diversity of immune strategies explained by adaptation to pathogen statistics - Mayer, Andreas and Mora, Thierry and Rivoire, Olivier and Walczak, Aleksandra M.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 1138630-8635 (2016) 
LPS


Abstract : Biological organisms have evolved a wide range of immune mechanisms to defend themselves against pathogens. Beyond molecular details, these mechanisms differ in how protection is acquired, processed, and passed on to subsequent generations-differences that may be essential to long-term survival. Here, we introduce a mathematical framework to compare the long-term adaptation of populations as a function of the pathogen dynamics that they experience and of the immune strategy that they adopt. We find that the two key determinants of an optimal immune strategy are the frequency and the characteristic timescale of the pathogens. Depending on these two parameters, our framework identifies distinct modes of immunity, including adaptive, innate, bet-hedging, and CRISPR-like immunities, which recapitulate the diversity of natural immune systems.
Local equilibrium in bird flocks - Mora, Thierry and Walczak, Aleksandra M. and Del Castello, Lorenzo and Ginelli, Francesco and Melillo, Stefania and Parisi, Leonardo and Viale, Massimiliano and Cavagna, Andrea and Giardina, Irene
Nature Physics 121153+ (2016) 
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Abstract : The correlated motion of flocks is an example of global order emerging from local interactions. An essential difference with respect to analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. This non-equilibrium characteristic has been studied theoretically, but its impact on actual animal groups remains to be fully explored experimentally. Here, we introduce a novel dynamical inference technique, based on the principle of maximum entropy, which accommodates network rearrangements and overcomes the problem of slow experimental sampling rates. We use this method to infer the strength and range of alignment forces from data of starling flocks. We find that local bird alignment occurs on a much faster timescale than neighbour rearrangement. Accordingly, equilibrium inference, which assumes a fixed interaction network, gives results consistent with dynamical inference. We conclude that bird orientations are in a state of local quasi-equilibrium over the interaction length scale, providing firm ground for the applicability of statistical physics in certain active systems.
 
2015
DOI
10
Flocking and Turning: a New Model for Self-organized Collective Motion - Cavagna, Andrea and Del Castello, Lorenzo and Giardina, Irene and Grigera, Tomas and Jelic, Asja and Melillo, Stefania and Mora, Thierry and Parisi, Leonardo and Silvestri, Edmondo and Viale, Massimiliano and Walczak, Aleksandra M.
JOURNAL OF STATISTICAL PHYSICS 158601-627 (2015) 
LPS


Abstract : Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system.
DOI
11
Dynamical Criticality in the Collective Activity of a Population of Retinal Neurons - Mora, Thierry and Deny, Stephane and Marre, Olivier
PHYSICAL REVIEW LETTERS 114 (2015) 
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Abstract : Recent experimental results based on multielectrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on the definition of arbitrary order parameters, or on models that do not address the dynamical nature of network activity. Here we introduce a novel approach to assess criticality that overcomes these limitations, while encompassing and generalizing previous criteria. We find a simple model to describe the global activity of large populations of ganglion cells in the rat retina, and show that their statistics are poised near a critical point. Taking into account the temporal dynamics of the activity greatly enhances the evidence for criticality, revealing it where previous methods would not. The approach is general and could be used in other biological networks.
DOI
12
How a well-adapted immune system is organized - Mayer, Andreas and Balasubramanian, Vijay and Mora, Thierry and Walczak, Aleksandra M.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 1125950-5955 (2015) 
LPS


Abstract : The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections. We develop a general framework for predicting the optimal repertoire that minimizes the cost of infections contracted from a given distribution of pathogens. The theory predicts that the immune system will have more receptors for rare antigens than expected from the frequency of encounters; individuals exposed to the same infections will have sparse repertoires that are largely different, but nevertheless exploit cross-reactivity to provide the same coverage of antigens; and the optimal repertoires can be reached via the dynamics of competitive binding of antigens by receptors and selective amplification of stimulated receptors. Our results follow from a tension between the statistics of pathogen detection, which favor a broader receptor distribution, and the effects of cross-reactivity, which tend to concentrate the optimal repertoire onto a few highly abundant clones. Our predictions can be tested in high-throughput surveys of receptor and pathogen diversity.
DOI
13
High Accuracy Decoding of Dynamical Motion from a Large Retinal Population - Marre, Olivier and Botella-Soler, Vicente and Simmons, Kristina D. and Mora, Thierry and Tkacik, Gasper and Berry, II, Michael J.
PLOS COMPUTATIONAL BIOLOGY 11 (2015) 
LPS


Abstract : Motion tracking is a challenge the visual system has to solve by reading out the retinal population. It is still unclear how the information from different neurons can be combined together to estimate the position of an object. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar's position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. We then took advantage of this unprecedented precision to explore the spatial structure of the retina's population code. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar's position. Instead, we found that most ganglion cells in the salamander fired sparsely and idiosyncratically, so that their neural image did not track the bar. Furthermore, ganglion cell activity spanned an area much larger than predicted by their receptive fields, with cells coding for motion far in their surround. As a result, population redundancy was high, and we could find multiple, disjoint subsets of neurons that encoded the trajectory with high precision. This organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.
DOI
14
Capturing coevolutionary signals in repeat proteins - Espada, Rocio and Parra, R. Gonzalo and Mora, Thierry and Walczak, Aleksandra M. and Ferreiro, Diego U.
BMC BIOINFORMATICS 16 (2015) 
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Abstract : Background: The analysis of correlations of amino acid occurrences in globular domains has led to the development of statistical tools that can identify native contacts - portions of the chains that come to close distance in folded structural ensembles. Here we introduce a direct coupling analysis for repeat proteins - natural systems for which the identification of folding domains remains challenging. Results: We show that the inherent translational symmetry of repeat protein sequences introduces a strong bias in the pair correlations at precisely the length scale of the repeat-unit. Equalizing for this bias in an objective way reveals true co-evolutionary signals from which local native contacts can be identified. Importantly, parameter values obtained for all other interactions are not significantly affected by the equalization. We quantify the robustness of the procedure and assign confidence levels to the interactions, identifying the minimum number of sequences needed to extract evolutionary information in several repeat protein families. Conclusions: The overall procedure can be used to reconstruct the interactions at distances larger than repeat-pairs, identifying the characteristics of the strongest couplings in each family, and can be applied to any system that appears translationally symmetric.
DOI
15
Physical Limit to Concentration Sensing Amid Spurious Ligands - Mora, Thierry
PHYSICAL REVIEW LETTERS 115 (2015) 
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Abstract : To adapt their behavior in changing environments, cells sense concentrations by binding external ligands to their receptors. However, incorrect ligands may bind nonspecifically to receptors, and when their concentration is large, this binding activity may interfere with the sensing of the ligand of interest. Here, I derive analytically the physical limit to the accuracy of concentration sensing amid a large number of interfering ligands. A scaling transition is found when the mean bound time of correct ligands is twice that of incorrect ligands. I discuss how the physical bound can be approached by a cascade of receptor states generalizing kinetic proofreading schemes.
DOI
16
Inferring processes underlying B-cell repertoire diversity - Elhanati, Yuval and Sethna, Zachary and Marcou, Quentin and Callan, Jr., Curtis G. and Mora, Thierry and Walczak, Aleksandra M.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES 370 (2015) 
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Abstract : We quantify the VDJ recombination and somatic hypermutation processes in human B cells using probabilistic inference methods on high-throughput DNA sequence repertoires of human B-cell receptor heavy chains. Our analysis captures the statistical properties of the naive repertoire, first after its initial generation via VDJ recombination and then after selection for functionality. We also infer statistical properties of the somatic hypermutation machinery (exclusive of subsequent effects of selection). Our main results are the following: the B-cell repertoire is substantially more diverse than T-cell repertoires, owing to longer junctional insertions; sequences that pass initial selection are distinguished by having a higher probability of being generated in a VDJ recombination event; somatic hypermutations have a non-uniform distribution along the V gene that is well explained by an independent site model for the sequence context around the hypermutation site.
DOI
17
Thermodynamics and signatures of criticality in a network of neurons - Tkacik, Gasper and Mora, Thierry and Marre, Olivier and Amodei, Dario and Palmer, Stephanie E. and Berry, II, Michael J. and Bialek, William
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 11211508-11513 (2015) 
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Abstract : The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.
DOI
18
Repeat proteins challenge the concept of structural domains - Espada, Rocio and Gonzalo Parra, R. and Sippl, Manfred J. and Mora, Thierry and Walczak, Aleksandra M. and Ferreiro, Diego U.
BIOCHEMICAL SOCIETY TRANSACTIONS 43844-849 (2015) 
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Abstract : Structural domains are believed to be modules within proteins that can fold and function independently. Some proteins show tandem repetitions of apparent modular structure that do not fold independently, but rather co-operate in stabilizing structural forms that comprise several repeat-units. For many natural repeat-proteins, it has been shown that weak energetic links between repeats lead to the breakdown of co-operativity and the appearance of folding sub-domains within an apparently regular repeat array. The quasi-1D architecture of repeat-proteins is crucial in detailing how the local energetic balances can modulate the folding dynamics of these proteins, which can be related to the physiological behaviour of these ubiquitous biological systems.
DOI
19
A Reassessment of IgM Memory Subsets in Humans - Bagnara, Davide and Squillario, Margherita and Kipling, David and Mora, Thierry and Walczak, Aleksandra M. and Da Silva, Lucie and Weller, Sandra and Dunn-Walters, Deborah K. and Weill, Jean-Claude and Reynaud, Claude-Agnes
JOURNAL OF IMMUNOLOGY 1953716-3724 (2015) 
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Abstract : From paired blood and spleen samples from three adult donors, we performed high-throughput VH sequencing of human B cell subsets defined by IgD and CD27 expression: IgD(+)CD27(+) (''marginal zone [MZ]''), IgD(-)CD27(+) (''memory,'' including IgM [''IgM-only''], IgG and IgA) and IgD 2 CD27(-) cells (''double-negative,'' including IgM, IgG, and IgA). A total of 91,294 unique sequences clustered in 42,670 clones, revealing major clonal expansions in each of these subsets. Among these clones, we further analyzed those shared sequences from different subsets or tissues for VH gene mutation, H-CDR3-length, and V-H/J(H) usage, comparing these different characteristics with all sequences from their subset of origin for which these parameters constitute a distinct signature. The IgM-only repertoire profile differed notably from that of MZ B cells by a higher mutation frequency and lower V(H)4 and higher J(H)6 gene usage. Strikingly, IgM sequences from clones shared between the MZ and the memory IgG/IgA compartments showed a mutation and repertoire profile of IgM-only and not of MZ B cells. Similarly, all IgM clonal relationships (among MZ, IgM-only, and double-negative compartments) involved sequences with the characteristics of IgM-only B cells. Finally, clonal relationships between tissues suggested distinct recirculation characteristics between MZ and switched B cells. The ``IgM-only'' subset (including cells with its repertoire signature but higher IgD or lower CD27 expression levels) thus appear as the only subset showing precursor-product relationships with CD27(+) switched memory B cells, indicating that they represent germinal center-derived IgM memory B cells and that IgM memory and MZ B cells constitute two distinct entities.
 
2014
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20
Dynamical maximum entropy approach to flocking - Cavagna, Andrea and Giardina, Irene and Ginelli, Francesco and Mora, Thierry and Piovani, Duccio and Tavarone, Raffaele and Walczak, Aleksandra M.
PHYSICAL REVIEW E 89 (2014) 
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Abstract : We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.