arXiv subjects

Olivier Rivoire

Publications and source records attributed to Olivier Rivoire.

30 records · Page 2Linked to original sources

arXiv2015

Informations in models of evolutionary dynamics

Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of evolutionary dynamics, and show how explicit results are obtained for a solvable subclass of these models. In several limits, the results coincide with those obtained in studies of information processing for communication, gambling or thermodynamics. In the most general case, however, information processing by biological populations shows unique features that motivate the analysis of specific models.

q-bio.PE↗

arXiv2014

Evolution of sparsity and modularity in a model of protein allostery

The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary constraints may take is important to interpret the information in protein sequences. To study this problem, we introduce a simple but physical model of protein evolution where selection targets allostery, the functional coupling of distal sites on protein surfaces. This model shows how the geometrical organization of couplings between amino acids within a protein structure can depend crucially on its evolutionary history. In particular, two scenarios are found to generate a spatial concentration of functional constraints: high mutation rates and fluctuating selective pressures. This second scenario offers a plausible explanation for the high tolerance of natural proteins to mutations and for the spatial organization of their least tolerant amino acids, as revealed by sequence analyses and mutagenesis experiments. It also implies a faculty to adapt to new selective pressures that is consistent with observations. Besides, the model illustrates how several independent functional modules may emerge within a same protein structure, depending on the nature of past environmental fluctuations. Our model thus relates the evolutionary history and evolutionary potential of proteins to the geometry of their functional constraints, with implications for decoding and engineering protein sequences.

q-bio.PE↗

arXiv2013

A Model for the Generation and Transmission of Variations in Evolution

The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it does not prescribe, per se, the mechanisms by which this is operated. The mechanisms of inheritance are not, however, unconstrained, since they are themselves subject to natural selection. We introduce a general, analytically solvable mathematical model to compare the adaptive value of different schemes of inheritance. Our model allows for variations to be inherited, randomly produced, or environmentally induced, and, irrespectively, to be either transmitted or not during reproduction. The adaptation of the different schemes for processing variations is quantified for a range of fluctuating environments, following an approach that links quantitative genetics with stochastic control theory.

q-bio.PE↗

arXiv2013

Synteny in Bacterial Genomes: Inference, Organization and Evolution

Genes are not located randomly along genomes. Synteny, the conservation of their relative positions in genomes of different species, reflects fundamental constraints on natural evolution. We present approaches to infer pairs of co-localized genes from multiple genomes, describe their organization, and study their evolutionary history. In bacterial genomes, we thus identify synteny units, or "syntons", which are clusters of proximal genes that encompass and extend operons. The size distribution of these syntons divide them into large syntons, which correspond to fundamental macro-molecular complexes of bacteria, and smaller ones, which display a remarkable exponential distribution of sizes. This distribution is "universal" in two respects: it holds for vastly different genomes, and for functionally distinct genes. Similar statistical laws have been reported previously in studies of bacterial genomes, and generally attributed to purifying selection or neutral processes. Here, we perform a new analysis based on the concept of parsimony, and find that the prevailing evolutionary mechanism behind the formation of small syntons is a selective process of gene aggregation. Altogether, our results imply a common evolutionary process that selectively shapes the organization and diversity of bacterial genomes.

q-bio.GN↗

arXiv2013

Elements of Coevolution in Biological Sequences

Studies of coevolution of amino acids within and between proteins have revealed two types of coevolving units: coevolving contacts, which are pairs of amino acids distant along the sequence but in contact in the three-dimensional structure, and sectors, which are larger groups of structurally connected amino acids that underlie the biochemical properties of proteins. By reconciling two approaches for analyzing correlations in multiple sequence alignments, we link these two findings together and with coevolving units of intermediate size, called `sectons', which are shown to provide additional information. By extending the analysis to the co-occurrence of orthologous genes in bacterial genomes, we also show that the methods and results are general and relevant beyond protein structures.

q-bio.BM↗

arXiv2010

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory.

q-bio.PE↗

arXiv2006

Exactly solvable models of adaptive networks

A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.

cond-mat.dis-nn↗

arXiv2006

Statistical mechanics of error exponents for error-correcting codes

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.

cond-mat.dis-nn↗

arXiv2006

Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel

We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error exponents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding.

cs.IT↗

arXiv2005

Landscape of solutions in constraint satisfaction problems

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.

cond-mat.dis-nn↗

arXiv2005

The cavity method for large deviations

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs. It is illustrated with two combinatorial optimization problems, the vertex-cover and coloring problems, for which the presence of replica symmetry breaking phases is taken into account. Applications include the analysis of models on adaptive graph structures.

cond-mat.dis-nn↗

arXiv2004

Properties of atypical graphs from negative complexities

The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare samples in spin-glass like models. This relation between large deviations and replica theory is explicited on different models where it is confronted to direct combinatorial calculations.

cond-mat.stat-mech↗