arXiv subjects

Jacques Rougemont

Publications and source records attributed to Jacques Rougemont.

5 recordsLinked to original sources

arXiv2019

Proteins: the physics of amorphous evolving matter

Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function performed by the protein within a hierarchy of interwoven interaction networks of the cell, the organism and the population. A physical theory of proteins therefore needs to unify both aspects, the biophysical and the evolutionary. Specifically, it should provide a model of how the DNA gene is mapped into the functional phenotype of the protein. We review several physical approaches to the protein problem, focusing on a mechanical framework which treats proteins as evolvable condensed matter: Mutations introduce localized perturbations in the gene, which are translated to localized perturbations in the protein matter. A natural tool to examine how mutations shape the phenotype are Green's functions. They map the evolutionary linkage among mutations in the gene (termed epistasis) to cooperative physical interactions among the amino acids in the protein. We discuss how the mechanistic view can be applied to examine basic questions of protein evolution and design.

q-bio.BM↗

arXiv2017

Two-Tier Mapper: a user-independent clustering method for global gene expression analysis based on topology

There is a growing need for unbiased clustering methods, ideally automated. We have developed a topology-based analysis tool called Two-Tier Mapper (TTMap) to detect subgroups in global gene expression datasets and identify their distinguishing features. First, TTMap discerns and adjusts for highly variable features in the control group and identifies outliers. Second, the deviation of each test sample from the control group in a high-dimensional space is computed and the test samples are clustered in a global and local network using a new topological algorithm based on Mapper. Validation of TTMap on both synthetic and biological datasets shows that it outperforms current clustering methods in sensitivity and stability; clustering is not affected by removal of samples from the control group, choice of normalization nor subselection of data. There is no user induced bias because all parameters are data-driven. Datasets can readily be combined into one analysis. TTMap reveals hitherto undetected gene expression changes in mouse mammary glands related to hormonal changes during the estrous cycle. This illustrates the ability to extract information from highly variable biological samples and its potential for personalized medicine.

q-bio.GN↗

arXiv2007

Representing perturbed dynamics in biological network models

We study the dynamics of gene activities in relatively small size biological networks (up to a few tens of nodes), e.g. the activities of cell-cycle proteins during the mitotic cell-cycle progression. Using the framework of deterministic discrete dynamical models, we characterize the dynamical modifications in response to structural perturbations in the network connectivities. In particular, we focus on how perturbations affect the set of fixed points and sizes of the basins of attraction. Our approach uses two analytical measures: the basin entropy $H$ and the perturbation size $Δ$, a quantity that reflects the distance between the set of fixed points of the perturbed network to that of the unperturbed network. Applying our approach to the yeast-cell cycle network introduced by Li \textit{et al.} provides a low dimensional and informative fingerprint of network behavior under large classes of perturbations. We identify interactions that are crucial for proper network function, and also pinpoints functionally redundant network connections. Selected perturbations exemplify the breadth of dynamical responses in this cell-cycle model.

q-bio.MN↗

arXiv2005

Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies

We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian oscillator and inspired our work. Linear stability analysis of the Fokker-Planck equation for an infinite population is amenable to exact solution and we show that the incoherent state is unstable passed a critical coupling strength $K_c(\ga, \sigf)$, where $\ga$ is the inverse characteristic drifting time and $\sigf$ the asymptotic frequency dispersion. Expectedly $K_c$ agrees with the noisy Kuramoto model in the large $\ga$ (Schmolukowski) limit but increases slower as $\ga$ decreases. Asymptotic expansion of the solution for $\ga\to 0$ shows that the noiseless Kuramoto model with Gaussian frequency distribution is recovered in that limit. Thus varying a single parameter allows to interpolate smoothly between two regimes: one dominated by the frequency dispersion and the other by phase diffusion.

q-bio.QM↗

arXiv2000

Space-Time Invariant Measures, Entropy, and Dimension for Stochastic Ginzburg-Landau Equations

We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the corresponding Markov process and we define the spatial densities of topological entropy, of measure-theoretic entropy, and of upper box-counting dimension. We prove inequalities relating these different quantities. The proof of existence of an invariant measure uses the compact embedding of some space of uniformly smooth functions into the space of locally square-integrable functions and a priori bounds on the semi-flow in these spaces. The bounds on the entropy follow from spatially localised estimates on the rate of divergence of nearby orbits and on the smoothing effect of the evolution.

math.AP↗