Inference of compressed Potts graphical models.

We consider the problem of inferring a graphical Potts model on a population of variables. This inverse Potts problem generally involves the inference of a large number of parameters, often larger than the number of available data, and, hence, requires the introduction of regularization. We study here a double regularization scheme, in which the number of Potts states (colors) available to each variable is reduced and interaction networks are made sparse. To achieve the color compression, only Potts states with large empirical frequency (exceeding some threshold) are explicitly modeled on each site, while the others are grouped into a single state. We benchmark the performances of this mixed regularization approach, with two inference algorithms, adaptive cluster expansion (ACE) and pseudolikelihood maximization (PLM), on synthetic data obtained by sampling disordered Potts models on Erdos-Rényi random graphs. We show in particular that color compression does not affect the quality of reconstruction of the parameters corresponding to high-frequency symbols, while drastically reducing the number of the other parameters and thus the computational time. Our procedure is also applied to multisequence alignments of protein families, with similar results.

Direct coevolutionary couplings reflect biophysical residue interactions in proteins.

Coevolution of residues in contact imposes strong statistical constraints on the sequence variability between homologous proteins. Direct-Coupling Analysis (DCA), a global statistical inference method, successfully models this variability across homologous protein families to infer structural information about proteins. For each residue pair, DCA infers 21 × 21 matrices describing the coevolutionary coupling for each pair of amino acids (or gaps). To achieve the residue-residue contact prediction, these matrices are mapped onto simple scalar parameters; the full information they contain gets lost. Here, we perform a detailed spectral analysis of the coupling matrices resulting from 70 protein families, to show that they contain quantitative information about the physico-chemical properties of amino-acid interactions. Results for protein families are corroborated by the analysis of synthetic data from lattice-protein models, which emphasizes the critical effect of sampling quality and regularization on the biochemical features of the statistical coupling matrices.

Interplay of migratory and division forces as a generic mechanism for stem cell patterns.

In many adult tissues, stem cells and differentiated cells are not homogeneously distributed: stem cells are arranged in periodic "niches," and differentiated cells are constantly produced and migrate out of these niches. In this article, we provide a general theoretical framework to study mixtures of dividing and actively migrating particles, which we apply to biological tissues. We show in particular that the interplay between the stresses arising from active cell migration and stem cell division give rise to robust stem cell patterns. The instability of the tissue leads to spatial patterns which are either steady or oscillating in time. The wavelength of the instability has an order of magnitude consistent with the biological observations. We also discuss the implications of these results for future in vitro and in vivo experiments.