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-Coupling Analysis of nucleotide coevolution facilitates RNA secondary and tertiary structure prediction.

Despite the biological importance of non-coding RNA, their structural characterization remains challenging. Making use of the rapidly growing sequence databases, we analyze nucleotide coevolution across homologous sequences via Direct-Coupling Analysis to detect nucleotide-nucleotide contacts. For a representative set of riboswitches, we show that the results of Direct-Coupling Analysis in combination with a generalized Nussinov algorithm systematically improve the results of RNA secondary structure prediction beyond traditional covariance approaches based on mutual information. Even more importantly, we show that the results of Direct-Coupling Analysis are enriched in tertiary structure contacts. By integrating these predictions into molecular modeling tools, systematically improved tertiary structure predictions can be obtained, as compared to using secondary structure information alone.