Gene prioritization based on random walks with restarts and absorbing states, to define gene sets regulating drug pharmacodynamics from single-cell analyses.

Prioritizing genes for their role in drug sensitivity, is an important step in understanding drugs mechanisms of action and discovering new molecular targets for co-treatment. To formalize this problem, we consider two sets of genes X and P respectively composing the gene signature of cell sensitivity at the drug IC50 and the genes involved in its mechanism of action, as well as a protein interaction network (PPIN) containing the products of X and P as nodes. We introduce Genetrank, a method to prioritize the genes in X for their likelihood to regulate the genes in P. Genetrank uses asymmetric random walks with restarts, absorbing states, and a suitable renormalization scheme. Using novel so-called saturation indices, we show that the conjunction of absorbing states and renormalization yields an exploration of the PPIN which is much more progressive than that afforded by random walks with restarts only. Using MINT as underlying network, we apply Genetrank to a predictive gene signature of cancer cells sensitivity to tumor-necrosis-factor-related apoptosis-inducing ligand (TRAIL), performed in single-cells. Our ranking provides biological insights on drug sensitivity and a gene set considerably enriched in genes regulating TRAIL pharmacodynamics when compared to the most significant differentially expressed genes obtained from a statistical analysis framework alone. We also introduce gene expression radars, a visualization tool embedded in MA plots to assess all pairwise interactions at a glance on graphical representations of transcriptomics data. Genetrank is made available in the Structural Bioinformatics Library (https://sbl.inria.fr/doc/Genetrank-user-manual.html). It should prove useful for mining gene sets in conjunction with a signaling pathway, whenever other approaches yield relatively large sets of genes.

Modeling the Lamb mode-coupling constant of quantum well semiconductor lasers.

We theoretically compute the coupling constant C between two emission modes of an extended cavity laser with a multiple quantum-well active layer. We use an optimized Monte Carlo model based on the Markov chain that describes the elementary events of carriers and photons over time. This model allows us to evaluate the influence on C of the transition from a class A laser to a class B laser and illustrates that the best stability of dual-mode lasers is obtained with the former. In addition, an extension of the model makes it possible to evaluate the influence of different mode profiles in the cavity as well as the spatial diffusion of the carriers and/or the inhomogeneity of the temperature. These results are in very good agreement with previous experimental results, showing the independence of C with respect to the beating frequency and its evolution versus the spatial mode splitting in the gain medium.

A stochastic multicellular model identifies biological watermarks from disorders in self-organized patterns of phyllotaxis.

Exploration of developmental mechanisms classically relies on analysis of pattern regularities. Whether disorders induced by biological noise may carry information on building principles of developmental systems is an important debated question. Here, we addressed theoretically this question using phyllotaxis, the geometric arrangement of plant aerial organs, as a model system. Phyllotaxis arises from reiterative organogenesis driven by lateral inhibitions at the shoot apex. Motivated by recurrent observations of disorders in phyllotaxis patterns, we revisited in depth the classical deterministic view of phyllotaxis. We developed a stochastic model of primordia initiation at the shoot apex, integrating locality and stochasticity in the patterning system. This stochastic model recapitulates phyllotactic patterns, both regular and irregular, and makes quantitative predictions on the nature of disorders arising from noise. We further show that disorders in phyllotaxis instruct us on the parameters governing phyllotaxis dynamics, thus that disorders can reveal biological watermarks of developmental systems.

A model-based approach for detecting coevolving positions in a molecule.

We present a new method for detecting coevolving sites in molecules. The method relies on a set of aligned sequences (nucleic acid or protein) and uses Markov models of evolution to map the substitutions that occurred at each site onto the branches of the underlying phylogenetic tree. This mapping takes into account the uncertainty over ancestral states and among-site rate variation. We then build, for each site, a "substitution vector" containing the posterior estimates of the number of substitutions in each branch. The amount of coevolution for a pair of sites is then measured as the Pearson correlation coefficient between the two corresponding substitution vectors and compared to the expectation under the null hypothesis of independence. We applied the method to a 79-species bacterial ribosomal RNA data set, for which extensive structural characterization has been done over the last 30 years. More than 95% of the intramolecular predicted pairs of sites correspond to known interacting site pairs.

The combinatorics of tandem duplication trees.

We developed a recurrence relation that counts the number of tandem duplication trees (either rooted or unrooted) that are consistent with a set of n tandemly repeated sequences generated under the standard unequal recombination (or crossover) model of tandem duplications. The number of rooted duplication trees is exactly twice the number of unrooted trees, which means that on average only two positions for a root on a duplication tree are possible. Using the recurrence, we tabulated these numbers for small values of n. We also developed an asymptotic formula that for large n provides estimates for these numbers. These numbers give a priori probabilities for phylogenies of the repeated sequences to be duplication trees. This work extends earlier studies where exhaustive counts of the numbers for small n were obtained. One application showed the significance of finding that most maximum-parsimony trees constructed from repeat sequences from human immunoglobins and T-cell receptors were tandem duplication trees. Those findings provided strong support to the proposed mechanisms of tandem gene duplication. The recurrence relation also suggests efficient algorithms to recognize duplication trees and to generate random duplication trees for simulation. We present a linear-time recognition algorithm.