Properties of Random Complex Chemical Reaction Networks and Their Relevance to Biological Toy Models

We investigate the properties of large random conservative chemical reaction networks composed of elementary reactions endowed with either mass-action or saturating kinetics, assigning kinetic parameters in a thermodynamically-consistent manner. We find that such complex networks exhibit qualitatively similar behavior when fed with external nutrient flux. The nutrient is preferentially transformed into one specific chemical that is an intrinsic property of the network. We propose a self-consistent proto-cell toy model in which the preferentially synthesized chemical is a precursor for the cell membrane, and show that such proto-cells can exhibit sustainable homeostatic growth when fed with any nutrient diffusing through the membrane, provided that nutrient is metabolized at a sufficient rate

Modeling and predicting all-α transmembrane proteins including helix–helix pairing

AbstractModeling and predicting the structure of proteins is one of the most important challenges of computational biology. Exact physical models are too complex to provide feasible prediction tools and other ab initio methods only use local and probabilistic information to fold a given sequence. We show in this paper that all-α transmembrane protein secondary and super-secondary structures can be modeled with a multi-tape S-attributed grammar. An efficient structure prediction algorithm using both local and global constraints is designed and evaluated. Comparison with existing methods shows that the prediction rates as well as the definition level are sensibly increased. Furthermore this approach can be generalized to more complex proteins

Conception d’une œuvre d’art : la statue du Bicentenaire

Les actions du bicentenaire ont permis à l’École d’enrichir son patrimoine d’oeuvres d’art. Il est probable que la réhabilitation par le général Chavannat de la toile du Centenaire, maintenant installée dans le salon d’honneur, a servi d’exemple et a pu militer en faveur de réalisations du même type. Le mécénat artistique étant devenu partie intégrante de la politique de communication des grands groupes industriels et des régions, il était assez naturel que le comité d’organisation du bicente..

Conception d’une œuvre d’art : la statue du Bicentenaire

Les actions du bicentenaire ont permis à l’École d’enrichir son patrimoine d’oeuvres d’art. Il est probable que la réhabilitation par le général Chavannat de la toile du Centenaire, maintenant installée dans le salon d’honneur, a servi d’exemple et a pu militer en faveur de réalisations du même type. Le mécénat artistique étant devenu partie intégrante de la politique de communication des grands groupes industriels et des régions, il était assez naturel que le comité d’organisation du bicente..

Expected distance between terminal nucleotides of RNA secondary structures.

International audienceIn "The ends of a large RNA molecule are necessarily close", Yoffe et al. (Nucleic Acids Res 39(1):292-299, 2011) used the programs RNAfold [resp. RNAsubopt] from Vienna RNA Package to calculate the distance between 5' and 3' ends of the minimum free energy secondary structure [resp. thermal equilibrium structures] of viral and random RNA sequences. Here, the 5'-3' distance is defined to be the length of the shortest path from 5' node to 3' node in the undirected graph, whose edge set consists of edges {i, i + 1} corresponding to covalent backbone bonds and of edges {i, j} corresponding to canonical base pairs. From repeated simulations and using a heuristic theoretical argument, Yoffe et al. conclude that the 5'-3' distance is less than a fixed constant, independent of RNA sequence length. In this paper, we provide a rigorous, mathematical framework to study the expected distance from 5' to 3' ends of an RNA sequence. We present recurrence relations that precisely define the expected distance from 5' to 3' ends of an RNA sequence, both for the Turner nearest neighbor energy model, as well as for a simple homopolymer model first defined by Stein and Waterman. We implement dynamic programming algorithms to compute (rather than approximate by repeated application of Vienna RNA Package) the expected distance between 5' and 3' ends of a given RNA sequence, with respect to the Turner energy model. Using methods of analytical combinatorics, that depend on complex analysis, we prove that the asymptotic expected 5'-3' distance of length n homopolymers is approximately equal to the constant 5.47211, while the asymptotic distance is 6.771096 if hairpins have a minimum of 3 unpaired bases and the probability that any two positions can form a base pair is 1/4. Finally, we analyze the 5'-3' distance for secondary structures from the STRAND database, and conclude that the 5'-3' distance is correlated with RNA sequence length

Counting RNA pseudoknotted structures

International audienceIn 2004, Condon and coauthors gave a hierarchical classification of exact RNA structure prediction algorithms according to the generality of structure classes that they handle. We complete this classification by adding two recent prediction algo- rithms. More importantly, we precisely quantify the hierarchy by giving closed or asymptotic formulas for the theoretical number of structures of given size n in all the classes but one. This allows to assess the tradeoff between the expressiveness and the computational complexity of RNA structure prediction algorithms

Necessary and sufficient conditions for protocell growth

International audienceWe consider a generic protocell model consisting of any conservative chemical reaction network embedded within a membrane. The membrane results from the self-assembly of a membrane precursor and is semi-permeable to some nutrients. Nutrients are metabolized into all other species including the membrane precursor, and the membrane grows in area and the protocell in volume. Faithful replication through cell growth and division requires a doubling of both cell volume and surface area every division time (thus leading to a periodic surface area-to-volume ratio) and also requires periodic concentrations of the cell constituents. Building upon these basic considerations, we prove necessary and sufficient conditions pertaining to the chemical reaction network for such a regime to be met. A simple necessary condition is that every moiety must be fed. A stronger necessary condition implies that every siphon must be either fed, or connected to species outside the siphon through a pass reaction capable of transferring net positive mass into the siphon. And in the case of nutrient uptake through passive diffusion and of constant surface area-to-volume ratio, a sufficient condition for the existence of a fixed point is that every siphon be fed. These necessary and sufficient conditions hold for any chemical reaction kinetics, membrane parameters or nutrient flux diffusion constants

transFold: a web server for predicting the structure and residue contacts of transmembrane beta-barrels

Transmembrane β-barrel (TMB) proteins are embedded in the outer membrane of Gram-negative bacteria, mitochondria and chloroplasts. The cellular location and functional diversity of β-barrel outer membrane proteins makes them an important protein class. At the present time, very few non-homologous TMB structures have been determined by X-ray diffraction because of the experimental difficulty encountered in crystallizing transmembrane (TM) proteins. The transFold web server uses pairwise inter-strand residue statistical potentials derived from globular (non-outer-membrane) proteins to predict the supersecondary structure of TMB. Unlike all previous approaches, transFold does not use machine learning methods such as hidden Markov models or neural networks; instead, transFold employs multi-tape S-attribute grammars to describe all potential conformations, and then applies dynamic programming to determine the global minimum energy supersecondary structure. The transFold web server not only predicts secondary structure and TMB topology, but is the only method which additionally predicts the side-chain orientation of transmembrane β-strand residues, inter-strand residue contacts and TM β-strand inclination with respect to the membrane. The program transFold currently outperforms all other methods for accuracy of β-barrel structure prediction. Available at

A complexity calculus for recursive tree algorithms

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