Hybrid stochastic simplifications for multiscale gene networks

<p>Abstract</p> <p>Background</p> <p>Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models.</p> <p>Results</p> <p>We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion <abbrgrp><abbr bid="B1">1</abbr><abbr bid="B2">2</abbr><abbr bid="B3">3</abbr></abbrgrp> which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples.</p> <p>Conclusion</p> <p>Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.</p

Convergence of stochastic gene networks to hybrid piecewise deterministic processes

We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system we distinguish four types of limits: continuous piecewise deterministic processes (PDP) with switching, PDP with jumps in the continuous variables, averaged PDP, and PDP with singular switching. We justify rigorously the convergence for the four types of limits. The convergence results can be used to simplify the stochastic dynamics of gene network models arising in molecular biology

Aspectele clinico-radiologice, microbiologice şi efi cacitatea tratamentului la pacienţi cu tuberculoza pulmonară diagnosticaţi prin Xpert MTB/RIF.

Xpert MTB/Rif este un test nou molecular pentru diagnosticarea precoce а tuberculozei și aprecierea rezistenței la unul din cele mai importante preparate antituberculoase - rifampicină. Scopul studiului a fost aprecierea aspectelor clinicoradiologice, microbiologice şi efi cacităţii tratamentului la pacienţi cu tuberculoză pulmonară diagnosticaţi prin Xpert MTB/Rif. A fost studiat un lot de 310 pacienţi cu tuberculoză pulmonară tratați la Spitalul clinic municipal de tuberculoză în 2014. Bolnavii au fost distribuiți în 2 eşantioane: eşantion I – 123 bolnavii cu rezultatul pozitiv Xpert MTB/Rif, sensibil la rifampicină şi eşantion II – 187 bolnavi cu Xpert MTB/Rif negativ. Sputa microscopic pozitivă a fost determinată în 72 (58,5%) cazuri în eşantionul I şi numai la 9 (4,8%) bolnavi - în eşantionul II,

Multi-dimensional computational pipeline for large-scale deep screening of compound effect assessment: an in silico case study on ageing-related compounds

Designing alternative approaches to efficiently screen chemicals on the efficacy landscape is a challenging yet indispensable task in the current compound profiling methods. Particularly, increasing regulatory restrictions underscore the need to develop advanced computational pipelines for efficacy assessment of chemical compounds as alternative means to reduce and/or replace in vivo experiments. Here, we present an innovative computational pipeline for large-scale assessment of chemical compounds by analysing and clustering chemical compounds on the basis of multiple dimensions—structural similarity, binding profiles and their network effects across pathways and molecular interaction maps—to generate testable hypotheses on the pharmacological landscapes as well as identify potential mechanisms of efficacy on phenomenological processes. Further, we elucidate the application of the pipeline on a screen of anti-ageing-related compounds to cluster the candidates based on their structure, docking profile and network effects on fundamental metabolic/molecular pathways associated with the cell vitality, highlighting emergent insights on compounds activities based on the multi-dimensional deep screen pipeline

Approximations hybrides de processus de Markov à sauts multi-échelles : applications aux modèles de réseaux de gènes en biologie moléculaire

The main goal of this thesis was to develop new mathematical tools for the study of the stochastic phenomena in molecular biology. The mathematical models used to describe the stochastic behaviour of a system of biochemical reactions are based on Markov jumps processes. We propose hybrid approximations for multi-scale Markov jumps processes. These approximations are obtained by partial Kramers-Moyal expansion which is equivalent to the application of the central limit theorem to a sub-model. Thus, different approximations are obtained: piecewise deterministic processes and hybrid diffusions. These processes are simulated with suitable numerical algorithms. Furthermore, we show the weak convergence of Markov jump processes to piecewise deterministic processes with or without jumps in the continuous variables. The hybrid approximations can be simplified even more by averaging. We propose some results for this type of reduction of the process.L'objectif principal de cette thèse a été de développer des nouveaux outils mathématiques pour l'étude des phénomènes stochastiques en biologique moléculaire. Les modèles mathématiques pour la dynamique stochastique des réseaux de réactions biochimiques sont basés sur les processus de Markov à sauts. On propose des approximations hybrides pour les processus de Markov à sauts multi-échelles. En utilisant comme argument heuristique un développement limité du générateur du processus à sauts (procédé connu en chimie et en physique sous le nom de développement de Kramers-Moyal) nous identifions plusieurs types d'asymptotiques hybrides : processus déterministes par morceaux et diffusions hybrides. Le développement de Kramers-Moyal permet d'obtenir de manière systématique des modèles hybrides, qui sont simulés par la suite avec des algorithmes adaptés. Les approximations déterministes par morceaux sont étudiées avec des méthodes mathématiques rigoureuses. On montre la convergence faible du processus de Markov à sauts vers deux types de processus déterministes par morceaux : avec et sans sauts dans les variables continues. Les approximations hybrides peuvent être simplifiées davantage en utilisant des méthodes de moyennisation. On propose aussi quelques résultats dans cette direction

Hybrid polarizable simulations of a conventional hydrophobic polyelectrolyte. Toward a theoretical tool for green science innovation

International audienceHybrid modeling approaches based on all-atom force fields to handle a solute and coarse grained models to account for the solvent are promising numerical tools that can be used to understand the properties of large and multi components solutions and thus to speed up the development of new industrial products that obey the standard of green and sustainable chemistry. Here w

Approximations hybrides de processus de Markov à sauts multi-échelles (applications aux modèles de réseaux de gènes en biologie moléculaire)

L'objectif principal de cette thèse a été de développer des nouveaux outils mathématiques pour l'étude des phénomènes stochastiques en biologique moléculaire. Les modèles mathématiques pour la dynamique stochastique des réseaux de réactions biochimiques sont basés sur les processus de Markov à sauts. On propose des approximations hybrides pour les processus de Markov à sauts multi-échelles. En utilisant comme argument heuristique un développement limité du générateur du processus à sauts (procédé connu en chimie et en physique sous le nom de développement de Kramers-Moyal) nous identifions plusieurs types d'asymptotiques hybrides : processus déterministes par morceaux et diffusions hybrides. Le développement de Kramers-Moyal permet d'obtenir de manière systématique des modèles hybrides, qui sont simulés par la suite avec des algorithmes adaptés. Les approximations déterministes par morceaux sont étudiées avec des méthodes mathématiques rigoureuses. On montre la convergence faible du processus de Markov à sauts vers deux types de processus déterministes par morceaux : avec et sans sauts dans les variables continues. Les approximations hybrides peuvent être simplifiées davantage en utilisant des méthodes de moyennisation. On propose aussi quelques résultats dans cette direction.The main goal of this thesis was to develop new mathematical tools for the study of the stochastic phenomena in molecular biology. The mathematical models used to describe the stochastic behaviour of a system of biochemical reactions are based on Markov jumps processes. We propose hybrid approximations for multi-scale Markov jumps processes. These approximations are obtained by partial Kramers-Moyal expansion which is equivalent to the application of the central limit theorem to a sub-model. Thus, different approximations are obtained: piecewise deterministic processes and hybrid diffusions. These processes are simulated with suitable numerical algorithms. Furthermore, we show the weak convergence of Markov jump processes to piecewise deterministic processes with or without jumps in the continuous variables. The hybrid approximations can be simplified even more by averaging. We propose some results for this type of reduction of the process.RENNES1-BU Sciences Philo (352382102) / SudocSudocFranceF