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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… (More)

- Manu, Svetlana Surkova, +8 authors John Reinitz
- PLoS biology
- 2009

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation… (More)

- Manu, Svetlana Surkova, +8 authors John Reinitz
- PLoS Computational Biology
- 2009

The variation in the expression patterns of the gap genes in the blastoderm of the fruit fly Drosophila melanogaster reduces over time as a result of cross regulation between these genes, a fact that we have demonstrated in an accompanying article in PLoS Biology (see Manu et al., doi:10.1371/journal.pbio.1000049). This biologically essential process is an… (More)

- Ovidiu Radulescu, Alexander N. Gorban, Andrei Yu. Zinovyev, Alain Lilienbaum
- BMC Systems Biology
- 2008

Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In… (More)

- Ovidiu Radulescu
- 2007

The concept of limiting step gives the limit simplification: the whole network behaves as a single step. This is the most popular approach for model simplification in chemical kinetics. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles the nonstationary behaviour is also… (More)

- Alina Crudu, Arnaud Debussche, Ovidiu Radulescu
- BMC Systems Biology
- 2009

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… (More)

- Ovidiu Radulescu
- 2007

The concept of limiting step gives the limit simplification: the whole network behaves as a single step. This is the most popular approach for model simplification in chemical kinetics. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles the nonstationary behaviour is also… (More)

- Ovidiu Radulescu, Alexander N. Gorban, A. Y. Zinovyev, Vernelle A. A. Noel
- Front. Gene.
- 2012

Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important… (More)

- Vincent Noel, Dima Grigoriev, Sergei Vakulenko, Ovidiu Radulescu
- Electr. Notes Theor. Comput. Sci.
- 2012

We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the cell cycle. We also propose a practical recipe for detecting quasi-equilibrium QE reactions and quasi-steady state QSS… (More)

– We show the existence of three well defined time scales in the dynamics of wormlike micelles after a step between two shear rates on the stress plateau. These time scales are compatible with the presence of a structured interface between bands of different viscosities and correspond to the isotropic band destabilization during the stress overshoot,… (More)