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http://hdl.handle.net/10985/11391
Chemical Master Equation Empirical Moment Closure
MAGNIN, Morgan; ROUX, Olivier; CUETO, Elias; AMMAR, Amine; CHINESTA SORIA, Francisco
The numerical solution of the Chemical Master Equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task due to its complexity, exponentially growing with the number of species involved. When considering separated representations of the probability distribution function within the Proper Generalized Decomposition-PGD-frame-work the complexity of the CME grows only linearly with the number of state space dimensions. In order to speed up calculations moment-based descriptions are usually preferred, however these descriptions involve the necessity of using closure relations whose impact on the calculated solution is most of time unpredictable. In this work we propose an empirical closure, fitted from the solution of the chemical master equation, the last solved within the PGD framework.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/113912016-01-01T00:00:00ZMAGNIN, MorganROUX, OlivierCUETO, EliasAMMAR, AmineCHINESTA SORIA, FranciscoThe numerical solution of the Chemical Master Equation (CME) governing gene regulatory networks and cell signaling processes remains a challenging task due to its complexity, exponentially growing with the number of species involved. When considering separated representations of the probability distribution function within the Proper Generalized Decomposition-PGD-frame-work the complexity of the CME grows only linearly with the number of state space dimensions. In order to speed up calculations moment-based descriptions are usually preferred, however these descriptions involve the necessity of using closure relations whose impact on the calculated solution is most of time unpredictable. In this work we propose an empirical closure, fitted from the solution of the chemical master equation, the last solved within the PGD framework.Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions
http://hdl.handle.net/10985/9964
Kinetic Theory Modeling and Efficient Numerical Simulation of Gene Regulatory Networks Based on Qualitative Descriptions
MAGNIN, Morgan; ROUX, Olivier; CUETO, Elias; AMMAR, Amine; CHINESTA SORIA, Francisco
In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/99642015-01-01T00:00:00ZMAGNIN, MorganROUX, OlivierCUETO, EliasAMMAR, AmineCHINESTA SORIA, FranciscoIn this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.Linking Discrete and Stochastic Models: The Chemical Master Equation as a Bridge between Process Hitting and Proper Generalized Decomposition
http://hdl.handle.net/10985/10259
Linking Discrete and Stochastic Models: The Chemical Master Equation as a Bridge between Process Hitting and Proper Generalized Decomposition
CHACELLOR, Courtney; MAGNIN, Morgan; ROUX, Olivier; AMMAR, Amine; CHINESTA SORIA, Francisco
Modeling frameworks bring structure and analysis tools to large and non-intuitive systems but come with certain inherent assumptions and limitations, sometimes to an inhibitive extent. By building bridges in existing models, we can exploit the advantages of each, widening the range of analysis possible for larger, more detailed models of gene regulatory networks. In this paper, we create just such a link between Process Hitting [6,7,8], a recently introduced discrete framework, and the Chemical Master Equation in such a way that allows the application of powerful numerical techniques, namely Proper Generalized Decomposition [1,2,3], to overcome the curse of dimensionality. With these tools in hand, one can exploit the formal analysis of discrete models without sacrificing the ability to obtain a full space state solution, widening the scope of analysis and interpretation possible. As a demonstration of the utility of this methodology, we have applied it here to the p53-mdm2 network [4,5], a widely studied biological regulatory network.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/102592013-01-01T00:00:00ZCHACELLOR, CourtneyMAGNIN, MorganROUX, OlivierAMMAR, AmineCHINESTA SORIA, FranciscoModeling frameworks bring structure and analysis tools to large and non-intuitive systems but come with certain inherent assumptions and limitations, sometimes to an inhibitive extent. By building bridges in existing models, we can exploit the advantages of each, widening the range of analysis possible for larger, more detailed models of gene regulatory networks. In this paper, we create just such a link between Process Hitting [6,7,8], a recently introduced discrete framework, and the Chemical Master Equation in such a way that allows the application of powerful numerical techniques, namely Proper Generalized Decomposition [1,2,3], to overcome the curse of dimensionality. With these tools in hand, one can exploit the formal analysis of discrete models without sacrificing the ability to obtain a full space state solution, widening the scope of analysis and interpretation possible. As a demonstration of the utility of this methodology, we have applied it here to the p53-mdm2 network [4,5], a widely studied biological regulatory network.