Menz, Stephan
[VerfasserIn]
;
Christof Schütte
[MitwirkendeR];
Tobias Jahnke
[MitwirkendeR]
Hybrid stochastic-deterministic approaches for simulation and analysis of biochemical reaction networks ; Hybrid stochastisch-determinstische Ansätze zur Simulation und Analyse von biochemischen Reaktionsnetzwerken
Titel:
Hybrid stochastic-deterministic approaches for simulation and analysis of biochemical reaction networks ; Hybrid stochastisch-determinstische Ansätze zur Simulation und Analyse von biochemischen Reaktionsnetzwerken
Beteiligte:
Menz, Stephan
[VerfasserIn]
Erschienen:
Freie Universität Berlin: Refubium (FU Berlin), 2013
Anmerkungen:
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Beschreibung:
Traditionally, quantitative models of reaction networks are based on classical chemical kinetics. Under the assumption of the thermodynamic limit (infinite number of molecules/volume limit), reactions are modeled as continuous, deterministic processes. It has become evident, however, that discrete fluctuations play a crucial role in cellular processes like gene expression and signal transduction, where constituents are typically present in small numbers. In this case, a modeling approach based on stochastic reaction kinetics is required, where reactions are modeled as discrete stochastic processes. The temporal evolution of the probability density function of the number of molecules is given by the chemical master equation (CME), which, however, is impractical to solve in most applications due to its high dimensionality. Instead, it is common practice to approximate an indirect solution of the CME by computing realizations of the underlying Markov jump process. A major aim is the development of such indirect approaches that enable the simulation of complex multi-scale reaction networks. This thesis deals with the promising development of hybrid methods, where fast reactions associated with large numbers of molecules are continuously and deterministically approximated, and all other reactions are modeled as discrete stochastic processes. We demonstrate the benefit of such a hybrid system description on an integrative model of the replication dynamics of the human immunodeficiency virus (HIV). Based on hybrid simulations, we are able to design and validate in silico a novel treatment strategy for HIV-infected patients that can lead to significant improvements compared to conventional treatment strategies. While current hybrid methods almost exclusively rely on indirect approximations, a novel hybrid approach is presented in this thesis that allows to solve the CME directly. Based on a multi-scale expansion, evolution equations are derived that couple a CME on a reduced state space to evolution equations of ...