07 Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/8

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    SiCaSMA : an alternative stochastic description via concatenation of Markov processes for a class of catalytic systems
    (2021) Wagner, Vincent; Radde, Nicole Erika
    The Chemical Master Equation is a standard approach to model biochemical reaction networks. It consists of a system of linear differential equations, in which each state corresponds to a possible configuration of the reaction system, and the solution describes a time-dependent probability distribution over all configurations. The Stochastic Simulation Algorithm (SSA) is a method to simulate sample paths from this stochastic process. Both approaches are only applicable for small systems, characterized by few reactions and small numbers of molecules. For larger systems, the CME is computationally intractable due to a large number of possible configurations, and the SSA suffers from large reaction propensities. In our study, we focus on catalytic reaction systems, in which substrates are converted by catalytic molecules. We present an alternative description of these systems, called SiCaSMA, in which the full system is subdivided into smaller subsystems with one catalyst molecule each. These single catalyst subsystems can be analyzed individually, and their solutions are concatenated to give the solution of the full system. We show the validity of our approach by applying it to two test-bed reaction systems, a reversible switch of a molecule and methyltransferase-mediated DNA methylation.
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    Efficient parametric analysis of the chemical master equation through model order reduction
    (2012) Waldherr, Steffen; Haasdonk, Bernard
    BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.RESULTS:In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.
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    Probabilistic modelling of population variability
    (2025) Wagner, Vincent; Radde, Nicole (Prof. Dr. rer. nat.)
    Vincent Wagner's dissertation summarises progress in the probabilistic modelling of population variability. It comprises two chapters with complementary approaches to this challenging and broad topic. The first chapter deals with the Method of Moments for the Chemical Master Equation, while the second chapter uses random variable transformations to estimate distributed simulation model parameters.