Numerical methods for high-dimensional stochastic reaction networks

Numerical methods for stochastic reaction networks are to be constructed, analyzed and applied. Such networks are described by a Markov jump process on a large and possibly high-dimensional state space. The corresponding time-dependent probability distribution is the solution of the chemical master equation (CME). For its numerical approximation, the main challenge is the curse of dimensionality: The number of degrees of freedom scales exponentially with the number of dimensions, making the application of traditional ODE methods impossible. The bimodality and metastability of many biological systems poses additional difficulties. Numerical methods for both the time-dependent and the stationary CME will be devised. The effects of metastability will be investigated by Transition Path Theory, which allows to compute the transition pathways and rates between metastates. The multi-scale nature of the problem will be exploited to derive hybrid models which reduce the huge number of degrees of freedom significantly by representing only the critical species by a CME and the majority of species by other differential equations.

DFG-Verfahren Schwerpunktprogramme

Teilprojekt zu SPP 1324:  Mathematische Methoden zur Extraktion quantifizierbarer Information aus komplexen Systemen