Analysis of Markovian Models

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Dr. Verena Wolf

Markov processes are an omnipresent modeling approach in the applied sciences. In systems biology they are used to describe noisy cellular processes, that is, processes where the discreteness and randomness of molecular interactions significantly influences the systems behavior. The main focus of the ALMA group is on Markov models of noisy biochemical reaction networks, which pose great computational challenges. Besides the development of approximate analysis and inference techniques, we investigate stochastic phenomena such as multistability and oscillatory behavior.

Our projects

We develop numerical approximation algorithms for transient and steady-state analysis of the stochastic dynamics of chemical reaction networks. These algorithms form the basis for the calibration of mathematical models using time-series data obtained from recent experimental imaging techniques such as high-resolution fluorescence microscopy. In order to cope with the enormous complexity of the underlying state space of the models, we employ stochastic hybrid approaches that perform a partial fluid approximation. We also represent genetic switches by stochastic hybrid models in order to determine the location of different modes and in order to calculate switching probabilities.