Computational Systems Biology aims at the construction and analysis of predictive mathematical models for the description of complex interactions in biological and biochemical systems. Modelling approaches range from stochastic microscopic description which follow the spatial movement and biochemical interactions of individual particles, over spatially well-mixed kinetics given by Markov jump processes, to deterministic systems given by ordinary differential equations (ODEs), that describe the concentrations of substances over time, or partial differential equations for spatially resolved dynamics.

Motivated by the multi-scale nature of biological systems, we consider hybrid models that combine the different mathematical formalisms, e.g. ODEs for metabolic networks with discrete dynamical systems for regulatory processes, or spatially well-mixed kinetics connected by rare diffusive jumps between cellular subdomains. Efficient numerical algorithms and computational techniques are developed and applied in order to study the dynamical systems. Applications range from cellular signalling pathways to physiological processes on a whole-organism level, for example endocrinological networks, and also include classical reaction kinetics.

Our work is highly interdisciplinary. Therefore we are actively establishing academic and industrial collaborations with different partners to validate and to improve our models.

Topics of interest

Neurotransmission processes

Modeling, simulation and analysis of synaptic vesicle fusion dynamics

Enzyme kinetics

Investigation of effective reaction systems for pH-dependent oscillatory dynamics

Social interaction systems

Concentration effects for stochastic dynamics on networks of interacting agents

Kinematics of artificial knee implants

Parameterization as function of geometric implant design

Gene expression

Approximation by spatio-temporal master equations

Receptor clustering on membranes

Modeling by particle-based models and stochastic PDEs