Stochastic simulation and analysis of biochemical networks

Stochastic effects in biochemical networks can affect the functioning of these systems significantly. Signaling pathways, such as calcium signal transduction, are particularly prone to random fluctuations. Thus, an important question is how this influences the information transfer in these pathways. First, a comprehensive overview and systematic classification of stochastic simulation methods is given as methodical basis for the thesis. Here, the focus is on approximate and hybrid approaches. Also, the hybrid solver in the software system Copasi is described whose implementation was part of this PhD work. Then, in most cases, the dynamic behavior of biochemical systems shows a transition from stochastic to deterministic behavior with increasing particle numbers. This transition is studied in calcium signaling as well as other test systems. It turns out that the onset of stochastic effects is very dependent on the sensitivity of the specific system quantified by its divergence. Systems with high divergence show stochastic effects even with high particle numbers and vice versa. Finally, the influence of noise on the performance of signaling pathways is investigated. Simulated and experimentally measured calcium time series are stochastically coupled to an intracellular target enzyme activation process. Then, the information transfer under different cellular conditions is estimated with the information-theoretic quantity transfer entropy. The amount of information that can be transferred increases with rising particle numbers. However, this increase is very dependent on the current dynamical mode of the system, such as spiking, bursting or irregular oscillations. The methods developed in this thesis, such as the use of the divergence as an indicator for the transition from stochastic to deterministic behavior or the stochastic coupling and information-theoretic analysis using transfer entropy, are valuable tools for the analysis of biochemical systems.