Robustness Analysis of Large-Scale Stochastic Systems

Stochasticity in biomolecular networks is an important factor in understanding the fundamental mechanisms behind various physiological responses. It has been shown that stochastic effects in molecular interactions cannot be ignored in many cases, since they have major impacts on the dynamics of the networks. On the other hand, the modelling and analysis of whole biological systems will usually result in extremely large size problems. Hence, as the requirement for the mathematical modelling of biological systems becomes more realistic, we have to deal with large-scale stochastic systems, and the corresponding robustness analysis problem is more complicated and difficult. In this research, we aim to extend current robustness analysis methodologies using a novel geometrical interpretation of robustness analysis combined with a probabilistic framework so that it can be applicable for large-scale stochastic systems. While robustness analysis problems have usually been formulated using linear algebra approaches, we suggest a geometrical approach, such that the robustness analysis problem can be posed as two manifold intersections. With this geometrical condition, the robustness analysis can be performed for the cases including stochastic noises and it can be applicable for large-scale systems because the algorithm could be parallelised so that the calculations are performed on a distributed computing system. This research will facilitate our understanding of the fundamental structures and sources of robustness of biological systems, which is a key factor in improving drug development for various diseases, since it will allow us to find the weakest (fragile) structure of the system and hence to develop efficient medical therapies.