Stochastic modelling of biological systems has become a very important research field in bioinformatics in recent years. Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. It is not appropriate to use deterministic models such as ordinary differential equations to describe the dynamics of the systems with small molecular numbers. Instead of studying the variation of concentrations in deterministic models based on the population of a large number of cells, stochastic models concentrate on the system dynamics in each cell by tracking the molecular number of each species.
One of the major challenges in stochastic modelling is the huge computing time of stochastic simulation. The stochastic simulation algorithm (SSA) is an essentially exact procedure for studying noise in biochemical reaction systems. This method takes time steps of variable length by taking proper account of the randomness inherent in such a system. However, the bottleneck in the application of the SSA is the huge computing time because of the possibility of having very small step sizes.
Dr Tianhai Tian and his colleages at ACMC at UQ have used UQ HPC supercomputers as an effective tool to reduce the huge computing time of stochastic simulation. For the system of the mitogen-activated protein (MAP) kinase cascade activated by epidermal growth factor (EGF), they have developed a stochastic model with 94 compounds (variables) and 224 reactions from a well-studied ordinary differential equation model. They have also studied different implementations by using OpenMP and MPI based on parallelism across the simulation and parallelism across the method. Their research gave the first reported simulation result for the stochastic properties of the MAP kinase pathway. The molecular numbers of the protein complexes differ from very small number of the internalized dimmer of the ligand-occupied receptors (EGF-EGFRi)2 to very large number of ppERR, the activated form of ERK that is dually phosphorylated. Stochastic properties of certain signal proteins may have profound impact on the study of the inhibitors for the anticancer therapies when the activities of the signal input such as EGF are low.
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| Figure 1: The MAP kinase cascade activated by surface and internalized EGF receptors |
Dr Tian and his colleagues have also used the UQ HPC supercomputing facilities for simulating other complex biological systems including genetic regulatory networks and cell signal transduction pathways. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale cellular processes.
Contact
Dr. Tianhai TianACMC, University of Queensland