Genetically identical cells are experimentally proven to exhibit considerable cell-to-cell variations in mRNA and protein levels. Such variability of phenotypes is driven by both the intrinsic noise, that is characterised by gene network structure, and the extrinsic noise, which acts globally on a single cell but varies from one to another. For intrinsic noise, a large community of mathematical biologist have been developing and improving simulation techniques to investigate the stochastic network under strict parameters, and discovered interesting behaviours, like noise-induced multistability and oscillations. However, global effect of extrinsic noise raises a few more questions: how does the internal stochastic behaviour change with respect to some perturbations of biophysical parameters? how may we define, quantify and predict these changes under stochastic context? Do these changes in a single cell apply similarly to a collection of cells? If not, how to identify the role of intrinsic and extrinsic noise in generating the variations in the experimental observations?

Under deterministic context, all these questions falls into the subject of bifurcation analysis, a theory describing the dependence of the steady state on continuous changes in parameters. But stochastic modelling, by contrast, is still lagging behind concerning appropriate parametric methods. The commonly-used Monte Carlo formulation becomes inefficient in parametric analysis as it requires separate simulations for different parameter combinations. On the other hand, equation-based models, like chemical master equation and its Fokker-Planck approximation, suffers from the so-called ‘bless of dimensionality’. In my talk, I will introduce the newly-developed tensor-structured data format, and demonstrate its prospective in: a) analysis of collective behaviour of cells, b) parameter estimation of stochastic systems, and c) stochastic bifurcation analysis of complex genetic regulatory network.