Various ways to model gene-regulatory networks exist, ranging from logical (Boolean), deterministic (ordinary differential equations) to stochastic models. The stochastic approach takes into account fluctuations due to the inherently random nature of biochemical reactions. This intrinsic noise gives rise to significant effects when either the molecular abundances of protein or mRNA molecules are small or the kinetics of the transitions between chemical states are slow. The disadvantage of detailed stochastic modelling is its computational intensity; this is due to the relatively large number of chemical species (tens or hundreds) in currently modelled biochemical pathways.
Since biochemical reactions occur over different time scales, the temporal evolution of the network can often be described by a smaller number of variables. We investigate the application of computational data mining techniques (in particular, spectral graph theory, diffusion maps and the resulting low-dimensional description of high-dimensional data) to gene regulatory network models to find suitable low-dimensional descriptions. Knowledge of good observables is vital to the creation of effective reduced models of complex gene regulatory networks. Having found such observables (either from experimental evidence or by computational data mining), we develop methods for analysis of gene regulatory network models.
We also study the reverse engineering of gene regulatory networks. Having the experimental gene expression data, we look for the unknown topology (wiring) of the gene regulatory network (for example using Shannon's entropy, theory of finite fields, or Bayesian networks). In particular, we investigate the connections between Boolean, algebraic, deterministic and stochastic approaches to modelling of gene regulation.
Please contact Professor Radek Erban for more details.
Key references in this area
- R. Erban, S. J. Chapman, I. Kevrekidis and T. Vejchodsky (2009). Analysis of a stochastic chemical system close to a SNIPER bifurcation of its mean-field model. SIAM J. Appl. Math. 70:984-1016. (eprints)