Barbel Finkenstadt
A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. Here we present an overview of the modeling approaches based on stochastic population dynamic models and their approximations. For an application on the mesoscopic scale, we present a two dimensional continuous-time Bayesian hierarchical diffusion model which has the potential to address the different sources of variability that are relevant to the stochastic modelling of transcriptional and translational processes at the molecular level, namely, intrinsic noise due to the stochastic nature of the birth and deaths processes involved in chemical reactions, extrinsic noise arising from the cell-to-cell variation of kinetic parameters associated with these processes and noise associated with the measurement process. Inference is complicated by the fact that only the protein and rarely other molecular species are observed which is typically entailing problems of parameter identification in dynamical systems.
For an application on the macroscopic scale, we introduce a mechanistic 'switch' model for encoding a continuous transcriptional profile of genes over time with the aim of identifying the timing properties of mRNA synthesis which is assumed to switch between periods of transcriptional activity and inactivity, each time leading to the transition of a new steady state, while mRNA degradation is an ongoing linear process. The model is rich enough to capture a wide variety of expression behaviours including periodic genes. Finally, I will also give a brief introduction to some recent work on inferring the periodicity of the expression of circadian and other oscillating genes.
Joint work with: Maria Costa, Dan Woodcock, Dafyd Jenkins, David Rand (all Warwick Systems Biology), Michal Komorowski (Imperial College London).
Barbel Finkenstadt
Time series relating to gene expression are now routinely measured in various important biological experiments such as microarrays, nanostring, etc as well as experiments based on bioluminescent imaging. One of the most important aim is to gain an understanding of the transcriptional regulation of genes, i.e. what determines their activation. A natural model is to assume that gene activation is a constant rate birth process but that the rate may change to different levels at unknown time points leading to the piecewise linear “switch� model. Statistical inference for such a model poses interesting and challenging problems, in particular since experiments can only measure events downstream whereas the processes of interest remain unobserved. We will give an overview of our experience with fitting such switch models to real data where, depending on the type of experiment, our assumptions range from stochastic differential equations to the use of ordinary differential equations, along with realistic stochastic formulations of the measurement processes. We will also present further results on extending this nonlinear approach to the multivariate case of identifying networks of interacting genes. Here we find that the concept of “thresholding� constitutes a simple yet realistic and very effective modelling device to help identifying network connections. Joint work with Dafyd Jenkins, Kirsty Hey, George Minas and David Rand.
