Minisymposium on Stochastic Modelling and Computer-intensive Inference in Biology
Organiser: Omiros Papaspiliopoulos
Tuesday 30 June 2009
Simon Cauchemez (Imperial, firstname.lastname@example.org) Early spread of the novel Influenza A(H1N1) virus: insights from mathematical modelling
Mark Girolami (Glasgow, email@example.com) Efficiently performing bayesian inference over dynamical biochemical system models with hamiltonian monte carlo on the riemann manifold
Formally characterising uncertainty in systems of differential equations within a statistical inferential framework is something which mathematicians and statisticians have only very recently started to consider. There is great motivation within the area of Computational Systems Biology to fully define and propagate all sources of uncertainty in model-based reasoning regarding the biochemical mechanisms initiating and regulating fundamental biological processes. The Bayesian methodology provides such an inferential framework, however, whilst beautifully elegant in principle the computational statistical challenges associated with its practical instantiation are formidable. This talk presents two contributions in addressing such challenges, the first presents a statistically and computationally efficient Markov Chain Monte Carlo Sampler for systems of nonlinear differential equations by the introduction of auxiliary functional processes into the overall model. The second contribution defines a non-separable Hamiltonian defined on the Riemann manifold and an explicit time reversible symplectic integrator is developed which provides a means of performing Hybrid Monte Carlo on the manifold defined by the nonlinear dynamic system described by the system of equations. Convergence to the stationary distribution in cases of, for example, time-delayed differential equations is improved four-hundred fold, additional biochemical model examples related to Circadian control in plants will be presented.
Michael Stumpf (Imperial, firstname.lastname@example.org) An approximate Bayesian computation perspectives on learning the structure of biological signalling systems from time-course data
Joint work with Kamil Erguler, Paul Kirk, Juliane Liepe, Maria Secrier and Tina Toni
For the vast majority of biological systems we lack reliable models let alone model parameters. Using well defined simulation models and real biological data collected for a range of biological signalling systems, we explore how much can be learned about biological systems from temporally resolved transcriptomic or proteomic data. We pay particular attention to qualitative properties of the underlying dynamical system and their impact on our ability to infer the system’s dynamics. We then illustrate how approximate Bayesian computation approaches can be employed to gain insights into the inferability of model parameters, and for model selection in the context of dynamical systems in biology.
Barbel Finkelstadt (Warwick, email@example.com) (talk will be at 16:15-17:15) Inferring molecular degradation rates in single cells: An application of Bayesian hierarchical modeling to SDEs
Joint with Dan J. Woodcock, Michal Komorowski, David A. Rand. Experiments: Claire V. Harper, Julian R. E. Davies, Michael R. H. White
Understanding biological processes at the molecular level is an important aspect of studying cellular phenomena. Recent development in fluorescent microscopy technology enabled us to measure levels of reporter proteins in vivo such as green fluorescent protein (GFP) and luciferase (luc) in individual cells. The understanding of how the observed fluorescence level relates to the dynamics of gene expression is facilitated by the knowledge of mRNA and reporter protein degradation rates. Provided with replicate single cell protein data we present a modeling approach together with a statistical methodology that overcomes many of the current problems in the estimation of the degradation rates. We formulate a suitable SDE model that has both the protein and the mRNA degradation rates as parameters. These can be inferred sequentially from the reporter protein data from two types of experiments where either transcription or translation is inhibited. The corresponding inference algorithm is challenging as we are confronted with a two-dimensional SDE system where one of the variables (mRNA abundance) is unobserved and the second variable (protein abundance) is measured discretely in time with measurement error. In order to quantify the extrinsic noise due to variation of the degradation between cells this model is extended towards a Bayesian hierarchical model.