Understanding the Dynamics of Intracellu

The aim of the research is to improve understanding of how biological cells respond to changes in their environment. Scientists refer to these changes as ‘signals‘ received by the cells. Often the response involves fluctuations in the calcium level inside the cell and the turning on or off of some of the cell‘s genes. When these processes over- or under-react, health problems often occur such as neurodegeneration and many cancers. However, the detailed workings of these cell signalling mechanisms are often not well understood, even in healthy cells. By using experiments on such cells in which signals are turned on artificially and large amounts of data recording the subsequent changes inside the cells are collected, scientists can develop mathematical models that describe and predict cellular responses. These responses usually involve networks of many interacting molecules and so finding good models is challenging science. The understanding gained can be used in future to illuminate the causes of disease and to design treatments. The scientists involved will be an interdisciplinary team at the University of Cambridge made up of several mathematical statisticians, a pharmacologist and a developmental biologist. The team will be coordinated by Dr Clive Bowsher of the Statistical Laboratory.

Understanding the Dynamics of Intracellular Responses to Signalling: Inference Using Stochastic Continuous Time Models

Abstract Stochastic continuous-time kinetic theory (SCKT) processes will be used to model the intracellular dynamics of signal transduction. The objective is to develop new, broadly applicable stochastic dynamic models and inference methods for signalling and gene regulatory networks. These will be applied to elucidate two signal transduction mechanisms of fundamental biological and medical importance - Ca2+ signalling and the modulation of gene expression by receptor activation. Both require the development of methods of statistical inference for highly multivariate, continuous time Markov processes observed discretely and with measurement error. Bayesian methods of inference will be used to identify the resultant ‘signal plus noise‘ models and these will be evaluated in terms of their probabilistic predictions. Experimental interventions will be designed and performed to assess the validity of the models‘ causal content.

Novel SCKT models of IP3 receptor (IP3R) interaction, ligand binding and gating will be developed using extremely high resolution patch clamp and TIRFM time series data. The dependent gating of IP3Rs in IP3-induced clusters will be studied using new methods. An important contribution will be the development of methods for analysis of TIRFM records of the simultaneous gating behaviour of many, spatially-mapped ion channels. Combining the stochastic models of IP3R function developed with processes for the diffusion of Ca2+ in the cytosol will provide the first detailed, data-derived models describing clustering, Ca2+ release by and coupling of IP3Rs. These will greatly improve understanding of the mechanisms underlying the spatio-temporal characteristics of Ca2+ signals and hence their downstream effects.

Notch receptor activation results directly in effects on gene expression and hence is ideal for studying this aspect of signal transduction. The objective is to develop effective methods for inferring the structure of gene networks from non-steady state time series data of expression levels subsequent to receptor activation. In original work, I will use stochastic differential equations based on the intracellular SCKT process to model the transition density for the latent biochemical state, thus accommodating irregularly-spaced observations and comparisons across experiments, and avoiding spurious connectivity due to temporal aggregation. The approach will employ sparsity priors having a ‘point-mass at zero mixture‘ form, thus addressing dimension reduction and scalability of the approach. In order to investigate variability and heterogeneity between cells, expression levels in individual cells will be measured using reverse transcriptase PCR methods, resulting in a ‘pseudo-time series‘ data structure. The identification of intracellular SCKT model parameters using such data will be explored.