1. INI Cambridge, June 24 th 2008 Data, models & computation for stochastic dynamic cellular networks in systems biology Mike West Department of Statistical Science Duke University

2. INI Cambridge, June 24 th 2008 Much intra-cellular behaviour (including gene expression) is intrinsically stochastic Cellular systems cannot be properly understood (hence predicted and controlled) unless appropriate stochastic components are incorporated into dynamic cellular network models Single cell studies - dynamic data

3. INI Cambridge, June 24 th 2008 Feed-Forward Positive Feedback Mammalian Rb/E2f pathway: Synthetic bacterial gene circuits “emulate” gene networks key to mammalian cell proliferation (and cancer) c.f. Studies on mammalian cells Stochastic models: States=RNA levels over time Data - movies: multiple genes over time Fit, assess, refine models: - evaluate cell-specific stochasticity - multiple cancer cell lines - predict network responses to interventions Mammalian cell development & fate network (Cancer Systems Biology)

4. INI Cambridge, June 24 th 2008 Synthetic circuit Partial data over time on elements of y t T7

5. INI Cambridge, June 24 th 2008 Aspects of inference & computation Many (#cells): stochastic cell-specific effects, experimental noise Parameters (rate constants) Unobserved (latent) time series of (1,2,..) RNAs Fine time scale model: crude time scale data Imputation of uncertain state variables Model fitting, assessment, comparison Simulation-based Bayesian analysis: parameters and latent states Markov chain Monte Carlo methods for dynamic, non-linear systems Integration of time course, single cell data with “marginal” data from flow cytometry - “snapshots in time on 10 5 + cells

6. INI Cambridge, June 24 th 2008 Stochastic imputation of latent processes HMM: Forward filtering backward sampling (FFBS) Latent “missing” states imputed Latent process t t+1t+k xtxt x t+k-1 x t+k ytyt y t+k x t+1 Filtering: Sampling :

7. INI Cambridge, June 24 th 2008 Mixture modelling Metropolis MCMC mixture

8. INI Cambridge, June 24 th 2008 Mixture modelling Metropolis MCMC mixture

9. INI Cambridge, June 24 th 2008 Information content: prior posterior Imputed trajectories + data Posterior for parameters

10. INI Cambridge, June 24 th 2008 Data extraction: single cell dynamic imaging Cell lineage reconstruction Novel hybrid-image-based segmentation algorithms & neighborhood-based cell tracking Open source software E-coli Budding yeast Mammalian cells

11. INI Cambridge, June 24 th 2008 People, papers, software etc www.stat.duke.edu/~mw Jarad Niemi Quanli Wang Statistical Science Lingchong You Chee-Meng Tan Bioengineering NSF-NIH Duke (NCI) Systems Cancer Biology Center NIH Duke (NIH) Systems Biology Center

12. INI Cambridge, June 24 th 2008 Stochastic imputation of latent processes

13. INI Cambridge, June 24 th 2008 Raw single cell data – snapshot images Frame 11 Frame 17 Frame 26 10 mins between frames - technical limit of time resolution