Learning and Inference in Computational Systems Biology

Gaussian process modelling of transcription factor networks using Markov Chain Monte-Carlo

author: Michalis K. Titsias, University of Manchester

Description

Ordinary differential equations (ODEs) can provide an useful framework for modelling the dynamics of biological networks. In this study, we focus on a small biological sub-system where a set of target genes are regulated by one transcription factor protein. The concentration of the protein and the gene specific kinetic parameters such as basal rates, decay rates and sensitivities are typically unknown. The objective of modelling is to estimate these quantities by making use of a set of observed gene expression levels. We consider a Bayesian framework for modelling the system of ODEs that is based on Gaussian processes. The Gaussian process is used as the prior for the transcription factor protein and allows us to infer the concentration of the protein in a time continuous manner. We present a Markov chain Monte Carlo algorithm for a full Bayesian statistical inference. The essential property of our MCMC algorithm is that we efficiently infer the protein concentration by applying a novel sampling algorithm for Gaussian process models. We apply our technique to linear and non-linear models.

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*Slides*
0:00	Gaussian Process Modelling of Transcription Factor Networks using Markov Chain Monte Carlo
0:10	Outline
0:25	Gaussian Processes - 1
0:42	Gaussian Processes - 2
1:09	Gaussian Processes for Bayesian Learning
1:54	Gaussian Processes for Bayesian Regression - 1
2:02	Gaussian Processes for Bayesian Regression - 2
2:16	Gaussian Processes for Bayesian Regression - 3
2:22	Gaussian Processes for Non-Gaussian Likelihoods
3:05	MCMC for Gaussian Processes
4:37	Sampling Using Control Points - 1
5:38	Sampling Using Control Points: Regression - Examples - 1
5:56	Sampling Using Control Points: Regression - Examples - 2
6:02	Sampling Using Control Points: Regression - Examples - 3
6:09	Sampling Using Control Points: Regression - Examples - 4
6:13	Sampling Using Control Points: Regression - Examples - 5
6:14	Sampling Using Control Points: Regression - Examples - 6
6:19	Sampling Using Control Points - 2
6:24	Sampling Using Control Points: Adaption of the Proposal
7:32	Transcriptional Regulation
8:50	Transcriptional Regulation Using Gaussian Processes
9:51	Results in E.Coli Data: Rogers, Khanin and Girolami (2007)
11:11	Results in E.Coli Data: Predicted Gene Expressions - 1
11:27	Results in E.Coli Data: Predicted Gene Expressions - 2
11:32	Results in E.Coli Data: Predicted Gene Expressions - 3
11:35	Results in E.Coli Data: Protein Concentration
11:57	Results in E.Coli Data: Kinetic Parameters
12:19	Results in E.Coli Data: Genes with Low Sensitivity Value
12:57	Results in E.Coli Data: Confidence Intervals for the Kinetic Parameters
13:10	Data Used by Barenco et al. [2006]
13:31	Data Used by Barenco et al. [2006]: Predicted Gene Expressions for the 1st Replica
13:37	Data Used by Barenco et al. [2006]: Protein Concentrations
14:17	Data Used by Barenco et al. [2006]: Kinetic Parameters
15:17	- Questions

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