Partner: David Rand

University of Warwick (GB)

Recent publications
1.Woodcock D.J., Vance K.W., Komorowski M., Koentges G., Finkenstädt B., Rand D.A., A hierarchical model of transcriptional dynamics allows robust estimation of transcription rates in populations of single cells with variable gene copy number, BIOINFORMATICS, ISSN: 1367-4803, DOI: 10.1093/bioinformatics/btt201, Vol.29, pp.1519-1525, 2013
Abstract:

Motivation: cis-regulatory DNA sequence elements, such as enhancers and silencers, function to control the spatial and temporal expression of their target genes. Although the overall levels of gene expression in large cell populations seem to be precisely controlled, transcription of individual genes in single cells is extremely variable in real time. It is, therefore, important to understand how these cis-regulatory elements function to dynamically control transcription at single-cell resolution. Recently, statistical methods have been proposed to back calculate the rates involved in mRNA transcription using parameter estimation of a mathematical model of transcription and translation. However, a major complication in these approaches is that some of the parameters, particularly those corresponding to the gene copy number and transcription rate, cannot be distinguished; therefore, these methods cannot be used when the copy number is unknown.

Results: Here, we develop a hierarchical Bayesian model to estimate biokinetic parameters from live cell enhancer–promoter reporter measurements performed on a population of single cells. This allows us to investigate transcriptional dynamics when the copy number is variable across the population. We validate our method using synthetic data and then apply it to quantify the function of two known developmental enhancers in real time and in single cells.

Affiliations:
Woodcock D.J.-University of Warwick (GB)
Vance K.W.-University of Warwick (GB)
Komorowski M.-IPPT PAN
Koentges G.-University of Warwick (GB)
Finkenstädt B.-University of Warwick (GB)
Rand D.A.-University of Warwick (GB)
2.Finkenstädt B., Woodcock D.J., Komorowski M., Harper C.V., Davis J.R.E., White M.R.H., Rand D.A., Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data, Annals of Applied Statistics, ISSN: 1932-6157, DOI: 10.1214/13-AOAS669, Vol.7, No.4, pp.1960-1982, 2013
Abstract:

A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability from cell to cell. Here we focus on the case where single-cell fluorescent protein imaging time series data are available for a population of cells. Based on van Kampen’s linear noise approximation, we derive a dynamic state space model for molecular populations which is then extended to a hierarchical model. This model has potential to address the sources of variability relevant to single-cell data, namely, intrinsic noise due to the stochastic nature of the birth and death processes involved in reactions and extrinsic noise arising from the cell-to-cell variation of kinetic parameters. In order to infer such a model from experimental data, one must also quantify the measurement process where one has to allow for nonmeasurable molecular species as well as measurement noise of unknown level and variance. The availability of multiple single-cell time series data here provides a unique testbed to fit such a model and quantify these different sources of variation from experimental data.

Keywords:

Linear noise approximation, kinetic parameter estimation, intrinsic and extrinsic noise, state space model and Kalman filter, Bayesian hierarchical modeling

Affiliations:
Finkenstädt B.-University of Warwick (GB)
Woodcock D.J.-University of Warwick (GB)
Komorowski M.-IPPT PAN
Harper C.V.-University of Manchester (GB)
Davis J.R.E.-University of Manchester (GB)
White M.R.H.-University of Manchester (GB)
Rand D.A.-University of Warwick (GB)
3.Komorowski M., Costa M.J., Rand D.A., Stumpf M.P.H., Sensitivity, robustness, and identifiability in stochastic chemical kinetics models, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, ISSN: 0027-8424, DOI: 10.1073/pnas.1015814108, Vol.108, No.21, pp.8645-8650, 2011
Abstract:

We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models without the need for Monte Carlo simulations. This methodology is then used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request.

Affiliations:
Komorowski M.-other affiliation
Costa M.J.-University of Warwick (GB)
Rand D.A.-University of Warwick (GB)
Stumpf M.P.H.-Imperial College London (GB)
4.Komorowski M., Finkenstädt B., Rand D., Using a single fluorescent reporter gene to infer half-life of extrinsic noise and other parameters of gene expression, BIOPHYSICAL JOURNAL, ISSN: 0006-3495, DOI: 10.1016/j.bpj.2010.03.032, Vol.98, pp.2759-2769, 2010
Abstract:

Fluorescent and luminescent proteins are often used as reporters of transcriptional activity. Given the prevalence of noise in biochemical systems, the time-series data arising from these is of significant interest in efforts to calibrate stochastic models of gene expression and obtain information about sources of nongenetic variability. We present a statistical inference framework that can be used to estimate kinetic parameters of gene expression, as well as the strength and half-life of extrinsic noise from single fluorescent-reporter-gene time-series data. The method takes into account stochastic variability in a fluorescent signal resulting from intrinsic noise of gene expression, kinetics of fluorescent protein maturation, and extrinsic noise, which is assumed to arise at transcriptional level. We use the linear noise approximation and derive an explicit formula for the likelihood of observed fluorescent data. The method is embedded in a Bayesian paradigm, so that certain parameters can be informed from other experiments allowing portability of results across different studies. Inference is performed using Markov chain Monte Carlo. Fluorescent reporters are primary tools to observe dynamics of gene expression and the correct interpretation of fluorescent data is crucial to investigating these fundamental processes of cellular life. As both magnitude and frequency of the noise may have a dramatic effect on the cell fitness, the quantification of stochastic fluctuation is essential to the understanding of how genes are regulated. Our method provides a framework that addresses this important question.

Affiliations:
Komorowski M.-other affiliation
Finkenstädt B.-University of Warwick (GB)
Rand D.-University of Warwick (GB)