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Statistical Estimation of Cellular Processes

Basic cellular processes such as gene expression are fundamentally stochastic with randomness in molecular machinery and interactions leading to cell-to-cell variations in mRNA and protein levels. This stochasticity has important consequences for cellular function and it is therefore important to quantify it.

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We dynamically measured the temperature coefficient, Q10, of mRNA synthesis and degradation rates of the Arabidopsis transcriptome. Our data show that less frequent chromatin states can produce temperature responses simply by virtue of their rarity and the difference between their thermal properties and those of the most common states.

Direct measurement of transcription rates reveals multiple mechanisms for configuration of the Arabidopsis ambient temperature response.
Kate Sidaway-Lee, Maria J. Costa, David Rand, Bärbel Finkenstadt, and Steven Penfield. Genome Biology 2014, 15:R45 (3 March 2014)

To address the sources of variability relevant to single-cell data, namely, intrinsic noise due to the stochastic nature of reactions, and extrinsic noise arising from the cell-to-cell variation of kinetic parameters we derive a dynamic state space model for molecular populations, extend it to a hierarchical model and apply it to multiple single-cell time series data.

Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: an application to single cell data.
Bärbel Finkenstädt, Dan J. Woodcock, Michal Komorowski, Claire V.Harper, Julian R.E. Davis, Mike R.H. White, David A. Rand. Annals of Applied Statistics , (2013) 7 (4) 1960–1982.

An algorithm that can estimate the transcription rates of genes even when transient transfections with variable gene copy numbers are involved. This can be used, for example, in projects where it is necessary to work with many different constructs.

A hierarchical model of transcriptional dynamics allows robust estimation of transcription rates in populations of single cells with variable gene copy number.
Dan J. Woodcock, Keith W. Vance, Michał Komorowski, Georgy Koentges, Bärbel Finkenstädt and David A. Rand. Bioinformatics (2013), pages 1–7 doi:10.1093/bioinformatics/btt201

State of the art algorithms to analyse circadian data.

Inference on periodicity of circadian time series.
Maria J. Costa, Bärbel Finkenstädt, Veronique Roche, Francis Levi, Peter D. Gould, Julia Foreman, Karen Halliday, Anthony Hall, David. A. Rand. Biostatistics (2013) 14 (4): 792-806 first published online June 6, 2013 doi:10.1093/biostatistics/kxt020

We use a mechanistic model to identify transcriptional switch points and the resulting algorithm contributes to efforts to elucidate and understand key biological processes, such as transcription and degradation.

A temporal switch model for estimating transcriptional activity in gene expression.
D. J. Jenkins, B. Finkenstädt and D. A. Rand, Bioinformatics (2013) 29(9): 1158-1165

The basic mathematical tools you need for experimental design and sensitivity analysis for stochastic regulatory or signalling systems. Uses the linear noise approximation.

Sensitivity of stochastic chemical kinetics models.
M. Komorowski, M. Costa, D. A. Rand, and M. L. Stumpf, PNAS 2011 108 (21) 8645-86

Transcription dynamics from two loci in real time in single cells. Evidence for a refractory period in the inactivation phase of transcription. New theoretical techniques for reconstructing transcription from imaging data.

Dynamic Analysis of Stochastic Transcription Cycles.
C. V. Harper, B. Finkenstädt, D. Woodcock, S Friedrichsen, S. Semprini, L Ashall, D. Spiller, J. J. Mullins, D. A. Rand, J. R.E. Davis, M. R. H. White. PLoS Biology 9(4): e1000607. doi:10.1371/journal.pbio.1000607

Multiparameter experimental and computational methods that integrate quantitative measurement and mathematical simulation of these noisy and complex processes are required to understand the highly dynamic mechanisms that control cell plasticity and fate.

Measurement of Single Cell Dynamics.
D G Spiller, C. D. Wood, D. A. Rand, M. R. H. White. Nature 465 (2010) 736-745

Feedbacks of NF-kappaB optimised to increase single-cell heterogeneity and population robustness.

Population Robustness Arising From Cellular Heterogeneity.
P. Paszek, S. Ryan, L. Ashall, K. Sillitoe, C. V. Harper, D. G. Spiller, D. A. Rand and M. R. H. White, PNAS doi/10.1073/pnas.0913798107

A new statistical inference framework 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 the fluorescent signal resulting from intrinsic noise of gene expression, kinetics of fluorescent protein maturation and extrinsic noise.

Using single fluorescent reporter gene to infer half-life of extrinsic noise and other parameters of gene expression.
M. Komorowski, B. Finkenstadt, D. A. Rand, Biophysical Journal 98(12) (2010) 2759-2769

New summation theorems that substantially generalise previous results to dynamic non-stationary solutions such as periodic orbits and transient signals and apply to both autonomous and non-autonomous systems such as forced nonlinear oscillators.

Network control analysis for time-dependent dynamical states.
D. A. Rand. Dynamics and Games in Science, in honour of Mauricio Peixoto and David Rand. Springer 2010.

A simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.

Bayesian inference of biochemical kinetic parameters using the linear noise approximation.
M. Komorowski, B. Finkenstadt, C. V. Harper and D. A. Rand. (2009) BMC Bioinformatics (2009) 10 343-353

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