Uterine smooth muscle cells remain quiescent throughout most of gestation, only generating spontaneous action potentials immediately prior to, and during, labor. This study presents a method that combines transcriptomics with biophysical recordings to characterise the conductance repertoire of these cells, the ‘conductance repertoire’ being the total complement of ion channels and transporters expressed by an electrically active cell.

Cell Surface Densities of Ion Pumps, Exchangers, and Channels from mRNA Expression, Conductance Kinetics, Whole-Cell Calcium, and Current-Clamp Voltage Recordings, with an Application to Human Uterine Smooth Muscle Cells

J. Atia, C. McCloskey, A. S. Shmygol, D. A. Rand, H. A. van den Berg and A. M. Blanks

PLoS Comput. Biol. 12(4): e1004828. doi:10.1371/journal.pcbi.10048282016 (2016)

PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities

PeTTSy : a computational tool for perturbation analysis of complex systems biology models.

Mirela Domijan, Paul E Brown, Boris V Shulgin and David A Rand.

BMC Bioinformatics 2016 17:124 DOI: 10.1186/s12859-016-0972-2

In Arabidopsis thaliana, changes in metabolism and gene expression drive increased drought tolerance and initiate diverse drought avoidance and escape responses. To address regulatory processes that link these responses, we set out to identify genes that govern early responses to drought. To do this, a high-resolution time series transcriptomics dataset was produced, coupled with detailed physiological and metabolic analyses of plants subjected to a slow transition from well-watered to drought conditions. A total of 1815 drought-responsive differentially expressed genes were identified. The early changes in gene expression coincided with a drop in carbon assimilation, and only in the late stages with an increase in foliar abscisic acid content. To identify gene regulatory networks (GRNs) mediating the transition between the early and late stages of drought, we used Bayesian network modelling of differentially expressed transcription factor (TF) genes. This approach identified AGAMOUS-LIKE22 as key hub gene in a TF GRN. It has previously been shown that AGL22 is involved in the transition from vegetative state to flowering but here we show that AGL22 expression influences steady state photosynthetic rates and lifetime water use. This suggests that AGL22 uniquely regulates a transcriptional network during drought stress, linking changes in primary metabolism and the initiation of stress responses.

Time-series transcriptomics reveals that AGAMOUS-LIKE22 affects primary metabolism and developmental processes in drought-stressed Arabidopsis.

U. Bechtold, C. A. Penfold, D. J. Jenkins, R. Legaie, J. D. Moore, T. Lawson, J. S.A. Matthews., S.R.M. Vialet-Chabrand, L. Baxter, S. Subramaniam1, R. Hickman, H. Florance, C. Sambles, D. L. Salmon, R. Feil, L. Bowden, C. Hill, N. R. Baker, J. E. Lunn, B. Finkenstadt, A. Mead, V. Buchanan-Wollaston, Jim Beynon, D. A. Rand, D. L. Wild, K. J. Denby, S. Ott, N. Smirnoff and P. M. Mullineaux.

Plant Cell, 28: 345–366, February 2016

Cellular heterogeneity resulting from stochastic or pulsatile transcription may be beneficial in some circumstances; however the role of stochastic gene expression in tissue systems where integrated acute responses to physiological changes are required is unclear. To investigate the dynamics of gene expression within a complex tissue environment, we quantitatively analysed prolactin gene expression from single living cells maintained in intact pituitary slices. Using novel stochastic switch modelling, we characterised the transcription dynamics of the prolactin gene from observed fluorescence reporter protein expression. Heterogeneous transcriptional responses were detected across a cell population, with alteration of this activity in embryonic pituitary tissue towards a more pulsatile behaviour. Quantitative assessment of gene expression dynamics in relation to tissue architecture revealed local co-ordination of activity between cells, which was in part dependent on gap junction signalling. Thus, transcription dynamics may be constrained between cells in tissue to ensure appropriate responses to physiological signals.

Spatially Coordinated Dynamic Gene Transcription in Living Pituitary Tissue.

K. Featherstone, K. Hey, H. Momiji, A. V. McNamara, A. L. Patist, J. Woodburn, D. G. Spiller4, H. C. Christian, A. S. McNeilly, J. J. Mullins, B. Finkenstädt, D. A. Rand*, M. R.H. White*, J. R.E. Davis*. *Corresponding author

eLife 2015;5:e08494. DOI: 10.7554/eLife.08494.

Stochastic Reaction Networks (SRNs) can be used to model the temporal behaviour of gene regulation in single cells. In particular, SRNs can capture the features of intrinsic variability arising from the intracellular biochemical processes. However, inference for SRNs is computationally demanding due to the intractability of the transition densities. This paper will show how state space models provide a unifying framework for approximating SRNs with particular attention given to the linear noise approximation (LNA) and an alternative model specific approximation. This methodology has been applied to single cell imaging data measuring expression levels of the human prolactin gene. Transcription is modelled by a random step function relating to bursts in transcriptional activity and we will demonstrate how reversible jump MCMC can be used to infer the switching regimes of this gene within single cells of mammalian tissue.

A stochastic transcriptional switch model for single cell imaging data.

Kirsty Hey, Hiroshi Momiji, Karen Featherstone, Julian Davis, Mike White, David Rand, Barbel Finkenstadt Biostatistics (2015), pp. 1–15 doi:10.1093/biostatistics/kxv010

We provide analytical tools to facilitate a rigorous assessment of the quality and value of the fit of a complex model to data. We use this to provide approaches to model fitting, parameter estimation, the design of optimization functions and experimental optimization. This is in the context where multiple constraints are used to select or optimize a large model defined by differential equations. We illustrate the approach using models of circadian clocks and the NF-kB signalling system.

Using constraints and their value for optimization of large ODE systems

Mirela Domijan and David A. Rand J. R. Soc. Interface 12: 20141303.

Nrf2 provides an adaptive response for protection of cells against toxic insults, oxidative stress and metabolic dysfunction and regulates a battery of protective genes by binding to regulatory anti-oxidant response elements (AREs). We show that that Nrf2 undergoes autonomous translocational oscillations between cytoplasm and nucleus whose period and amplitude decrease upon stimulation, We propose a mechanism whereby oscillations are produced by negative feedback involving successive de-phosphorylation and phosphorylation steps.

Frequency Modulated Translocational Oscillations of Nrf2 Mediate the ARE Cytoprotective Transcriptional Response.

Mingzhan Xue, Hiroshi Momiji, Naila Rabbani, Guy Barker, Till Bretschneider, Anatoly Shmygol, David A. Rand, and Paul J. Thornalley. Antioxidants & Redox Signaling (in press).

In the absence of other signals, the cell cycle and circadian clock robustly phase-lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronised way with a common frequency. However, there are additional clock states: as well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock and a different frequency ratio.

Phase-locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.

C. Feillet, P. Krusche, F. Tamanini, R. C. Janssens, M. J. Downey, P. Martin, M. Teboul, S. Saito, F. Levi, T. Bretschneider, G. T. J. van der Horst, F. Delaunay, D. A. Rand. PNAS (2014) www.pnas.org/cgi/doi/10.1073/pnas.1320474111

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

Using new data and mathematical modelling and analysis we test two hypotheses: that the targets of light regulation are sufficient to mediate temperature compensation and that, rather than using specific molecular mechanisms to achieve temperature compensation, the plant clock uses non-specific network balancing.

Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures.
Peter D Gould, Nicolas Ugarte, Mirela Domijan, Maria Costa, Julia Foreman, Dana MacGregor, Ken Rose, Jayne Griffiths, Andrew J Millar, Bärbel Finkenstädt, Steven Penfield, David A Rand, Karen J Halliday & Anthony J W Hall. Molecular Systems Biology (2013) 9 Article number: 650 doi:10.1038/msb.2013.7

High-resolution temporal expression profiling and network reconstruction to study defence against Botrytis cinerea as part of the PRESTA Project.

Arabidopsis defence against Botrytis cinerea: chronology and regulation deciphered by high-resolution temporal transcriptomic analysis.
O. Windram et al. Plant Cell. 2012 24: 3530-3557.

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

High-resolution temporal expression profiling and network reconstruction to study plant senescence as part of the PRESTA Project.

Temporal Profiling of Transcripts during Arabidopsis Leaf Senescence Reveals a Distinct Chronology of Processes and Regulation.
E Breeze et al. High-Resolution Plant Cell, Vol. 23: (2011) 1–22.

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

Clocks need to track more than one phase

Quantitative analysis of regulatory flexibility under changing environmental conditions.
K. D. Edwards, , O. E. Akman, K. Knox, P. J. Lumsden, A. W. Thomson, P. E. Brown, A. Pokhilko, L. Kozma-Bognar, F. Nagy, D. A.  Rand, and A. J. Millar, Molecular Systems Biology 6:424.

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

Describing the heterogenious response of low-dose stimulation of the NF-kB system

Physiological levels of TNFa stimulation induce stochastic dynamics of NF-kB responses in single living cells.
D. A. Turner, P. Paszek, D. J. Woodcock, D. E. Nelson, C. A. Horton, Y. Wang, D. G. Spiller, D. A. Rand, M. R. H. White, and C. V. Harper, Journal of Cell Science 123: 2834-2843 (2010)

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

Analysis of a new model for the Neurospora circadian clock

Robustness from flexibility in the fungal circadian clock.
O. E. Akman, D. A. Rand, P. E. Brown and A. J. Millar. BMC Systems Biology 2010, 4:88

Modelling the photoperiod switch in plants predicts new role for FKF1.

Prediction of Photoperiodic Regulators from Quantitative Gene Circuit Models.
J. D. Salazar, T. Saithong, P. E. Brown, J. Foreman, J. C. W. Locke, K. J. Halliday, I. A. Carre, D. A. Rand and A. J. Millar. Cell 139, 1170–1179, DOI 10.1016/j.cell.2009.11.029

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

Stimulation frequency modulates differential gene expression by NF-kappaB; IkappaBepsilon feedback regulates heterogeneithy of oscillations; and the structure and role of A20 feedback is predicted.

Pulsatile stimulation determines timing and specificity of NF-kappa B-dependent transcription.
L. Ashall, C.A. Horton, D.E. Nelson, P. Paszek, C.V. Harper, K. Sillitoe, S. Ryan, D.G. Spiller, J.F. Unitt, D.S. Broomhead, D.B. Kell, D.A. Rand, V. Sée, and M.R.H. White. Science 324 (2009) 242-246

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

Analysis of a new kinetic model for G protein-coupled receptor signaling has identified a dynamic network motif that shows how inclusion of an inactive GTP-bound state for the Gα produces the non-monotone signal level seen in eour experiments and resulting from the way in which RGS-mediated GTP hydrolysis acts as both a negative (low stimulation) and positive (high stimulation) regulator of signaling

Dual positive and negative regulation of GPCR signaling by GTP Hydrolysis.
B. Smith, C. Hill, L. Godfrey, D A Rand, H van den Berg, S Thornton, M Hodgkin, J Davey and G Ladds. Cellular Signalling 21 (209)1151-1160 doi:10.1016/j.cellsig.2009.03.00

Epigenetic Control of Vernalisation in Arabidopsis thaliana.

Mathematical Model of the Epigenetic Control of Vernalisation in Arabidopsis thaliana.
J.D. Salazar, J. Foreman, I.A. Carre, D.A. Rand and A. J. Millar. Acta Horticulturae Number 803, November 2008

In the absence of other signals, the cell cycle and circadian clock robustly phase-lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronised way with a common frequency. However, there are additional clock states: as well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock and a different frequency ratio.

Phase-locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.

C. Feillet, P. Krusche, F. Tamanini, R. C. Janssens, M. J. Downey, P. Martin, M. Teboul, S. Saito, F. Levi, T. Bretschneider, G. T. J. van der Horst, F. Delaunay, D. A. Rand. PNAS (2014) www.pnas.org/cgi/doi/10.1073/pnas.1320474111

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

Using new data and mathematical modelling and analysis we test two hypotheses: that the targets of light regulation are sufficient to mediate temperature compensation and that, rather than using specific molecular mechanisms to achieve temperature compensation, the plant clock uses non-specific network balancing.

Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures.
Peter D Gould, Nicolas Ugarte, Mirela Domijan, Maria Costa, Julia Foreman, Dana MacGregor, Ken Rose, Jayne Griffiths, Andrew J Millar, Bärbel Finkenstädt, Steven Penfield, David A Rand, Karen J Halliday & Anthony J W Hall. Molecular Systems Biology (2013) 9 Article number: 650 doi:10.1038/msb.2013.7

High-resolution temporal expression profiling and network reconstruction to study defence against Botrytis cinerea as part of the PRESTA Project.

Arabidopsis defence against Botrytis cinerea: chronology and regulation deciphered by high-resolution temporal transcriptomic analysis.
O. Windram et al. Plant Cell. 2012 24: 3530-3557.

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

High-resolution temporal expression profiling and network reconstruction to study plant senescence as part of the PRESTA Project.

Temporal Profiling of Transcripts during Arabidopsis Leaf Senescence Reveals a Distinct Chronology of Processes and Regulation.
E Breeze et al. High-Resolution Plant Cell, Vol. 23: (2011) 1–22.

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

Clocks need to track more than one phase

Quantitative analysis of regulatory flexibility under changing environmental conditions.
K. D. Edwards, , O. E. Akman, K. Knox, P. J. Lumsden, A. W. Thomson, P. E. Brown, A. Pokhilko, L. Kozma-Bognar, F. Nagy, D. A.  Rand, and A. J. Millar, Molecular Systems Biology 6:424.

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

Describing the heterogenious response of low-dose stimulation of the NF-kB system

Physiological levels of TNFa stimulation induce stochastic dynamics of NF-kB responses in single living cells.
D. A. Turner, P. Paszek, D. J. Woodcock, D. E. Nelson, C. A. Horton, Y. Wang, D. G. Spiller, D. A. Rand, M. R. H. White, and C. V. Harper, Journal of Cell Science 123: 2834-2843 (2010)

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

Analysis of a new model for the Neurospora circadian clock

Robustness from flexibility in the fungal circadian clock.
O. E. Akman, D. A. Rand, P. E. Brown and A. J. Millar. BMC Systems Biology 2010, 4:88

Modelling the photoperiod switch in plants predicts new role for FKF1.

Prediction of Photoperiodic Regulators from Quantitative Gene Circuit Models.
J. D. Salazar, T. Saithong, P. E. Brown, J. Foreman, J. C. W. Locke, K. J. Halliday, I. A. Carre, D. A. Rand and A. J. Millar. Cell 139, 1170–1179, DOI 10.1016/j.cell.2009.11.029

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

Stimulation frequency modulates differential gene expression by NF-kappaB; IkappaBepsilon feedback regulates heterogeneithy of oscillations; and the structure and role of A20 feedback is predicted.

Pulsatile stimulation determines timing and specificity of NF-kappa B-dependent transcription.
L. Ashall, C.A. Horton, D.E. Nelson, P. Paszek, C.V. Harper, K. Sillitoe, S. Ryan, D.G. Spiller, J.F. Unitt, D.S. Broomhead, D.B. Kell, D.A. Rand, V. Sée, and M.R.H. White. Science 324 (2009) 242-246

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

Analysis of a new kinetic model for G protein-coupled receptor signaling has identified a dynamic network motif that shows how inclusion of an inactive GTP-bound state for the Gα produces the non-monotone signal level seen in eour experiments and resulting from the way in which RGS-mediated GTP hydrolysis acts as both a negative (low stimulation) and positive (high stimulation) regulator of signaling

Dual positive and negative regulation of GPCR signaling by GTP Hydrolysis.
B. Smith, C. Hill, L. Godfrey, D A Rand, H van den Berg, S Thornton, M Hodgkin, J Davey and G Ladds. Cellular Signalling 21 (209)1151-1160 doi:10.1016/j.cellsig.2009.03.00

Epigenetic Control of Vernalisation in Arabidopsis thaliana.

Mathematical Model of the Epigenetic Control of Vernalisation in Arabidopsis thaliana.
J.D. Salazar, J. Foreman, I.A. Carre, D.A. Rand and A. J. Millar. Acta Horticulturae Number 803, November 2008

In the absence of other signals, the cell cycle and circadian clock robustly phase-lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronised way with a common frequency. However, there are additional clock states: as well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock and a different frequency ratio.

Phase-locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.

C. Feillet, P. Krusche, F. Tamanini, R. C. Janssens, M. J. Downey, P. Martin, M. Teboul, S. Saito, F. Levi, T. Bretschneider, G. T. J. van der Horst, F. Delaunay, D. A. Rand. PNAS (2014) www.pnas.org/cgi/doi/10.1073/pnas.1320474111

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

Using new data and mathematical modelling and analysis we test two hypotheses: that the targets of light regulation are sufficient to mediate temperature compensation and that, rather than using specific molecular mechanisms to achieve temperature compensation, the plant clock uses non-specific network balancing.

Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures.
Peter D Gould, Nicolas Ugarte, Mirela Domijan, Maria Costa, Julia Foreman, Dana MacGregor, Ken Rose, Jayne Griffiths, Andrew J Millar, Bärbel Finkenstädt, Steven Penfield, David A Rand, Karen J Halliday & Anthony J W Hall. Molecular Systems Biology (2013) 9 Article number: 650 doi:10.1038/msb.2013.7

High-resolution temporal expression profiling and network reconstruction to study defence against Botrytis cinerea as part of the PRESTA Project.

Arabidopsis defence against Botrytis cinerea: chronology and regulation deciphered by high-resolution temporal transcriptomic analysis.
O. Windram et al. Plant Cell. 2012 24: 3530-3557.

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

High-resolution temporal expression profiling and network reconstruction to study plant senescence as part of the PRESTA Project.

Temporal Profiling of Transcripts during Arabidopsis Leaf Senescence Reveals a Distinct Chronology of Processes and Regulation.
E Breeze et al. High-Resolution Plant Cell, Vol. 23: (2011) 1–22.

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

Clocks need to track more than one phase

Quantitative analysis of regulatory flexibility under changing environmental conditions.
K. D. Edwards, , O. E. Akman, K. Knox, P. J. Lumsden, A. W. Thomson, P. E. Brown, A. Pokhilko, L. Kozma-Bognar, F. Nagy, D. A.  Rand, and A. J. Millar, Molecular Systems Biology 6:424.

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

Describing the heterogenious response of low-dose stimulation of the NF-kB system

Physiological levels of TNFa stimulation induce stochastic dynamics of NF-kB responses in single living cells.
D. A. Turner, P. Paszek, D. J. Woodcock, D. E. Nelson, C. A. Horton, Y. Wang, D. G. Spiller, D. A. Rand, M. R. H. White, and C. V. Harper, Journal of Cell Science 123: 2834-2843 (2010)

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

Analysis of a new model for the Neurospora circadian clock

Robustness from flexibility in the fungal circadian clock.
O. E. Akman, D. A. Rand, P. E. Brown and A. J. Millar. BMC Systems Biology 2010, 4:88

Modelling the photoperiod switch in plants predicts new role for FKF1.

Prediction of Photoperiodic Regulators from Quantitative Gene Circuit Models.
J. D. Salazar, T. Saithong, P. E. Brown, J. Foreman, J. C. W. Locke, K. J. Halliday, I. A. Carre, D. A. Rand and A. J. Millar. Cell 139, 1170–1179, DOI 10.1016/j.cell.2009.11.029

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

Stimulation frequency modulates differential gene expression by NF-kappaB; IkappaBepsilon feedback regulates heterogeneithy of oscillations; and the structure and role of A20 feedback is predicted.

Pulsatile stimulation determines timing and specificity of NF-kappa B-dependent transcription.
L. Ashall, C.A. Horton, D.E. Nelson, P. Paszek, C.V. Harper, K. Sillitoe, S. Ryan, D.G. Spiller, J.F. Unitt, D.S. Broomhead, D.B. Kell, D.A. Rand, V. Sée, and M.R.H. White. Science 324 (2009) 242-246

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

Analysis of a new kinetic model for G protein-coupled receptor signaling has identified a dynamic network motif that shows how inclusion of an inactive GTP-bound state for the Gα produces the non-monotone signal level seen in eour experiments and resulting from the way in which RGS-mediated GTP hydrolysis acts as both a negative (low stimulation) and positive (high stimulation) regulator of signaling

Dual positive and negative regulation of GPCR signaling by GTP Hydrolysis.
B. Smith, C. Hill, L. Godfrey, D A Rand, H van den Berg, S Thornton, M Hodgkin, J Davey and G Ladds. Cellular Signalling 21 (209)1151-1160 doi:10.1016/j.cellsig.2009.03.00

Epigenetic Control of Vernalisation in Arabidopsis thaliana.

Mathematical Model of the Epigenetic Control of Vernalisation in Arabidopsis thaliana.
J.D. Salazar, J. Foreman, I.A. Carre, D.A. Rand and A. J. Millar. Acta Horticulturae Number 803, November 2008