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 but 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.
C. Feillet, P. Krusche, F. Tamanini, R. C. Janssens, M. J. Downey, P. Martin1, M. Teboul1, S. Saito, F. Levi, T. Bretschneider, G. T. J. van der Horst, F. Delaunay, D. A. Rand. Phase-locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle. PNAS (to appear)

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.

Kate Sidaway-Lee, Maria J. Costa, David Rand, Bärbel Finkenstadt, and Steven Penfield. Direct measurement of transcription rates reveals multiple mechanisms for configuration of the Arabidopsis ambient temperature response. 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.
Bärbel Finkenstädt, Dan J. Woodcock, Michal Komorowski, Claire V.Harper, Julian R.E. Davis, Mike R.H. White, David A. Rand. Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: an application to single cell data. 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.

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

State of the art algorithms to analyse circadian data.
Maria J. Costa, Bärbel Finkenstädt, Veronique Roche, Francis Levi, Peter D. Gould, Julia Foreman, Karen Halliday, Anthony Hall, David. A. Rand. Inference on periodicity of circadian time series. 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.
D. J. Jenkins, B. Finkenstädt and D. A. Rand, A temporal switch model for estimating transcriptional activity in gene expression. Bioinformatics (2013) 29(9): 1158-1165 [IF=5.468]

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.

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.
Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures. Molecular Systems Biology 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.
O. Windram et al. Arabidopsis defence against Botrytis cinerea: chronology and regulation deciphered by high-resolution temporal transcriptomic analysis. 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.
M. Komorowski, M. Costa, D. A. Rand, and M. L. Stumpf,
Sensitivity of stochastic chemical kinetics models. PNAS 2011 108 (21) 8645-8650

High-resolution temporal expression profiling and network reconstruction to study plant senescence as part of the PRESTA Project.
E Breeze et al.
High-Resolution Temporal Profiling of Transcripts during Arabidopsis Leaf Senescence Reveals a Distinct Chronology of Processes and Regulation. The 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.
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.
Dynamic Analysis of Stochastic Transcription Cycles. PLoS Biology 9(4): e1000607. doi:10.1371/journal.pbio.1000607

Clocks need to track more than one phase
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, Quantitative analysis of regulatory flexibility under changing environmental conditions. 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.
D G Spiller, C. D. Wood, D. A. Rand, M. R. H. White.
Measurement of Single Cell Dynamics. Nature 465 (2010) 736-745

Describing the heterogenious response of low-dose stimulation of the NF-kB system
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, Physiological levels of TNFa stimulation induce stochastic dynamics of NF-kB responses in single living cells. Journal of Cell Science 123: 2834-2843 (2010)

Feedbacks of NF-kappaB optimised to increase single-cell heterogeneity and population robustness.
P. Paszek, S. Ryan, L. Ashall, K. Sillitoe, C. V. Harper, D. G. Spiller, D. A. Rand and M. R. H. White,
Population Robustness Arising From Cellular Heterogeneity. PNAS doi/10.1073/pnas.0913798107

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

Modelling the photoperiod switch in plants predicts new role for FKF1.
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.
Prediction of Photoperiodic Regulators from Quantitative Gene Circuit Models. 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.
M. Komorowski, B. Finkenstadt, D. A. Rand,
Using single fluorescent reporter gene to infer half-life of extrinsic noise and other parameters of gene expression. 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.
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.
Pulsatile stimulation determines timing and specificity of NF-kappa B-dependent transcription. 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.
D. A. Rand.
Network control analysis for time-dependent dynamical states. 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.
M. Komorowski, B. Finkenstadt, C. V. Harper and D. A. Rand.
Bayesian inference of biochemical kinetic parameters using the linear noise approximation. (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
B. Smith, C. Hill, L. Godfrey, D A Rand, H van den Berg, S Thornton, M Hodgkin, J Davey and G Ladds.
Dual positive and negative regulation of GPCR signaling by GTP Hydrolysis. Cellular Signalling 21 (209)1151-1160 doi:10.1016/j.cellsig.2009.03.00

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