David Rand

Stacks Image 627

RECENT BIOLOGICAL PUBLICATIONS



Recent studies have established that the circadian clock influences onset, progression and therapeutic outcomes in a number of diseases including cancer and heart disease. Therefore, there is a need for tools to measure the functional state of the circadian clock and its downstream targets in patients. We provide such a tool and demonstrate its clinical relevance by an application to breast cancer where we find a strong link between survival and our measure of clock dysfunction. We use a machine-learning approach and construct an algorithm called TimeTeller which uses the multi-dimensional state of the genes in a transcriptomics analysis of a single biological sample to assess the level of circadian clock dysfunction. We demonstrate how this can distinguish healthy from malignant tissues and demonstrate that the molecular clock dysfunction metric is a potentially new prognostic and predictive breast cancer biomarker that is independent of the main established prognostic factors.
TimeTeller: a New Tool for Precision Circadian Medicine and Cancer Prognosis.

Denise F Vlachou, Georg A Bjarnason, Sylvie Giacchetti, Sylvie Giacchetti, Francis Levi & David A Rand.

biorxiv DOI: 10.1101/622050

IWe provide experimental evidence suggesting that the NF-κB transcription factor can multiplex information about changes in multiple signals in the sense that the NF-κB target genes response can identify which of these signals have changed. In view of this, we consider how a signalling system can act as an information hub by multiplexing multiple signals. We formally define multiplexing, mathematically characterise which systems can multiplex and how well they can do it. We believe this may resolve the apparent paradox of how a system like NF-κB that regulates cell fate and inflammatory signalling in response to diverse stimuli can appear to have the low information carrying capacity suggested by recent studies on scalar signals. In carrying out our study, we introduce new methods for the analysis of large, nonlinear stochastic dynamic models, and develop computational algorithms that facilitate the calculation of fundamental constructs of information theory such as Kullback--Leibler divergences and sensitivity matrices, and link these methods to new theory about multiplexing information. We show that many current models such as those of the NF-κB system cannot multiplex effectively and provide models that overcome this limitation using post-transcriptional modifications.
Multiplexing information flow through dynamic signalling systems.

G. Minas, D. J. Woodcock, L. Ashall, C. V. Harper, M. R. H. White, D. A. Rand,

Preprint biorxiv. https://doi.org/10.1101/863159

Prolactin is a major hormone product of the pituitary gland, the central endocrine regulator. We recently showed prolactin gene transcription is highly dynamic and stochastic yet shows space-time coordination in an intact tissue slice. Here we address the question of what kind of cellular communication mediates the observed space-time organization. The analysis presented here suggests that juxtacrine signalling dominates. To further determine whether the coupling is coordinating transcription or post-transcriptional activities we used stochastic switch modelling to infer the transcriptional profiles of cells and estimated their similarity measures to deduce that their spatial cellular coordination involves coupling of transcription via juxtacrine signalling. We developed a computational model that involves an inter-cell juxtacrine coupling, yielding simulation results that show space-time coordination in the transcription level that is in agreement with the above analysis. This model is expected to serve as the prototype for the further study of tissue-level organised gene expression for epigenetically regulated genes, such as prolactin.
Disentangling juxtacrine from paracrine signalling in dynamic tissue,

Hiroshi Momiji, Kirsty L. Hassall, Karen Featherstone, Anne V. McNamara, Amanda L. Patist, David G. Spiller, Helen C. Christian, Michael R. H. White, Julian R. E. Davis, Bärbel F. Finkenstädt, David A. Rand.

PLOS Computational Biology, 15(6):e1007030 DOI: 10.1371/journal.pcbi.1007030

This article develops a general methodology for analysing the sensitivity of probability distributions of stochastic processes describing the time-evolution of biochemical reaction networks to changes in their parameter values. We derive the coefficients that efficiently summarise the sensitivity of the probability distribution of the network to each parameter and discuss their properties. The methodology is scalable to large and complex stochastic reaction networks involving many parameters and can be applied to oscillatory networks. We use the two-dimensional Brusselator system as an illustrative example and apply our approach to the analysis of the Drosophila circadian clock. We investigate the impact of using stochastic over deterministic models and provide an analysis that can support key decisions for experimental design, such as the choice of variables and time-points to be observed.
Parameter sensitivity analysis for biochemical reaction networks.

Giorgos Minas, David A Rand,

Mathematical Biosciences and Engineering, 2019, 16(5): 3965-3987. doi: 10.3934/mbe.2019196.

NF-κB signaling plays a pivotal role in control of the inflammatory response. We investigated how the dynamics and function of NF-κB were affected by temperature within the mammalian physiological range (34 °C to 40 °C). An increase in temperature led to an increase in NF-κB nuclear/cytoplasmic oscillation frequency following Tumor Necrosis Factor alpha (TNFα) stimulation. Mathematical modeling suggested that this temperature sensitivity might be due to an A20-dependent mechanism, and A20 silencing removed the sensitivity to increased temperature. The timing of the early response of a key set of NF-κB target genes showed strong temperature dependence. The cytokine-induced expression of many later genes was insensitive to temperature change (suggesting that they might be functionally temperature-compensated). Moreover, a set of temperature- and TNFα-regulated genes were implicated in NFκB cross-talk with key cell-fate–controlling pathways. In conclusion, NF-κB dynamics and target gene expression are modulated by temperature and can accurately transmit multidimensional information to control inflammation.
Temperature regulates NF-κB dynamics and function through timing of A20 transcription

C. V. Harper, D. J. Woodcock, C. Lam, M. Garcia-Albornoz, A. Adamson, L. Ashall, W. Rowe, P. Downton, L. Schmidt, S. West, D. G. Spiller, D. A. Rand* and M. R. H. White*

Proceedings of the National Academy of Sciences. 2018, DOI: 10.1073/pnas.1803609115, PMID: 29760065 *Communicating author.

In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.
Long-time analytic approximation of large stochastic oscillators: simulation, analysis and inference.

Giorgos Minas, David A Rand.

PLoS Computational Biology (2017) 13(7):e1005676 doi.org/10.1371/journal.pcbi.1005676.

Transcription in eukaryotic cells occurs in gene-specific bursts or pulses of activity. Recent studies identified a spectrum of transcriptionally active “on-states,” interspersed with periods of inactivity, but these “off-states” and the process of transcriptional deactivation are poorly understood. To examine what occurs during deactivation, we investigate the dynamics of switching between variable rates. We found that transcriptional activation occurs predominantly as a single switch, whereas deactivation occurs with graded, stepwise decreases in transcription rate.
Asymmetry between Activation and Deactivation during a Transcriptional Pulse

L.S.S. Dunham, H. Momiji, C.V. Harper, P.J. Downton, K. Hey, A. McNamara, K. Featherstone, D.G. Spiller, D.A. Rand, B. Finkenstadt, M.R.H. White & J.R.E. Davis.

Cell Systems (2017) 5:1-18, https://doi.org/10.1016/j.cels.2017.10.013 126

Discusses genomic analysis in the context of rhythmic data such as that arising from the study of circadian rhythms.

Guidelines for genome-scale analysis of biological rhythms. M E Hughes et al. Journal of Biological Rhythms (2017) 32(5):380–393.


This is a review about Chronotherapeutics which is aimed at treating illnesses according to the endogenous biologic rhythms, which moderate xenobiotic metabolism and cellular drug response. many mechanisms of diseases and drug effects are controlled by the circadian timing system. The tolerability of nearly 500 medications varies by up to fivefold according to circadian scheduling, Improved patient outcomes on circadian-based treatments (chronotherapy) have been demonstrated in randomized clinical trials, especially for cancer and inflammatory diseases. Multiscale systems chronopharmacology approaches currently combine mathematical modeling based on cellular and whole-body physiology to preclinical and clinical investigations toward the design of patient-tailored chronotherapies.
Systems Chronotherapeutics.

Annabelle Ballesta, Pasquale F. Innominato, Robert Dallmann, David A. Rand, Francis A. Lévi.

Pharmacological Reviews (2017), 69 (2) 161-199; DOI: https://doi.org/10.1124/pr.116.013441

The ReTrOS toolbox (Reconstructing Transcription Open Software) provides MATLAB-based implementations of two related methods for reconstructing the temporal transcriptional activity profile of a gene from given mRNA expression time series or protein reporter time series. The methods are based on fitting a differential equation model incorporating the processes of transcription, translation and degradation. Data from any organism and obtained from a range of technologies can be used as input due to the flexible and generic nature of the model and implementation. The output from this software provides a useful analysis of time series data and can be incorporated into further modelling approaches or in hypothesis generation.
ReTrOS: A MATLAB Toolbox for Reconstructing Transcriptional Activity from Gene and Protein Expression Data.

Giorgos Minas, Hiroshi Momiji, Dafyd J Jenkins, Maria J Costa, David A Rand and Bärbel Finkenstädt.

BMC Bioinformatics (2017) 18:316 DOI 10.1186/s12859-017-1695-8.

We propose a novel method for inferring transcriptional regulation using a simple, yet biologically interpretable, model to find the logic by which a set of candidate genes and their associated transcription factors (TFs) regulate the transcriptional process of a gene of interest. A trans-dimensional Markov Chain Monte Carlo (MCMC) algorithm is used to efficiently sample the regulatory logic under different combinations of parents and rank the estimated models by their posterior probabilities. We show that our method is able to detect complex regulatory interactions that are consistent under multiple experimental conditions.
Inferring transcriptional logic from multiple dynamic experiments

Giorgos Minas, Hiroshi Momiji, Dafyd J Jenkins1, David A Rand & Bärbel Finkenstädt.

Bioinformatics (2017), 1-8 doi:10.1093/bioinformatics/btx407.

We discuss the relevant technical considerations to generate reproducible, statistically sound, and broadly useful genome-scale data. Rather than suggest a set of rigid rules, we aim to codify principles by which investigators, reviewers, and readers of the primary literature can evaluate the suitability of different experimental designs for measuring different aspects of biological rhythms.
Guidelines for genome-scale analysis of biological rhythms.

M E Hughes et al.

Journal of Biological Rhythms (2017) 32(5):380-393.

We study how cells respond dynamically to pulsatile cytokine stimulation and find a a heterogeneous refractory state that is regulated downstream of TNFR and upstream of IKK, and depends on the level of the NF-κB system negative feedback protein A20. We suggest that this refractory state constitutes an inherent design motif of the inflammatory response and that this may avoid harmful homogenous cellular activation.
Signal transduction controls heterogeneous NF-B dynamics and target gene expression through cytokine-specific refractory states

A. Adamson, C. Boddington, P. Downton, W. Rowe, J. Bagnall, C. Lam, A. Maya-Mendoza, L. Schmidt, C. V. Harper, D. G. Spiller, D. A. Rand, D. A. Jackson, M. R.H. White, P. Paszek.

Nature Communications 7:12057 (2016) DOI: 10.1038/ncomms12057

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


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.


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


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