CURRENT RESEARCH INTERESTS

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Nuclear Factor kappa B (NF-κB)

My work in this area is almost all in collaboration with Mike White (Manchester). Most of our work Is concerned with understanding the function of the oscillations in the NF-κB system, whereby the transcription factor NF-κB locates in and out of the nucleus in a periodic fashion when the system is activated. These oscillations were discovered in Mike's lab, initially in cell cultures but now in primary cells as well. My basic hypothesis in this area is that NF-κB acts as an information hub with the oscillations allowing it to carry much more information than would be possible otherwise.

Discovered over 25 years ago,the NF-κB transcription factor controls inflammation and in different contexts has varying effects on cell death and cell division. It is found in almost all animal cell types and is involved in cellular responses to stimuli such as stress, cytokines, free radicals, ultraviolet irradiation, oxidized LDL, and bacterial or viral antigens. It plays a key role in regulating the immune response to infection. Incorrect regulation of NF-κB has been linked to cancer, inflammatory, and autoimmune diseases, septic shock, viral infection, and improper immune development. NF-κB has also been implicated in processes of synaptic plasticity and memory.

NF-κB binding sites are found in the promoter regions of around 300 genes, including cytokines (e.g. TNFα, LTβ, IL-1 and GM-CSF). NF-κB is activated by various stress stimuli, including inflammatory cytokines such as TNFα and IL-1β. NF-κB signalling involves phosphorylation of IκB proteins by the IKK kinase complex. This allows the translocation of an NF-κB dimer (typically RelA:p50) into the nucleus.

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A schematic representation of the NF-κB network.

Real-time fluorescence imaging and mathematical modelling have shown that the activity of the NF-κB system can be oscillatory. After stimulation with TNFa, target gene expression can be regulated by negative feedback loops that modulate the cytoplasmic-nuclear translocation of NF-κB. One of these feedbacks is mediated by IkBa, which upon binding to NF-kB in the nucleus shuttles the NF-κB protein complex back to the cytoplasm. These oscillations have been observed in single cells expressing the fluorescently labeled NF-κB subunit RelA and IkBa in cell lines and primary cells.

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A schematic representation of how the NF-κB network oscillations work. The incoming signal causes phosphorylated of the inhibitory IκBα which is bound to the NF-κB, allowing the transcription factor NF-κB to be liberated and to enter the nucleus. There it turns on the transcription of the IκBα gene causing the production of IκBα mRNA which is then translated in the cytoplasm into protein. This returns to the nucleus, binds to the NF-κB and pulls it back into the cytoplasm so the whole process can run again.

Papers

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

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.

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

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


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


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

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


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

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


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

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


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


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.


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