David Rand's current research interests
On this page I list some of my current research interests.
Circadian clocks
Current Collaborators: Andrew Millar, Isobelle Carre, Ozgur Akman, Paul Brown.
Funding: EPSRC & BBSRC
Publications & preprints: Design principles underlying circadian clocks, D. A. Rand, B. V. Shulgin, J. D. Salazar & A. J. Millar. Journal of The Royal Society, Interface 1 (2004) online at DOI: 10.1098/rsif.2004.0014 (new Royal Society journal specifically for the physical & mathematical sciences interface with biology) (to appear) PDF Supplementary Info
Uncovering the design principles of circadian clocks: Mathematical analysis of flexibility and evolutionary goals. D. A. Rand, B. V. Shulgin, J. D. Salazar & A. J. Millar. 45 pp Journal of Theoretical Biology, 238(3) (2006) 616-635. PDF
Global temperature compensation and extended functionality for the Neurospora crassa circadian clock. O. E. Akman, J.C.W. Locke, S. Tang, I. Carré, A. J. Millar & D. A. Rand, . Submitted
Bifurcation analysis of phase bistability in circadian clocks forced by skeleton photoperiod, B. V. Shulgin, A. J. Millar and D. A. Rand. to be submitted
D. A. Rand. Mapping the global sensitivity of cellular network dynamics.. Submitted.
Software. See my main web page.
More details: See web page. Millar Lab
. web site.
Statistical estimation of parameters and structure of regulatory networks
Collaborators: Baebel Finkenstadt, Alex Morton, Elizabeth Horton, Paul Anderson.
Funding: EPSRC & BBSRC
Publications & preprints:
Heron E., Finkenstadt B., Rand D. Statistical inference for delayed transcriptional gene regulation, an application to the Hes1 system. Bioinformatics (2007) doi: 10.1093/bioinformatics/btm367
D. A. Rand. Mapping the global sensitivity of cellular network dynamics.. Submitted.
B F Finkenstädt, A Morton & D. A. Rand, Measuring antigenic drift and surge in Influenza: statistical inference on immunity loss. Statistics in Medicine. 24(22) (2005) 3447-3461.
More details: IPCR Newsletter
NF-kB and Other Signalling and Transcription Systems
Collaborators: Michael White, Julian Davis, Claire Harper, Baerbel Finkenstadt
Major Grant. Dynamics and functon of the NF-kB signaling system.
Grant from Systems Approaches to Biological Research (SABR) initiative, 2007. Joint bid led by Prof. M White (Liverpool) and Rand. Project co-directors Mike White and Rand will be assisted by a small management team.
Total grant funding: approx. £5.8m (100% FEC).
Warwick share: £931,771 (100% FEC), £745,416.81 (80% FEC)
Summary. We will develop an integrated systems biology programme to analyse the dynamic and physiological function of the NF-kappaB signalling system. We previously applied iterative real-time imaging and mathematical modelling approaches to show that the NF-kappaB system is oscillatory and uses delayed negative feedback to direct nuclear to cytoplasmic cycling of transcription factor(s) that regulate gene expression. Our recent work has made clear how little is currently understood about even the core parts of the NF-kappaB system and only included a small subset of the NF-?B proteins and feedback loops. We will develop and apply a set of quantitative experimental tools coupled to an intensive theoretical analysis to properly analyse the dynamic function of the system. A key question is how cells achieve appropriate cell fate decisions in response to time-varying signals. Our team includes the expertise to measure and simulate the important processes involved in the core NF-?B network and is supported by leading technology companies.. The experimental work (involving network perturbations) will integrate dynamic cell and single molecule imaging, quantitative proteomics (for measurement of absolute protein and phosphoprotein levels and rates of turnover), chromatin immunoprecipitation (ChIP) analysis (for the dynamics of NF-kappaB binding to target promoters) and RT-PCR and DNA microarray analysis (for measurement of endogenous gene expression). The theoretical work will develop: 1) new data analysis tools to interpret and direct experimental strategy, 2) deterministic and 3) stochastic mathematical models of the system. The computer simulations will develop new experimentally testable hypotheses. Our goal is complete understanding of this complex and non-linear system. We will determine how the set of complex feedback loops controls NF-kappaB dynamics and controls downstream gene
Signalling networks in plant stress responses
Collaborators: J L Beynon, V Buchanan-Wollaston, K Denby, M Grant (Exeter), P Mullineaux (Essex), S. Ott, D Wild.
Major Grant. Transcriptional response to stress in plants. Grant from Systems Approaches to Biological Research (SABR) initiative, 2007. Joint bid led by WSB and WHRI with Essex and Exeter. The project will be led by JB (biology) and DR (theory) and managed by a steering group consisting of the named applicants. Collaborators: (Warwick) Beynon, Buchanan-Wollaston, Denby, Ott, Rand, Wild. Key (External) M Grant (Exeter), P Mullineaux (Essex).
Total grant funding: approx. £5.6m (100% FEC).
Warwick share: £4,408,159 (100% FEC), £3,549,385 (80% FEC
Summary. We aim to build a mathematical model of how the plant leaf switches between alternative responses during environmental challenges (e.g. pathogens, water limitation, changes in light intensity, senescence). Plants respond to biotic and abiotic stress using a range of transcriptional and physiological response pathways many of which are shared between different stress stimuli. A crucial question is how plants switch between different stress responses and the balance of these response pathways when multiple stresses are perceived. In this project using systems modelling we propose to integrate the response pathways from three biotic (infection by Pseudomonas syringae, Hyaloperonospora parasitica, Botrytis cinerea) and two abiotic (drought and high light) stress responses in the leaf. Initially we will produce high resolution time course transcript profiles of our stress responses. We will cluster genes based on their temporal expression profiles. Using these data and prior information we will use state space modelling to create course grain network models. Networks common to more than one stress or containing key genes with different targets will be analysed further. A reiterative process will be used to verify the models by producing mutations or overexpression constructs for the nodal genes and measuring their consequence on gene expression and host plant phenotype. Promoter motif modelling will be used to aid in identification of gene regulatory networks. As the project develops we will focus on 2-4 networks to model at a higher resolution where we will identify and confirm the linkages between genes using a range of experimental techniques. We aim to produce a linking course grain network that models plant leaf responses to environmental stress and detailed models of 2-4 networks involved in switching between different stress responses. This is intimately related to the €12m Plant Systems Biology Integrated Project AGRON-OMICS that we are members of (led for us by Jim Beynon).
Regulation Of Biological Signalling by Temperature (ROBuST).
Major Grant. Regulation Of Biological Signalling by Temperature (ROBuST).
Grant from Systems Approaches to Biological Research (SABR) initiative, 2007. Joint bid led by Dr K Halliday (Edinburgh) and joint with Edinburgh’s SB Centre CSBE. Rand is Warwick PI.
Total grant funding: approx. £5.8m (100% FEC).
Warwick share: £822,444 (100% FEC), £657,955 (80% FEC)
Summary. Understanding robustness and sensitivity of networks is a key goal of systems biology. We will investigate for the first time how a complex signalling network responds to temperature. Our system comprises the Arabidopsis light, circadian clock and cold tolerance pathways, parts of which are buffered against temperature while other responses are exquisitely sensitive. The system is well characterised under standard conditions, and the applicants are leaders in identifying and modelling the effects of temperature on this network. We will, therefore, abstract a model capturing this knowledge, incorporating and expanding on our published model of the circadian clock. A comprehensive assessment of how each component responds to temperature will be key to understanding the buffering capacity of the system. Using specific expertise and facilities at the collaborating institutions, we will investigate:
- promoter activity, RNA expression, RNA/protein abundance and degradation, and protein/protein interaction at the molecular level
- localisation and co-localisation at the sub-organelle, sub-cellular and cellular level
- how mutating genes within the network alters the buffer capacity
- how altering the temperature sensitivity of this system affects whole-plant performance
The experimental data will be compiled in order to estimate new parameter values: here, recently-developed statistical methods can make best use of our high-quality, timeseries data from intact plants. A new mathematical approach to model simplification will allow us to focus our studies on reduced models of the key components identified from the data, in a rigorous and principled way. As demonstrated by the enthusiastic support from industry, the knowledge base and modelling tools will contribute to developing higher-yielding crops resistant to environmental stresses, such as increasing global temperatures. Our programme will also provide extensive training of personnel in systems biology.
Systems approach to tissue level electro-genesis in smooth muscle
Collaborators: Andy Blanks, Hugo van den Berg, Tony Shmygol, Steve Thornton, Hen Gui Zhang (Manchester), Aran Holden (Leeds), Mike Taggart (Manchester).
Research Project. Measuring and modelling coupled heterogeneous networks; a systems approach to tissue level electro-genesis in smooth muscle
PI was Dr Tony Shmygol (WMS) who led the experimental side. Hugo van den Berg (WSB) led the mathematical/theoy side. Warwick co-PIs: A Blanks (WMS), D A Rand (WSB), M. Richardson (WSB), S Thornton (WMS). External co-PIs: M Taggart (Manchester), H, Zhang (Manchester), A Holden (Leeds)
Total grant funding: approx. £4.3m (100% FEC).
Warwick share: £2,477,730 (100% FEC), £2,008,184 (80% FEC)
Summary. An ubiquitous challenge, cutting across different levels of biological organization, is to infer the functional characteristics of a complex tissue on the basis of gene expression profiles within the heterogeneous cell population. Taking one such complex electrically excitable tissue / the uterus - as our model, a principle goal of this proposal is to "add a layer of physiology to genomics": to predict tissue level physiological changes on the basis of expression patterns of genes encoding proteins involved in electrogenesis, and, moreover, to understand how various cell types interact to form complex action potential waveforms that initiate uterine contraction and childbirth. Tackling such a complex problem requires multidisciplinary approach. This research programme involves collaboration between Warwick Centre for Systems Biology, the Warwick Medical School, Maternal & Fetal Health Research Centre and School of Physics and Astronomy at Manchester University and Institute for Membrane and Systems Biology at the of University Leeds in order to develop a systems biology approach to mechanisms of tissue level electrogenesis in uterine smooth muscle. In a "middle-out" approach we propose to integrate genomics, in situ proteomics, electrophysiology (at both the cellular and tissue levels), 3D histology, bioinformatics, dynamical modelling and advanced statistical data analysis techniques to characterize how tissue-level electro-genesis emerges from events at the molecular and cellular levels. Building on these cutting-edge, but proven, techniques, we will pioneer a new genomics-driven approach, predicting changes in tissue-level physiology on the basis of shifts in gene expression patterns, which can be readily determined in high-throughput assays. This new approach should have wide applicability, since the challenge of inferring tissue-level physiology from data at the molecular and cellular levels arises in many biological systems.
Spatio-temporal patterning of flowers
Collaborators: Sanyi Tang.
Funding: EPSRC & BBSRC
Timing of flowering
Collaborators: Andrew Millar, Isobelle Carre, Domingo Salazar, Paul Brown.
J D Salazar, T Saithong, P E. Brown, J Foreman, J C.W. Locke, I. A. Carré, D A. Rand and A J. Millar, Prediction of unknown regulators from gene circuit models based on molecular data: the photoperiod response in Arabidopsis thaliana. Submitted.
Funding: EPSRC & BBSRC
Immunology: T cell activation
Collaborators: Hugo van den Berg, Nigel Burroughs, Zorana Najdanovic
Funding: EPSRC & BBSRC
More details: survey article, IPCR Newsletter
Publications:(with H. A. van den Berg & N. J. Burroughs), A reliable and safe T cell repertoire based on low-affinity receptors. J. Theor. Biol. 209 (2001) 465-486. PDF
(with H van den Berg and N J Burroughs) Quantifying the strength of ligand antagonism in TCR triggering. Bull. Math. Biol. 64 (2002) 781-808. PDF
(with H van den Berg) Antigen presentation as a diversity filter that enhances immune efficacy. J. Theor. Biol. 224(2) 2003 249-267. PDF
H A van den Berg & D. A. Rand, Dynamics of T cell activation threshold tuning. J. Theor. Biol. 228 (2004) 397-416. PDF
H van den Berg & D. A. Rand, Foreigness as a matter of degree: The relative immunogenicity of peptide/MHC ligands. J. Theor. Biol. 231 (2004) 535-548
H van den Berg & D. A. Rand, Quantitative theories of T cell responsiveness. Immunological Reviews. 216(1) (2007) 81-92.
Games played on networks
Publications:Games with correlations. 35pp.
Correlations and the invasion of cooperation in the Prisoner’s Dilemma. 4pp.
More details: preprint.
Hyperbolic systems on surfaces; explicit construction of geometric measures; smooth pseudo-Anosov systems; rigidity of circle maps and foliatiations
Collaborators: A A Pinto, F. Ferreira
Publications: A. A. Pinto & D. A. Rand, Classifying C1+ structures on dynamical fractals: 1. The moduli space of solenoid functions for Markov maps on train tracks. Ergodic Theory and Dynamical Systems. 15 (1995) 697-734.
A. A. Pinto & D. A. Rand, Classifying C1+ structures on dynamical fractals: 2. Embedded trees. Ergodic Theory and Dynamical Systems. 15 (1995) 969-992
A. A. Pinto & D. A. Rand, Existence, uniqueness and ratio decomposition for Gibbs states via duality. Ergodic Theory & Dynamical Systems 21 (2) (2001) 533-544.
A. A. Pinto & D. A. Rand, Smoothness of holonomies for codimension 1 hyperbolic dynamics.. Bull. London Mathematical Society 34 (2002) 341-352
A. A. Pinto & D. A. Rand, Teichmüller spaces and HR structures for hyperbolic surface dynamics. Ergodic Theory and Dynamical Systems 22(6) (2002) 1905-1931.
A. A. Pinto & D. A. Rand, Rigidity of hyperbolic surface dynamics. J. Lond. Math. Soc. 71(2) (2004) 481-502.
(with F. Ferreira & A. A. Pinto) Hausdorff dimension bounds smoothness of holonomies for codimension one hyperbolic attractors. Preprint to appear in J. Diff. Eqns. PDF
F. Ferreira, A. A. Pinto & D. A. Rand, Cantor exchange systems and renormalization. J. Diff. Eqns. (to appear)
A. A. Pinto & D. A. Rand, Geometric measures for hyperbolic surface dynamics. Submitted Preprint 40pp PDF
A Pinto & D. A. Rand, Solenoid functions for hyperbolic sets on surfaces. Recent Progress in Dynamics, MSRI Publications 54, (2007), 145-178.
Address:
Mathematics Institute
University of Warwick
Coventry CV4 7AL
United Kingdom