David Rand

Warwick Mathematics Institute & Zeeman Institute


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The circadian clock and cancer

TimeTeller Algorithm

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Graphical abstract for the TimeTeller algorithm. (A-E) From a transcriptomics analysis of a tissue sample the TimeTeller algorithm produces a likelihood curve as in C. From this TimeTeller uses the associated likelihood ratio curve to provide an estimate of the functionality of the clock in this tissue for this individual, One of the dysfunction metrics is called Θ. E Shows how the distributions for health and cancer tumour samples differ. Current work demonstrates a link between Θ and survival in a breast cancer clinical trial. See below.

TimeTeller & the REMAGUS Breast Cancer Clinical Trial

The circadian timing system controls several critical molecular pathways for cancer processes and treatment effects. While in the cells of most healthy tissues the cell cycle is gated or phase-locked by the circadian clock, cancer cells often escape this control and display altered molecular clocks. Dysregulation of clock genes promotes tumorigenesis through mechanisms involving the cell cycle, DNA damage, and metabolism. Moreover, the circadian clock rhythmically controls many molecular pathways which are responsible for large time-of-day dependent changes in drug toxicity and efficacy, whilst clock gene expression is correlated to anti-cancer drug sensitivity in cancer cell lines. Altered expression of clock genes is associated with key oncogenic pathways and patient survival, and the correlation between clock genes and other genes is altered in cancerous tissues.

We have developed a machine-learning approach to measuring circadian clock functionality from the expression levels of 10-16 key genes in a single tissue sample. The availability of our single sample algorithm TimeTeller potentially allows the determination of clock dysfunction in an individual patient along the course of his or her disease and treatments, the study of its relations with patient outcomes, and the use of such measurements in clinical practice.

To illustrate its utility we applied applied TimeTeller to breast cancer where previous studies have highlighted the relevance of circadian clocks for carcinogenesis and treatment effects but where no simple method would currently allow its measurement in daily oncology practice. We find a strong association between overall and disease-free survival and our measure of clock dysfunction in breast cancer patients.

Recent papers in this area.

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

Coupling between the mamalian clock and cell cycle

Click the movie to start it.
Horizontal axis is clock phase and vertical axis is cell cycle phase. This is data from an experiment, not simulated data. Each dot and triangle corresponds to a cell and if they are joined if they are daughter cells of the same mother cell. The yellow horizontal lines correspond to the cell-cycle phases corresponding to cell division (the top one) and escape from G1 phase to S phase.

This video comes from our paper below. It shows the temporal progression of clock and cell-cycle phases for unstimulated cells in 15% Fetal bovine serum. We show the clock phase on the horizontal axis, illustrated by a bar on the top that shows the relative clock marker level. The vertical axis shows the progression of the cell cycle. The colored bar on the right-hand side illustrates the relative levels of the cell cycle markers (black to red in G1, and grey to yellow in S–G2–M). We also mark the G1–S transition and cell division as horizontal yellow lines. Cells are drawn as blue dots (turning gray once they become confluent) that move from the bottom to the top as they progress through the cell cycle, and from the left to the right according to their clock phase (in this diagram measured as the normalized time between two clock peaks). When they are connected it means that they were the two offspring of a cell that divided during the last circuit. In the background, we show an estimated vector field that indicates the mean direction cells are taking at each point in this phase space. On the sides, we show density estimates for the fraction of cells in each phase. We see that most cells follow a main stream through the middle of the image, crossing the G1–S transition and cell-division lines at a distinct mean clock phase each. Moreover, we observe that some cells skip: They leave the main stream of cells because they progress through the cell cycle phase at a slower speed and rejoin the other cells once they arrive at the main trajectory again. Note that we connect sibling cells by a dashed line when possible. The video was made by Peter Krusche.

Recent paper in this area.

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. Martin1, M. Teboul1, S. Saito, F. Levi, T. Bretschneider, G. T. J. van der Horst, F. Delaunay, D. A. Rand. PNAS (2014) 111(27) 9828-33 www.pnas.org/cgi/doi/10.1073/pnas.1320474111 F1000 recommended.


Francis Levi (Warwick & INSERM), Robert Dallmann (Warwick), Sylvie Giacchetti (Paris), Georg A Bjarnason (Toronto), Denise Vlachou (GSK), G. T. J. van der Horst (Rotterdam), Franck Delaunay (Nice)

Some other papers on the circadian clock

A new mathematical approach to uncovering the link berween structure and function for circadian clocks

Design principles underlying circadian clocks.
D. A. Rand , B. V. Shulgin, D. Salazar , A. J. Millar, Journal of The Royal Society, Interface 1 (2004) online at DOI: 10.1098/rsif.2004.0014

A new mathematical approach to the design principles of circadian clocks

Uncovering the design principles of circadian clocks: Mathematical analysis of flexibility and evolutionary goals.
D.A. Rand, B.V. Shulgin, J.D. Salazar and A.J. Millar Journal of Theoretical Biology, 238(3) (2006) 616-635.

Mathematical analysis of temperature compensation for the Neurospora crassa circadian clock that integrates a large amount of data.

Isoform switching facilitates period control in the Neurospora crassa circadian clock
O. E. Akman, J.C.W. Locke, S. Tang, I. Carré, A. J. Millar & D. A. Rand, Molecular Systems Biology. 4:164 http://www.nature.com/doifinder/10.1038/msb.2008.5 doi:10.1038/msb.2008.5

A new approach to sensitivity analysis

Mapping the global sensitivity of cellular network dynamics: Sensitivity heat maps and a global summation law.
D. A. Rand. J. R. Soc. Interface (2008) 5 S59-S69 doi:10.1098/rsif.2008.0084.focus

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.

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

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

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.

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

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 9 Article number: 650 doi:10.1038/msb.2013.7

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 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)

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. Martin1, M. Teboul1, S. Saito, F. Levi, T. Bretschneider, G. T. J. van der Horst, F. Delaunay, D. A. Rand. PNAS (2014) 111(27) 9828-33 www.pnas.org/cgi/doi/10.1073/pnas.1320474111 F1000 recommended.

Discusses demonic 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.

© David Rand
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