I am an Associate Professor of Applied Mathematics in the School of Mathematical Sciences at the University of Nottingham.
Prior to that I was an Assistant Professor and I held a Leverhulme Trust Early Career fellowship at the University of Nottingham.
Research
My research focuses on mathematical cell physiology and computational cell biology with a strong emphasis on intracellular calcium signalling. I am particularly interested in how the spatial organisation of intracellular signalling cascades and intrinsic molecular fluctuations shape the formation of signalling micro-domains and whole cell responses. I have developed models for intracellular calcium waves and oscillations using bottom-up as well as top-down approaches. While the former is based on partial differential equations with appropriate descriptions of the calcium signalling toolkit, the latter employs Bayesian ideas and stochastic point processes.
From a more mathematical perspective I have been investigating non-smooth dynamical systems both deterministically and stochastically. Non-smooth dynamical systems provide a natural language for describing a wide variety of real world phenomena ranging from engineering to neuroscience. At the same time, they allow for a deep mathematical analysis, which often requires the generalisation of techniques for smooth dynamical systems such as the master stability function.
Phd students
- Sunil Modhara - Pattern formation in biological neural networks with rebound currents
- Tomas Dean - Multiscale modelling of signalling microdomains
- Jake Powell - Heterogeneity driven cell signalling
- Mustafa Sayli - Nonsmooth network dynamics
- Hayley Mills - Shaping sustainable food production through understanding plant calcium dynamics
- Joshua Veasy - Subcellular calcium patterns in ventricular myocytes (2018)
- Emma McIvor - Modelling store operated calcium entry (2018)
- Agnė Tilūnaitė - Modelling of intracellular calcium dynamics (2017)
- Wilhelm Braun - First passage dynamics in neuron models with stochastic threshold (2015)
- Kyle Wedgwood - Dynamical systems techniques in the analysis of neural systems (2013)
Publications
- Y. M. Lai,
S. Coombes, R. Thul , Calcium buffers and L-type
calcium channels as modulators of cardiac subcellular alternans
, Communications in Nonlinear Science and Numerical
Simulation (2020), accepted
- J. Powell, M.
Falcke, A. Skupin, T. C. Bellamy, T. Kypraios, R. Thul ,
A statistical view on calcium oscillations, Advances in
Experimental Medicine and Biology, 1131, 799 (2020)
DOI
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eprints - M. Sayli, Y.
M. Lai, R. Thul, S. Coombes, , Synchrony in
networks of Franklin bells, IMA Journal of Applied
Mathematics, 85, 1001 (2019)
DOI
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eprints - Y. M. Lay, J.
Veasy, S. Coombes, R. Thul , A master stability
function approach to cardiac alternans, Applied Network
Science, 4, 1812 (2019)
DOI
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eprints - J. Veasy,
Y.M. Lai, S. Coombes, R. Thul, Complex patterns of
subcellular cardiac alternans, Journal of Theoretical
Biology, 478, 102 (2019)
DOI
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eprints - Y. M. Lai, R.
Thul, S. Coombes, Analysis of networks where
discontinuities and nonsmooth dynamics collide: understanding
synchrony, European Physical Journal Special Topics, 227,
1251 (2018)
- E. McIvor, S.
Coombes, R. Thul, Three-dimensional spatio-temporal
modelling of store operated Ca2+ entry: insights into
ER refilling and the spatial signature of Ca2+
signals, Cell Calcium, 73, 11 (2018)
- M. Falkce, M.
Moein, A. Tilunaite, R. Thul, A. Skupin, On the
phase space structure of IP3 induced Ca2+
signalling and concepts for predictive modeling, Chaos, 28,
045115 (2018)
- S. Coombes,
Y. M. Lay, M. Sayli, R. Thul, Networks of piecewise
linear neural mass models, European Journal of Applied
Mathematics (2018)
- A. Tilunaite,
W. Croft, N. Russell, T. C. Bellamy, R. Thul, A
Bayesian approach to modelling heterogeneous calcium responses
in cell populations, PLoS Computational Biology, 13,
e1005794 (2017)
- W. Braun, R.
Thul, A. Longtin, Evolution of moments and
correlations in non-renewal escape-time processes, Physical
Review E, 95, 052127 (2017)
- W. Braun, R.
Thul, Sign changes as a universal concept in
first-passage-time calculations, Physical Review E, 95,
012114 (2017)
- S. Coombes,
R. Thul, Synchrony in networks of coupled non-smooth
dynamical systems: Extending the master stability function,
European Journal of Applied Mathematics, 27, 904 (2016)
- R. Thul, S.
Coombes, C. R. Laing, Neural Field Models with
Threshold Noise, The Journal of Mathematical Neuroscience
6, 1 (2016)
- W. Croft, K. Reusch, A. Tilunaite, N. Russel, R. Thul, T. C. Bellamy, Probabilistic encoding of stimulus strength in astrocyte global calcium signals, Glia. 64, 537 (2016)
- W. Braun, P. C. Matthews, R. Thul, First-passage
times in integrate-and-fire neurons with stochastic thresholds,
Physical Review E, 91, 052701 (2015)
- D. S. Barrack, R. Thul, M. Owen,
Modelling cell cycle synchronisation in networks of coupled
radial glial cells, Journal of Theoretical Biology, 377, 85
(2015)
- R. Thul, K. Rietdorf, M. D. Bootman, S.
Coombes, Unifying principles of calcium wave
propagation — insights from a three-dimensional model for atrial
myocytes, Biochimica et Biophysica Acta - Molecular Cell
Research, 1853, 2131 (2015)
- M Zachariou, R. Thul,
Cannabinoid-mediated short-term plasticity in hippocampus, Journal
of Computational Neuroscience, 37, 533 (2014)
- D. S. Barrack, R. Thul, M. Owen, Modelling
the coupling between intracellular calcium release and the cell
cycle during cortical brain development, Journal of
Theoretical Biology, 347, 17 (2014)
- R. Thul, Translating
intracellular calcium signaling into models, Cold Spring
Harbor Protocols, pdb.top066266 (2014)
- K.C. Wedgwood, K. K. Lin, R. Thul, S.
Coombes, Phase-amplitude descriptions of neural
oscillator models, The Journal of Mathematical
Neuroscience, 3 (2013)
- M. D. Bootman, R. Thul, Calcium:
A Local and Global Messenger in Cells, in V. N. Uversky, R.
H. Kretsinger, E. A. Permyakov (eds), Encyclopedia of
Metalloproteins, 493, (2013)
- R. Thul, S. Coombes, M. D. Bootman, Persistence
of pro-arrhythmic spatio-temporal calcium patterns in atrial
myocytes: a computational study of ping waves, Frontiers in
Computational Physiology and Medicine, 3, 279 (2012)
- R. Thul, S. Coombes, H. L. Roderick, M. D.
Bootman, Subcellular calcium dynamics in a
whole-cell model of an atrial mycoyte, Proceedings of the
National Academy of Sciences, 209, 2150 (2012)
- K. Thurley, A. Skupin, R. Thul, M. Falcke,
Fundamental properties of Ca2+ signals,
Biochimica et Biophysica Acta, 1820, 1185 (2012)
- T. Schendel, R.Thul, J. Sneyd, M. Falcke,
How does the ryanodine receptor in the ventricular myocyte
wake up: by a single or by multiple open L-type Ca2+
channels? European Biophysics Journal, 41, 27 (2012)
- S. Coombes, R. Thul, K. C. A. Wedgwood,
Nonsmooth dynamics in spiking neuron models, Physica D,
241, 2042 (2012)
- S. Coombes, R. Thul, J. Laudanski, A. R.
Palmer, C. J. Sumner, Neuronal spike-train responses
in the presence of threshold noise, Frontiers in Life
Sciences, 5, 91 (2011)
- M. D. Bootman, I. Smyrnias, R. Thul, S.
Coombes, H. L. Roderick, Atrial cardiomyocyte
calcium signalling, Biochimica et Biophysica Acta, 1813,
922 (2011)
- M. Fink, S. A. Niederer, E. M. Cherry, F. H.
Fenton, J. T. Koivumäki, G. Seemann, R. Thul, H. Zhang, F. B.
Sachse, D. Beard, E. J. Crampin, N. P. Smith, Cardiac
cell modelling: Observations from the heart of the cardiac
physiome project, Progress in Biophysics and Molecular
Biology, 104, 2 (2011)
- R. Thul, S. Coombes, Understanding
cardiac alternans: a piecewise linear modelling framework,
Chaos, 20, 045102 (2010)
- R. Thul, S. Coombes, G.D. Smith, Sensitisation
waves in a bidomain fire-diffuse-fire model of intracellular Ca2+
dynamics, Physica D, 238, 2142 (2009)
- R. Thul, K. Thurley, M. Falcke, Torward
a predictive model of Ca2+ puffs, Chaos, 19,
037108 (2009)
- R. Thul, T. C. Bellamy, H. L. Roderick, M.
D. Bootman, S. Coombes, Calcium Oscillations,
in Miguel Maroto and Nick Monk (eds), Cellular Oscillatory
Mechanisms, Springer, Advances in Experimental Medicine and
Biology (2009)
- R. Thul, G. D. Smith, S. Coombes, A
bidomain threshold model of propagating calcium waves,
Journal of Mathematical Biology, 56, 435 (2008)
- R. Thul, M. Falcke, Waiting time
distributions for clusters of complex molecules,
Europhysics Letters, 79, 38003 (2007)
- R. Thul, M. Falcke, Building
oscillations bottom up: elemental time scales of intracellular
calcium dynamics ,in L. Schimansky-Geier, B. Fiedler, J.
Kurths and E. Schöll (eds), Analysis and Control of Complex
Nonlinear Processes in Physics, Chemistry and Biology, World
Scientific (2006)
- R. Thul, M. Falcke, Frequency of
elemental events of intracellular Ca2+ dynamics,
Physical Review E, 73, 061923 (2006)
- R. Thul, M. Falcke, Reactive
clusters on a membrane, Physical Biology, 2, 51 (2005)
- R. Thul, M. Falcke, Stability of
membrane bound reactions, Physical Review Letters, 93,
188103 (2004)
- R. Thul, M. Falcke, Release
currents of IP3 receptor channel clusters and
concentration profiles, Biophysical Journal, 86, 2660
(2004)
- J. Bünemann, F. Gebhard, R. Thul, Landau-Gutzwiller
quasiparticles, Physical Review B, 67, 075103 (2003)
Work with me
Surfing the calcium wave
All of us know calcium. We get a healthy dose of it with every sip of
milk – and doctors tell us that it is good for us. But there is
another facet to it. Without calcium, our heart would stop beating,
information would not be relayed in our brain and our pancreas would
stop producing insulin. The reason for this is that calcium controls
the behaviour of many cells in our body. For example, it determines
the behaviour of millions of muscle cells in the heart, telling them
to contract more than one billion times during an average human
lifespan – which is what we perceive as a heartbeat.
The question that fascinates me is: how does calcium do all of this? It turns out that at the single cell level, the concentration of calcium changes over space and time. It can be in high concentration in only one part of a cell for a small period of time, or it can travel through a cell in the form of a wave – similar to the rippling patterns that we observe when dropping a pebble in a pond. Depending on these different dynamics, cells exhibit different behaviour.
I construct and analyse mathematical models that describe the rich dynamical repertoire of intracellular calcium. I am interested in how cellular geometry shapes calcium signals, and how the random activation and inactivation of molecular switches further controls the intracellular calcium concentration. This requires the application of mathematical techniques from a variety of fields, including network theory. And sometimes we need to develop novel mathematical approaches to unravel the dynamics of this truly universal controller of cellular life.
Potential projects include
- Understanding the dynamics of calcium microdomains in humans and plants
- Bayesian approaches to whole cell calcium spiking
- From molecular dynamics to intracellular calcium waves
The eyes provide a window into the mind
Eye-tracking technology can in part make this statement a reality. It
allows us to monitor people’s eye-movements to determine what they are
attending to and for how long while reading, which allows us to make
inferences about how much cognitive effort they expend doing so.
Importantly, eye-tracking provides a rich moment-to-moment data source
that tells us that it takes us longer to read words that we are not
familiar with, or when there are ambiguities.
One of the things that we can investigate with eye-tracking is the
processing of formulaic language, which is the umbrella term for
constructs such as idioms (“break the ice”), binomials (“salt and
pepper”), collocations (“strong coffee”), etc. More than half of our
daily discourse is made up formulaic language. Eye-tracking
demonstrates that reading is faster for formulaic language (“break the
ice” vs. “crack the ice”) and particularly for their final highly
predictable word(s) – “the straw that broke…. the camel’s back”.
I have become interested in modelling reading behaviour. Given a text, I would like to know how we can predict where our eyes land, and how long we fixate a word. This research is conducted in close collaboration with Dr Kathy Conklin from the School of English, who is an expert in eye-tracking for reading research.
Potential projects include
- Stress testing the EZ reader model
- People with smaller social networks change their language more rapidly