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Modelling cell cycle synchronisation in networks of coupled radial glial cells (2015)
Journal Article
Barrack, D., Thul, R., & Owen, M. R. (2015). Modelling cell cycle synchronisation in networks of coupled radial glial cells. Journal of Theoretical Biology, 377, https://doi.org/10.1016/j.jtbi.2015.04.013

Radial glial cells play a crucial role in the embryonic mammalian brain. Their proliferation is thought to be controlled, in part, by ATP mediated calcium signals. It has been hypothesised that these signals act to locally synchronise cell cycles, so... Read More about Modelling cell cycle synchronisation in networks of coupled radial glial cells.

Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes (2015)
Journal Article
Thul, R., Rietdorf, K., Bootman, M. D., & Coombes, S. (2015). Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1853(9), https://doi.org/10.1016/j.bbamcr.2015.02.019

Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heartbeat exhibit complex spatio-temporal dynamics. These calcium patterns arise from saltatory calcium waves tha... Read More about Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes.

Cannabinoid-mediated short-term plasticity in hippocampus (2014)
Journal Article
Zachariou, M., & Thul, R. (2014). Cannabinoid-mediated short-term plasticity in hippocampus. Journal of Computational Neuroscience, 37(3), https://doi.org/10.1007/s10827-014-0518-4

Endocannabinoids modulate both excitatory and inhibitory neurotransmission in hippocampus via activation of pre-synaptic cannabinoid receptors. Here, we present a model for cannabinoid mediated short-term depression of excitation (DSE) based on our r... Read More about Cannabinoid-mediated short-term plasticity in hippocampus.

Time to blip – stochastic simulation of single channel opening (2014)
Journal Article
Thul, R. (2014). Time to blip – stochastic simulation of single channel opening. Cold Spring Harbor protocols, https://doi.org/10.1101/pdb.prot073239

The stochastic dynamics of the inositol-1,4,5-trisphosphate (IP3) receptor (IP3R) is key to understanding a wide range of observed calcium (Ca2+) signals (Falcke 2004). The stochastic nature results from the constant binding and unbinding of Ca2+ and... Read More about Time to blip – stochastic simulation of single channel opening.

Oscillations in a point models of the intracellular Ca2+ concentration (2014)
Journal Article
Thul, R. (2014). Oscillations in a point models of the intracellular Ca2+ concentration. Cold Spring Harbor protocols, https://doi.org/10.1101/pdb.prot073221

Oscillations in the intracellular calcium (Ca2+) concentration form one of the main pathways by which cells translate external stimuli into physiological responses (Thul et al. 2008; Dupont et al. 2011; Parekh 2011). The mechanisms that underlie the... Read More about Oscillations in a point models of the intracellular Ca2+ concentration.

Translating intracellular calcium signaling into models (2014)
Journal Article
Thul, R. (2014). Translating intracellular calcium signaling into models. Cold Spring Harbor protocols, https://doi.org/10.1101/pdb.top066266

The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review... Read More about Translating intracellular calcium signaling into models.

Modelling the coupling between intracellular calcium release and the cell cycle during cortical brain development (2014)
Journal Article
Barrack, D., Thul, R., & Owen, M. R. (2014). Modelling the coupling between intracellular calcium release and the cell cycle during cortical brain development. Journal of Theoretical Biology, 347, https://doi.org/10.1016/j.jtbi.2014.01.004

Most neocortical neurons formed during embryonic brain development arise from radial glial cells which communicate, in part, via ATP mediated calcium signals. Although the intercellular signalling mechanisms that regulate radial glia proliferation ar... Read More about Modelling the coupling between intracellular calcium release and the cell cycle during cortical brain development.

Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves (2012)
Journal Article
Thul, R., Coombes, S., & Bootman, M. D. (2012). Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves. Frontiers in Physiology, 3, Article 279. https://doi.org/10.3389/fphys.2012.00279

Clusters of ryanodine receptors within atrial myocytes are confined to spatially separated layers. In many species, these layers are not juxtaposed by invaginations of the plasma membrane (transverse tubules; 'T-tubules'), so that calcium-induced-cal... Read More about Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves.

Neuronal spike-train responses in the presence of threshold noise (2012)
Journal Article
Coombes, S., Thul, R., Laudanski, J., Palmer, A., & Sumner, C. (in press). Neuronal spike-train responses in the presence of threshold noise. Frontiers in Life Science, 5(3-4), https://doi.org/10.1080/21553769.2011.556016

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent chan... Read More about Neuronal spike-train responses in the presence of threshold noise.

Subcellular calcium dynamics in a whole-cell model of an atrial myocyte (2012)
Journal Article
Thul, R., Coombes, S., Roderick, H. L., & Bootman, M. D. (2012). Subcellular calcium dynamics in a whole-cell model of an atrial myocyte. Proceedings of the National Academy of Sciences, 109(6), 2150-2155. https://doi.org/10.1073/pnas.1115855109

In this study, we present an innovative mathematical modeling approach that allows detailed characterization of Ca 2+ movement within the three-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic re... Read More about Subcellular calcium dynamics in a whole-cell model of an atrial myocyte.

Fundamental properties of Ca²⁺ signals (2011)
Journal Article
Thurley, K., Skupin, A., Thul, R., & Falcke, M. (2011). Fundamental properties of Ca²⁺ signals. BBA - General Subjects, 1820(8), https://doi.org/10.1016/j.bbagen.2011.10.007

Background Ca²⁺ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca²⁺ concentration. Recent investigations changed basic ideas on the dynamic character of Ca²⁺ signals and challenge tradition... Read More about Fundamental properties of Ca²⁺ signals.

Nonsmooth dynamics in spiking neuron models (2011)
Journal Article
Coombes, S., Thul, R., & Wedgwood, K. C. (2012). Nonsmooth dynamics in spiking neuron models. Physica D: Nonlinear Phenomena, 241(22), https://doi.org/10.1016/j.physd.2011.05.012

Large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue. One approach in computational neuroscience has been to consider the detailed electrophysiological propertie... Read More about Nonsmooth dynamics in spiking neuron models.

Cardiac cell modelling: observations from the heart of the cardiac physiome project (2011)
Journal Article
Fink, M., Niederer, S. A., Cherry, E. M., Fenton, F. H., Koivumäki, J. T., Seemann, G., …Smith, N. P. (2011). Cardiac cell modelling: observations from the heart of the cardiac physiome project. Progress in Biophysics and Molecular Biology, 104(1-3), https://doi.org/10.1016/j.pbiomolbio.2010.03.002

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In... Read More about Cardiac cell modelling: observations from the heart of the cardiac physiome project.

Understanding cardiac alternans: a piecewise linear modeling framework (2010)
Journal Article
Thul, R., & Coombes, S. (2010). Understanding cardiac alternans: a piecewise linear modeling framework. Chaos, 20, https://doi.org/10.1063/1.3518362

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca²⁺) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of the... Read More about Understanding cardiac alternans: a piecewise linear modeling framework.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics (2009)
Journal Article
Thul, R., Coombes, S., & Smith, G. (2009). Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D: Nonlinear Phenomena, 238, https://doi.org/10.1016/j.physd.2009.08.011

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitl... Read More about Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics.

Towards a predictive model of Ca²⁺ puffs (2009)
Journal Article
Thul, R., Thurley, K., & Falcke, M. (2009). Towards a predictive model of Ca²⁺ puffs. Chaos, 19, https://doi.org/10.1063/1.3183809

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dim... Read More about Towards a predictive model of Ca²⁺ puffs.

A bidomain threshold model of propagating calcium waves (2007)
Journal Article
Thul, R., Smith, G., & Coombes, S. (2008). A bidomain threshold model of propagating calcium waves. Journal of Mathematical Biology, 56(4), https://doi.org/10.1007/s00285-007-0123-5

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travell... Read More about A bidomain threshold model of propagating calcium waves.

Waiting time distributions for clusters of complex molecules (2007)
Journal Article
Thul, R., & Falcke, M. (2007). Waiting time distributions for clusters of complex molecules. EPL, 79(3), https://doi.org/10.1209/0295-5075/79/38003

Waiting time distributions are in the core of theories for a large variety of subjects ranging from the analysis of patch clamp records to stochastic excitable systems. Here, we present a novel exact method for the calculation of waiting time distrib... Read More about Waiting time distributions for clusters of complex molecules.

Frequency of elemental events of intracellular Ca²⁺ dynamics (2006)
Journal Article
Thul, R., & Falcke, M. (2006). Frequency of elemental events of intracellular Ca²⁺ dynamics. Physical Review E, 73, Article 061923. https://doi.org/10.1103/PhysRevE.73.061923

The dynamics of intracellular Ca²⁺ is driven by random events called Ca²⁺ puffs, in which Ca²⁺ is liberated from intracellular stores. We show that the emergence of Ca²⁺ puffs can be mapped to an escape process. The mean first passage times that corresp... Read More about Frequency of elemental events of intracellular Ca²⁺ dynamics.