RUEDIGER THUL's Outputs (52)

Oscillatory networks: insights from piecewise-linear modelling (2024)
Journal Article
Coombes, S., Şayli, M., Thul, R., Nicks, R., Porter, M. A., & Lai, Y. M. (2024). Oscillatory networks: insights from piecewise-linear modelling. SIAM Review, 66(4), 619-679. https://doi.org/10.1137/22M1534365

There is enormous interest-both mathematically and in diverse applications-in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology, and more. It is... Read More about Oscillatory networks: insights from piecewise-linear modelling.

EXPRESS: Stratified Distributional Analysis -- a Novel Perspective on RT Distributions (2024)
Journal Article
Thul, R., Marsh, J., Dijkstra, T., & Conklin, K. (2024). EXPRESS: Stratified Distributional Analysis -- a Novel Perspective on RT Distributions. Quarterly Journal of Experimental Psychology, https://doi.org/10.1177/17470218241288516

Response times and their distributions serve as a powerful lens into cognitive processes. We present a novel statistical methodology called Stratified Distributional Analysis (SDA) to quantitatively assess how key determinants of response times (word... Read More about EXPRESS: Stratified Distributional Analysis -- a Novel Perspective on RT Distributions.

The Conversationality Index: A quantitative assessment of conversation in social media interactions (2024)
Journal Article
Cotgrove, L., Thul, R., & Conklin, K. (in press). The Conversationality Index: A quantitative assessment of conversation in social media interactions. Internet Pragmatics,

There has been an explosion in social media use, with Statista estimating that worldwide, Facebook has over 3 billion regular active users, YouTube 2.5 billion, and Instagram and WhatsApp 2 billion. While social media allows one to connect and intera... Read More about The Conversationality Index: A quantitative assessment of conversation in social media interactions.

The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective (2022)
Journal Article
Şaylı, M., Skeldon, A. C., Thul, R., Nicks, R., & Coombes, S. (2023). The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective. Physica D: Nonlinear Phenomena, 444, Article 133595. https://doi.org/10.1016/j.physd.2022.133595

Since its inception four decades ago the two-process model introduced by Borbély has provided the conceptual framework to explain sleep–wake regulation across many species, including humans. At its core, high level notions of circadian and homeostati... Read More about The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective.

Word and Multiword Processing (2022)
Book Chapter
Conklin, K., & Thul, R. (2022). Word and Multiword Processing. In A. Godfroid, & H. Hopp (Eds.), The Routledge Handbook of Second Language Acquisition and Psycholinguistics (203-215). Routledge. https://doi.org/10.4324/9781003018872-20

When we encounter linguistic input, both spoken and written, we need to identify words and multiword sequences (e.g., “spill the beans” meaning “to reveal a secret”), ascertain their meaning, and integrate them into our unfolding understanding of a s... Read More about Word and Multiword Processing.

Neural fields with rebound currents: Novel routes to patterning (2021)
Journal Article
Modhara, S., Lai, Y. M., Thul, R., & Coombes, S. (2021). Neural fields with rebound currents: Novel routes to patterning. SIAM Journal on Applied Dynamical Systems, 20(3), 1596-1620. https://doi.org/10.1137/20M1364710

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. Replicating this success for subcortical tissues, such as the thalamus, r... Read More about Neural fields with rebound currents: Novel routes to patterning.

Using GAMMs to model trial-by-trial fluctuations in experimental data: More risks but hardly any benefit (2021)
Journal Article
Thul, R., Conklin, K., & Barr, D. J. (2021). Using GAMMs to model trial-by-trial fluctuations in experimental data: More risks but hardly any benefit. Journal of Memory and Language, 120, Article 104247. https://doi.org/10.1016/j.jml.2021.104247

Data from each subject in a repeated-measures experiment forms a time series , which may include trial-by-trial fluctuations arising from human factors such as practice or fatigue. Concerns about the statistical implications of such effects have incr... Read More about Using GAMMs to model trial-by-trial fluctuations in experimental data: More risks but hardly any benefit.

Neural Fields with Rebound Currents: Novel Routes to Patterning (2021)
Journal Article
Modhara, S., Lai, Y. M., Thul, R., & Coombes, S. (2021). Neural Fields with Rebound Currents: Novel Routes to Patterning. SIAM Journal on Applied Dynamical Systems, 20(3), 1596-1620. https://doi.org/10.1137/20M1364710

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. To replicate this success for sub-cortical tissues, such as the thalamus,... Read More about Neural Fields with Rebound Currents: Novel Routes to Patterning.

Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans (2020)
Journal Article
Lai, Y. M., Coombes, S., & Thul, R. (2020). Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans. Communications in Nonlinear Science and Numerical Simulation, 85, Article 105181. https://doi.org/10.1016/j.cnsns.2020.105181

In cardiac myocytes, calcium cycling links the dynamics of the membrane potential to the activation of the contractile filaments. Perturbations of the calcium signalling toolkit have been demonstrated to disrupt this connection and lead to numerous p... Read More about Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans.

A master stability function approach to cardiac alternans (2019)
Journal Article
Lai, Y. M., Veasy, J., Coombes, S., & Thul, R. (2019). A master stability function approach to cardiac alternans. Applied Network Science, 4(1), Article 90. https://doi.org/10.1007/s41109-019-0199-z

During a single heartbeat, muscle cells in the heart contract and relax. Under healthy conditions, the behaviour of these muscle cells is almost identical from one beat to the next. However, this regular rhythm can be disturbed giving rise to a varie... Read More about A master stability function approach to cardiac alternans.

A statistical view on calcium oscillations (2019)
Journal Article
Powell, J., Falcke, M., Skupin, A., Bellamy, T., Kypraios, T., & Thul, R. (2019). A statistical view on calcium oscillations. Advances in Experimental Medicine and Biology, 1131, 799-826. https://doi.org/10.1007/978-3-030-12457-1_32

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, whic... Read More about A statistical view on calcium oscillations.

Synchrony in networks of Franklin bells (2019)
Journal Article
Sayli, M., Lai, Y. M., Thul, R., & Coombes, S. (2019). Synchrony in networks of Franklin bells. IMA Journal of Applied Mathematics, 84(5), 1001-1021. https://doi.org/10.1093/imamat/hxz023

The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal be... Read More about Synchrony in networks of Franklin bells.

Complex patterns of subcellular cardiac alternans (2019)
Journal Article
Veasy, J., Lai, Y. M., Coombes, S., & Thul, R. (2019). Complex patterns of subcellular cardiac alternans. Journal of Theoretical Biology, 478, 102-114. https://doi.org/10.1016/j.jtbi.2019.06.016

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A... Read More about Complex patterns of subcellular cardiac alternans.

Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony (2018)
Journal Article
Yi Ming, L., Thul, R., & Coombes, S. (2018). Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony. European Physical Journal - Special Topics, 227(10-11), 1251-1265. https://doi.org/10.1140/epjst/e2018-800033-y

Integrate-and-fire networks have proven remarkably useful in modelling the dynamics of real world phenomena ranging from earthquakes, to synchrony in neural networks, to cascading activity in social networks. The reset process means that such models... Read More about Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony.

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling (2018)
Journal Article
Falcke, M., Moein, M., Tilunaite, A., Thul, R., & Skupin, A. (2018). On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling. Chaos, 28(4), Article 045115. https://doi.org/10.1063/1.5021073

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems, and is the basis of the predictive power of theoretical physics. While physicists have confidence... Read More about On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling.

Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals (2018)
Journal Article
McIvor, E., Coombes, S., & Thul, R. (2018). Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals. Cell Calcium, 73, https://doi.org/10.1016/j.ceca.2018.03.006

The spatial organisation of Orai channels and SERCA pumps within ER-PM junctions is important for enhancing the versatility and specificity of subcellular Ca2+ signals generated during store operated Ca2+ entry (SOCE). In this paper we present a nove... Read More about Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals.

Networks of piecewise linear neural mass models (2018)
Journal Article
Coombes, S., Lai, Y. M., Sayli, M., & Thul, R. (2018). Networks of piecewise linear neural mass models. European Journal of Applied Mathematics, 29(Special issue 5), 869-890. https://doi.org/10.1017/S0956792518000050

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ordinary differential equations with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlase... Read More about Networks of piecewise linear neural mass models.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations (2017)
Journal Article
Tilunaite, A., Croft, W., Russell, N. A., Bellamy, T. C., & Thul, R. (2017). A Bayesian approach to modelling heterogeneous calcium responses in cell populations. PLoS Computational Biology, 13(10), Article e1005794. https://doi.org/10.1371/journal.pcbi.1005794

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding i... Read More about A Bayesian approach to modelling heterogeneous calcium responses in cell populations.

Evolution of moments and correlations in non-renewal escape-time processes (2017)
Journal Article
Braun, W., Thul, R., & Longtin, A. (in press). Evolution of moments and correlations in non-renewal escape-time processes. Physical Review E, 95, https://doi.org/10.1103/PhysRevE.95.052127

The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained... Read More about Evolution of moments and correlations in non-renewal escape-time processes.

Sign changes as a universal concept in first-passage-time calculations (2017)
Journal Article
Braun, W., & Thul, R. (2017). Sign changes as a universal concept in first-passage-time calculations. Physical Review E, 95(12114), https://doi.org/10.1103/PhysRevE.95.012114

First-passage-time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage-time calculations have p... Read More about Sign changes as a universal concept in first-passage-time calculations.

Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function (2016)
Journal Article
Coombes, S., & Thul, R. (2016). Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function. European Journal of Applied Mathematics, 27(6), 904-922. https://doi.org/10.1017/S0956792516000115

The master stability function is a powerful tool for determining synchrony in high-dimensional networks of coupled limit cycle oscillators. In part, this approach relies on the analysis of a low-dimensional variational equation around a periodic orbi... Read More about Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function.

Neural field models with threshold noise (2016)
Journal Article
Thul, R., Coombes, S., & Laing, C. R. (2016). Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6, Article 3. https://doi.org/10.1186/s13408-016-0035-z

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate funct... Read More about Neural field models with threshold noise.

Probabilistic encoding of stimulus strength in astrocyte global calcium signals (2015)
Journal Article
Croft, W., Reusch, K., Tilunaite, A., Russell, N. A., Thul, R., & Bellamy, T. C. (2016). Probabilistic encoding of stimulus strength in astrocyte global calcium signals. Glia, 64(4), 537-552. https://doi.org/10.1002/glia.22947

© 2016 Wiley Periodicals, Inc. Astrocyte calcium signals can range in size from subcellular microdomains to waves that spread through the whole cell (and into connected cells). The differential roles of such local or global calcium signaling are unde... Read More about Probabilistic encoding of stimulus strength in astrocyte global calcium signals.

First passage times in integrate-and-fire neurons with stochastic thresholds (2015)
Journal Article
Braun, W., Matthews, P. C., & Thul, R. (2015). First passage times in integrate-and-fire neurons with stochastic thresholds. Physical Review E, 91, Article 052701. https://doi.org/10.1103/PhysRevE.91.052701

We consider a leaky integrate--and--fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widesprea... Read More about First passage times in integrate-and-fire neurons with stochastic thresholds.

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.

Exploring Oscillations in a Point Model of the Intracellular Ca2+ Concentration (2014)
Journal Article
Thul, R. (2014). Exploring Oscillations in a Point Model of the Intracellular Ca2+ Concentration. Cold Spring Harbor Protocols, 2014(5), 552-555. https://doi.org/10.1101/pdb.prot073221

Intracellular calcium (Ca2+) oscillations are a key signaling mechanism in most cell types. A prominent approach to modeling intracellular Ca2+ oscillations is the use of ordinary differential equations (ODEs), which treat the intracellular Ca2+ conc... Read More about Exploring Oscillations in a Point Model of the Intracellular Ca2+ Concentration.

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.

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.

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.

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.

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.

Atrial cardiomyocyte calcium signalling (2011)
Journal Article
Bootman, M. D., Smyrnias, I., Thul, R., Coombes, S., & Roderick, H. L. (2011). Atrial cardiomyocyte calcium signalling. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1813(5), 922-934. https://doi.org/10.1016/j.bbamcr.2011.01.030

Whereas Ca2+ signalling in ventricular cardiomyocytes is well described, much less is known regarding the Ca2+ signals within atrial cells. This is surprising given that atrial cardiomyocytes make an important contribution to the refilling of ventric... Read More about Atrial cardiomyocyte calcium signalling.

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.

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.

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.

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.

Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics (2007)
Book Chapter
Thul, R., & Falcke, M. (2007). Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics. In L. Schimansky-Geier, B. Fiedler, J. Kurths, & E. Schöll (Eds.), Analysis and control of complex nonlinear processes in physics, chemistry and biology (293-324). World Scientific. https://doi.org/10.1142/9789812706911_0011

We analyze the elemental time scale of intracellular calcium dynamics. It is determined by the time course of Ca2+ puffs, which represent the fundamental quantum of Ca2+ release from intracellular storage compartments. Since Ca2+ puffs are truly rand... Read More about Building oscillations bottom up: Elemental time scales of intracellular calcium dynamics.

Calcium oscillations (2007)
Book Chapter
Thul, R., Bellamy, T., Roderick, L., Bootman, M., & Coombes, S. (2007). Calcium oscillations. In M. Maroto, & N. Monk (Eds.), Cellular Oscillatory Mechanisms. Springer

Changes in cellular calcium concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Calcium can also trigger cell death throu... Read More about Calcium oscillations.

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.

Reactive clusters on a membrane (2005)
Journal Article
Thul, R., & Falcke, M. (2005). Reactive clusters on a membrane. Physical Biology, 2, https://doi.org/10.1088/1478-3967/2/1/007

We investigate the reaction dynamics of diffusive molecules with immobile binding partners. The fixed reactants build clusters that comprise just a few tens of molecules, which leads to small cluster sizes. These molecules participate in the reaction... Read More about Reactive clusters on a membrane.

Release currents of IP₃ receptor channel clusters and concentration profiles (2004)
Journal Article
Thul, R., & Falcke, M. (2004). Release currents of IP₃ receptor channel clusters and concentration profiles. Biophysical Journal, 86(5),

We simulate currents and concentration profiles generated by Ca2+ release from the endoplasmic reticulum (ER)
to the cytosol through IP3 receptor channel clusters. Clusters are described as conducting pores in the lumenal membrane with a diameter f... Read More about Release currents of IP₃ receptor channel clusters and concentration profiles.

Stability of membrane bound reactions (2004)
Journal Article
Thul, R., & Falcke, M. (2004). Stability of membrane bound reactions. Physical Review Letters, 93(18), https://doi.org/10.1103/+PhysRevLet+t.93.188103

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space e.g. by binding to a membrane. The non-diffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length... Read More about Stability of membrane bound reactions.

Landau-Gutzwiller quasi-particles (2003)
Journal Article
Bünemann, J., Gebhard, F., & Thul, R. (2003). Landau-Gutzwiller quasi-particles. Physical Review B, 67, Article 075103. https://doi.org/10.1103/PhysRevB.67.075103

We define Landau quasiparticles within the Gutzwiller variational theory and derive their dispersion relation for general multiband Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were ba... Read More about Landau-Gutzwiller quasi-particles.

Phase-amplitude descriptions of neural oscillator models
Journal Article
Wedgwood, K. C., Lin, K. K., Thul, R., & Coombes, S. Phase-amplitude descriptions of neural oscillator models. Journal of Mathematical Neuroscience, 3(2), https://doi.org/10.1186/2190-8567-3-2

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well... Read More about Phase-amplitude descriptions of neural oscillator models.