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Modeling electrocortical activity through improved local approximations of integral neural field equations (2007)
Journal Article
Coombes, S., Venkov, N., Shiau, L., Bojak, I., Liley, D., & Laing, C. (2007). Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76(5), https://doi.org/10.1103/PhysRevE.76.051901

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equatio... Read More about Modeling electrocortical activity through improved local approximations of integral neural field equations.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities (2007)
Journal Article
Owen, M. R., Laing, C., & Coombes, S. (2007). Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities. New Journal of Physics, 9(378), https://doi.org/10.1088/1367-2630/9/10/378

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model... Read More about Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities.

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.

Dynamic instabilities in scalar neural field equations with space-dependent delays (2007)
Journal Article
Venkov, N. A., Coombes, S., & Matthews, P. C. (2007). Dynamic instabilities in scalar neural field equations with space-dependent delays. Physica D: Nonlinear Phenomena, 232(1), 1-15. https://doi.org/10.1016/j.physd.2007.04.011

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynam... Read More about Dynamic instabilities in scalar neural field equations with space-dependent delays.

Liquid film dynamics in horizontal and tilted tubes: dry spots and sliding drops (2007)
Journal Article
King, A. A., Cummings, L. J., Naire, S., & Jensen, O. E. (2007). Liquid film dynamics in horizontal and tilted tubes: dry spots and sliding drops. Physics of Fluids, 19(4), Article 042102. https://doi.org/10.1063/1.2714569

Using a model derived from lubrication theory, we consider the evolution of a thin viscous film coating the interior or exterior of a cylindrical tube. The flow is driven by surface tension and gravity and the liquid is assumed to wet the cylinder p... Read More about Liquid film dynamics in horizontal and tilted tubes: dry spots and sliding drops.

Branching dendrites with resonant membrane: a "sum-over-trips" approach (2007)
Journal Article
Coombes, S., Timofeeva, Y., Svennson, C., Lord, G., Josic, K., Cox, S. J., & Colbert, C. (2007). Branching dendrites with resonant membrane: a "sum-over-trips" approach. Biological Cybernetics, 97(2), https://doi.org/10.1007/s00422-007-0161-5

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dend... Read More about Branching dendrites with resonant membrane: a "sum-over-trips" approach.

Elucidating the interactions between the adhesive and transcriptioanl functions of beta-catenin in normal and cancerous cells (2007)
Journal Article
van Leeuwen, I. M. M., Byrne, H. M., Jensen, O. E., & King, J. R. (2007). Elucidating the interactions between the adhesive and transcriptioanl functions of beta-catenin in normal and cancerous cells. Journal of Theoretical Biology, 247(1), 77-102. https://doi.org/10.1016/j.jtbi.2007.01.019

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential... Read More about Elucidating the interactions between the adhesive and transcriptioanl functions of beta-catenin in normal and cancerous cells.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation (2007)
Journal Article
Coombes, S., & Owen, M. R. (2007). Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognize... Read More about Exotic dynamics in a firing rate model of neural tissue with threshold accommodation.

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.

Conditional moment closure for chemical reactions in laminar chaotic flows (2007)
Journal Article
Vikhansky, A., & Cox, S. M. (2007). Conditional moment closure for chemical reactions in laminar chaotic flows. AIChE Journal, 53(1),

We implement conditional moment closure (CMC) for simulation of chemical reactions in laminar chaotic flows. The CMC approach predicts the expected concentration of reactive species, conditional upon the concentration of a corresponding nonreactive s... Read More about Conditional moment closure for chemical reactions in laminar chaotic flows.

Two-dimensional Stokes flow driven by elliptical paddles (2007)
Journal Article
Cox, S. M., & Finn, M. D. (2007). Two-dimensional Stokes flow driven by elliptical paddles. Physics of Fluids, 19(11), https://doi.org/10.1063/1.2789970

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods.... Read More about Two-dimensional Stokes flow driven by elliptical paddles.

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.