Calcium signalling

Y Timofeeva | Dept of Computer Science | Centre for Complexity Science| University of Warwick

Calcium signalling

DYK model - FDF model - Stochastic FDF model - Intercellular waves

Ca²⁺ dynamics

The discovery of Ca²⁺ oscillations is one of the most significant findings in the field of intracellular signalling within the last two decades. This has radically affected the way biochemical oscillations are viewed. Ca²⁺ oscillations are of interest for a variety of reasons. First, they occur in a large number of cell types, either spontaneously or as a result of stimulation by an external signal such as a hormone or a neurotransmitter. Second, it is now clear that, besides the rhythms encountered in electrically excitable cells, they represent the most widespread oscillatory phenomenon at the cellular level. Third, Ca²⁺ oscillations are often associated with the propagation of Ca²⁺ waves within the cytosol, and sometimes between adjacent cells. This phenomenon has become one of the most important examples of spatio-temporal organisation at the cellular level.

Ca²⁺ is a highly versatile intra- and inter-cellular signal that operates over a wide temporal range that is now known to regulate many different cellular processes, from cell division and differentiation to cell death. Many of the Ca²⁺-signalling components are organised into macromolecular complexes in which Ca²⁺-signalling functions are carried out within highly localised environments. These complexes can operate as autonomous units that can be multiplied or mixed and matched to create larger, more diverse signalling systems, as illustrated by cardiac Ca²⁺ signalling. Rapid highly localised Ca²⁺ spikes regulate fast responses, whereas repetitive global transients or intracellular Ca²⁺ waves control slower responses. Cells respond to such oscillations using sophisticated mechanisms including an ability to interpret changes in frequency. Such frequency-modulated signalling can regulate specific responses such as exocytosis and differential gene transcription.

Cellular Ca²⁺ dynamics involves the exchange of Ca²⁺ ions between intracellular stores and the cytosol, the interior and exterior of a cell or between cells, as well as transport by diffusion and buffering due to the binding of Ca²⁺ to proteins. The mechanism of Ca²⁺ oscillations relies on feedback processes that regulate Ca²⁺ levels within the cell. Two classes of oscillations are readily distinguished: those that depend primarily on the influx of Ca²⁺ through channels from the extracellular space, and those that depend primarily on Ca²⁺ release from internal stores. In this latter class, distinctions can be made on the basis of whether the release of Ca²⁺ is dominated by the ryanodine receptor (RyR), the inositol (1,4,5)- trisphosphate receptor (IP₃R) or a combination of both. The IP₃Rs are Ca²⁺ channels which are opened by the binding of IP₃, generating a gradient-driven flux of Ca²⁺ from the endoplasmic reticulum (ER) into the cytosol (non-muscle cells). RyRs are Ca²⁺ sensitive and control the release of Ca²⁺ from the sarcoplasmic reticulum (SR) (cardiac and skeletal muscle). The autocatalytic release of Ca²⁺ terminates once [Ca²⁺] reaches a sufficiently high level. Beyond this level processes which take up Ca²⁺ from the cytosol dominate the dynamics. These involve transport of Ca²⁺ into the extracellular medium and into the ER/SR by exchangers and pumps. This nonlinear feedback process called Ca²⁺-induced Ca²⁺ release (CICR) generating oscillations in the concentration of cytosolic free Ca²⁺ is believed to underlie the waves that propagate via Ca²⁺ diffusion in a variety of cell types.

Abstract of thesis

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. A fundamental approach for studying cellular signalling is the combination of state of the art experimental techniques, in particular high resolution fluorescence imaging, with spatio-temporal mathematical models of intracellular calcium regulation. Experimental findings can be incorporated into mathematical models and, vice versa, model predictions can be directly tested in experiments. This approach provides a powerful tool to clarify the very complex mechanisms involved in cellular Ca²⁺ signalling.

The aim of this thesis is to provide insight into oscillations and waves of cytosolic Ca²⁺ in both single and multi-cellular systems from a mathematical perspective. We focus on two models of Ca²⁺ release for a systematic mathematical and numerical analysis of Ca²⁺ dynamics. One of them is a biophysically detailed model which we study using tools from bifurcation theory, numerical continuation and numerical simulation. The other is a much simpler minimal model of Ca²⁺ dynamics that emphasises the fundamental space and time scales of cellular Ca²⁺ dynamics and allows for exact mathematical analysis. For the detailed biophysical model we calculate the speed and stability of travelling waves as a function of physiologically significant parameters. The minimal model of Ca²⁺ dynamics is obtained via a systematic reduction of the biophysical model and its analytically obtained behaviour is shown to be in excellent agreement with the original biophysical model. This minimal model is then used to gain insight into the effects of spatial heterogeneity and biologically realistic sources of noise on intra- and inter-cellular cell signalling. In particular we pursue issues of wave propagation, wave propagation failure and the role of noise in generating coherent whole cell rhythms.

Keywords: calcium, puffs/sparks, Fire-diffuse-fire model, noise, stochastic propagation, intracellular and intercellular waves, non-equilibrium phase-transition.

Y Timofeeva | Dept of Computer Science | Centre for Complexity Science| University of Warwick

y.timofeeva@warwick.ac.uk

http://www.dcs.warwick.ac.uk/~yulia/