Abstract
We investigate the key characteristics of Ca(2+) puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP(3) receptor channel clusters. In the first step, we numerically study the Ca(2+) liberation in a three-dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca(2+) concentrations at a releasing cluster range from 80 to 170 microM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca(2+) concentrations eliminate Ca(2+) oscillations in a deterministic model of an IP(3)R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP(3)R gating dynamics, so that only fluctuations can restore experimentally observed Ca(2+) oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca(2+) puffs and hence the stochastic time scale of intracellular Ca(2+) dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca(2+) oscillations.
Highlights
A paramount task of all cells is to maintain reliable and precise signalling
They catalyse the formation of cyclic adenosine monophosphate (cAMP) from adenosine triphosphate (ATP), which diffuses through the cytosol. cAMP triggers a multitude of reactions including gene expression
This corresponds to a transition from deterministic ordinary differential equations to partial differential equations coupled to stochastic schemes that describe the dynamics of IP3 receptors (IP3Rs) channels
Summary
A paramount task of all cells is to maintain reliable and precise signalling. Such signalling events often consist of cascades of interactions, where the output of one step serves as input to the succeeding one. When hormones in the extracellular space stimulate G–protein coupled receptors that are located in the plasma membrane, membrane bound adenylate cyclases are activated They catalyse the formation of cAMP from adenosine triphosphate (ATP), which diffuses through the cytosol. The traditional route was based on the assumption that cells correspond to well–stirred reactors, i.e. all dynamics was deterministic and spatially homogenous Studies in this spirit [10,11,12,13,14] yielded valuable insights and paved the way for more sophisticated experimental and theoretical investigations. In the quest to unravel the full dynamical repertoire of intracellular Ca2+ dynamics, we need to proceed along new avenues of spatially resolved models that treat Ca2+ release as a stochastic variable This corresponds to a transition from deterministic ordinary differential equations to partial differential equations coupled to stochastic schemes that describe the dynamics of IP3R channels. We suggest a non-Markovian formulation of intracellular Ca2+ dynamics circumventing the drawbacks of partial differential equations and state space explosion at the cell level
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