Building a Wave – Models of the Puff-to-Wave Transition

Abstract

Ca²⁺ release channels open and close randomly because of random binding and dissociation of Ca²⁺ and IP3 to their subunits. They are arranged in clusters on the membrane of the endoplasmic reticulum with each cluster containing a small number of channels only. The concentration profile of free Ca²⁺ resulting from open channels in a cluster decays almost not at all within a cluster but considerably on the length of cluster spacing. Hence, the spatial coupling within clusters is strong but weak between clusters. These circumstances set the stage for modelling of intracellular Ca²⁺ as an array of active stochastic elements. This chapter deals with the consequences of random behavior of single channels for global dynamics. First, experimental findings on the relation between elemental and global events are reviewed. Next, a frame work of stochastic modelling on length scales of many cluster spacings is set up. Modelling starts with the stochastic reaction of Ca²⁺ and IP3 with the receptor subunit. These random events are then coupled by diffusion profiles of single clusters. Global concentration profiles can be obtained as superposition of single cluster profiles.

The random behavior on the cluster level shows up on the global level as nucletion events initiating waves or oscillations with variable period. The consequences for the dependence of the period on experimentally accessible parameters are discussed. We will consider the deterministic limit of the stochastic model. Finally, a more abstract approach is presented allowing to investigate more general principles underlying the stochastic pattern formation.