Deriving Cellular Ca(2+) Dynamics from Puff Characteristics - A New Approach in Mathematical Modeling

Abstract

It has recently been shown that Ca(2+) spikes are stochastic and that the Ca(2+) concentration is subject to huge intracellular gradients. These findings underline the need for stochastic models taking single molecule state transitions into account (Master Equations are impossible due to the high number of states). We developed such a modeling concept based on the fact that for cellular concentration dynamics, it is only relevant whether channels are open or closed, but not in which open or closed state they are. That requires a non-Markovian formulation of the theory which we will present. This formulation permits direct integration of measurable quantities into the model, whereas detailed knowledge of physiologic parameters is not necessary. Therefore, input and output can be directly compared with experiments, if we consider observables like the probability that no spike happens or the average spike length. The model covers experimentally observed modes of system behavior like bursting, spiking or local events. Statistic properties of interspike intervals are in good accordance with experimental data. Since we have developed an analytic description as well as an efficient simulation algorithm, we are in a position to analyze a broad range of possible system configurations based on a solid theoretical background. In particular, we find that the spiking pattern can be predicted merely from two parameters, the cluster coupling and the average channel open time. The latter is probably constant and the former can be regulated by second messengers or by the number of active clusters, e. g. This implies that local dynamics emerges to a single control parameter determining global dynamics. Since we expect similar mechanisms to work in various fields of biology (e.g. cAMP dynamics and DNA replication), our theory should be widely applicable.