Langevin modeling of intracellular calcium dynamics

Recent progress in fluorescent imaging technology has revealed that Ca 2+ is released from the endoplasmic reticulum (ER) through clusters that are about 0.1µm in extent and comprise no more than 20-50 release channels. The calcium flux released by such small channel clusters exhibits significant stochasticity due to thermal fluctuations. These fluctuations have been simulated successfully by using Markov models for the binding and unbinding processes at the subunits based on the DeYoung-Keizer model (DeYoung and Keizer 1992). For whole cell and intercellular modeling of Ca 2+ signaling the DeYoung-Keizer model with its numerous variables is computationally too demanding. Hence, computationally less expensive but yet accurate algorithms are desirable. In this chapter we report on recent work of our group towards a Langevin approach for calcium dynamics. The starting point is the stochastic DeYoung-Keizer model. In a first step, we simplify towards a stochastic Li-Rinzel approach where the slow inactivation process is treated stochastically by a Markov process, but the other faster processes are approximated by their mean values. In a second step, the Markov process is described by a master equation that is then approximated by a Fokker-Planck equation and subsequently by a Langevin equation. The Langevin equation has the same form as the deterministic 2-variable Li-Rinzel model except that a noise-term is added where the strength is related to the size of the release cluster. We compare characteristic quantities of the calcium release such as mean values and variances, puff amplitude distributions, puff-width distributions and inter-puff interval distributions generated by an isolated cluster of release channels with all three methods and discuss conditions under which the stochastic Li-Rinzel model and the Langevin approach produce results consistent with the DeYoung-Keizer model. The Langevin approach produces results consistent with the other methods although the necessary compute time is reduced by more than a factor of 10 even for cluster sizes of 20 channels. Furthermore, the compute time required by the Langevin approach to mimic a single cluster does not increase with the size of the cluster.