Simulation Strategies for Calcium Microdomains and Calcium Noise

In this article, we present an overview of simulation strategies in the context of subcellular domains where calcium-dependent signaling plays an important role. The presentation follows the spatial and temporal scales involved and represented by each algorithm. As an exemplary cell type, we will mainly cite work done on striated muscle cells, i.e. skeletal and cardiac muscle. For these cells, a wealth of ultrastructural, biophysical and electrophysiological data is at hand. Moreover, these cells also express ubiquitous signaling pathways as they are found in many other cell types and thus, the generalization of the methods and results presented here is straightforward.The models considered comprise the basic calcium signaling machinery as found in most excitable cell types including Ca²⁺ ions, diffusible and stationary buffer systems, and calcium regulated calcium release channels. Simulation strategies can be differentiated in stochastic and deterministic algorithms. Historically, deterministic approaches based on the macroscopic reaction rate equations were the first models considered. As experimental methods elucidated highly localized Ca²⁺ signaling events occurring in femtoliter volumes, stochastic methods were increasingly considered. However, detailed simulations of single molecule trajectories are rarely performed as the computational cost implied is too large. On the mesoscopic level, Gillespie's algorithm is extensively used in the systems biology community and with increasing frequency also in models of microdomain calcium signaling. To increase computational speed, fast approximations were derived from Gillespie's exact algorithm, most notably the chemical Langevin equation and the τ-leap algorithm. Finally, in order to integrate deterministic and stochastic effects in multiscale simulations, hybrid algorithms are increasingly used. These include stochastic models of ion channels combined with deterministic descriptions of the calcium buffering and diffusion system on the one hand, and algorithms that switch between deterministic and stochastic simulation steps in a context-dependent manner on the other. The basic assumptions of the listed methods as well as implementation schemes are given in the text. We conclude with a perspective on possible future developments of the field.