A Mathematical Analysis of the Generation and Termination of Calcium Sparks

Abstract

Calcium sparks are local regenerative releases of Ca(2+) from a cluster of ryanodine receptors on the sarcoplasmic reticulum. During excitation-contraction coupling in cardiac cells, Ca(2+) sparks are triggered by Ca(2+) entering the cell via the T-tubules (Ca(2+)-induced Ca(2+) release). However under conditions of calcium overload, Ca(2+) sparks can be triggered spontaneously. The exact process by which Ca(2+) sparks terminate is still an open question, although both deterministic and stochastic processes are likely to be important. In this article, asymptotic methods are used to analyze a single Ca(2+) spark model, which includes both deterministic and stochastic biophysical mechanisms. The analysis calculates both spark frequencies and spark duration distributions, and shows under what circumstances stochastic transitions are important. Additionally, a model of the coupling of the release channels via the FK-binding protein is analyzed.

Sparks and embers of skeletal muscle: the exciting events of contractile activation

“…Although a clear depletion of the SR that mirrors the spark (termed "blink" [7]) was described in cardiac cells, skeletal muscle fibres lack such events. In cardiac myocytes where the depletion in the SR can reach 40% or more [7], its role in the termination of calcium sparks seems to be established [16,22,53]. In skeletal muscle, where this value is 10% or less [35], the drop in SR calcium concentration is unlikely to cause the termination of the event.…”

Nonlinear onset of calcium wave propagation in cardiac cells

“…To proceed we follow our previous work [27], which is based on Hinch et al [28], and consider the large N limit where the birth-death process can be mapped to the continuum. Then, if we define the fraction of channels in the open state as x = n/N , the detailed balance between the states of the cluster gives an equilibrium distribution,…”

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

“…Note that depending on the experiment that the model addresses, not all of these calcium transport mechanisms need to be represented. For example, pathways involving the SR may be omitted in a study of inhibited luminal dynamics (Michailova et al 2002), and plasma membrane processes can be excluded if the emphasis lies on spark generation and statistics (Nguyen et al 2005, Hinch 2004). The degree of detail to which ion channels, transporters and pumps are described is tightly coupled to their numbers as well as to the size of the spatial domain under investigation.…”