Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca2+ dynamics

Abstract

We present a bidomain threshold model of intracellular calcium (Ca 2+ ) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca 2+ liberation is modulated by the Ca 2+ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

Unifying principles of calcium wave propagation — Insights from a three-dimensional model for atrial myocytes

“…A linear SERCA pump description corresponds to a low-affinity approximation of a biophysical model (27,28). Linear SERCA pumps have been used successfully in the past for the mathematical analysis of travelling Ca 2+ waves and three-dimensional numerical simulations of interacting Ca 2+ release events (29)(30)(31)(32). The current I corresponds to Ca 2+ liberation from the SR through RyR channels.…”

Synchrony of Cardiomyocyte Ca2+ Release is Controlled by t-tubule Organization, SR Ca2+ Content, and Ryanodine Receptor Ca2+ Sensitivity

“…The value used, b ¼ 1 mM, is qualified and interpreted into a biological setting in the Supporting Material. Following Thul et al (23,25), the SERCA pump current is described as…”

“…With a few exceptions, e.g., models that include the SR Ca 2þ signal as a variable to describe sensitization of RyR by [Ca 2þ ] SR (25), most models of spatiotemporal Ca 2þ dynamics in cardiomyocytes are univariable. In most of our simulations, the SR Ca 2þ signal induced by release from neighboring sites affected the quantities of SR Ca 2þ release to such a minor extent that, to a good approximation, it could have been neglected.…”

Translating Intracellular Calcium Signaling into Models

“…Instead of running a large number of simulations all that is needed is to evaluate analytical expressions, which can be done in a fraction of the time that is required for the numerical simulations. For example, the impact of SERCA pumps on Ca 2+ wave propagation has been studied in (Coombes 2001), and investigating the interplay between the cytosol and the SR provided explanations for two novel wave types: tango waves (Li 2003;Thul et al 2008b) and sensitization waves (Keller et al 2007;Thul et al 2009a). While deterministic models such as the original FDF description are still instrumental in advancing our understanding of intracellular Ca 2+ waves, hybrid frameworks that incorporate the stochastic nature of Ca 2+ release have gained considerable attention.…”