Abstract
We review a theoretical, coarse-grained description for cardiomyocytes calcium dynamics that is motivated by experiments on RyR channel dynamics and provides an analogy to other spontaneously oscillating systems. We show how a minimal model, that focuses on calcium channel and pump dynamics and kinetics, results in a single, easily understood equation for spontaneous calcium oscillations (the Van-der-Pol equation). We analyze experiments on isolated RyR channels to quantify how the channel dynamics depends both on the local calcium concentration, as well as its temporal behavior (“adaptation”). Our oscillator model analytically predicts the conditions for spontaneous oscillations, their frequency and amplitude, and how each of those scale with the small number of relevant parameters related to calcium channel and pump activity. The minimal model is easily extended to include the effects of noise and external pacing (electrical or mechanical). We show how our simple oscillator predicts and explains the experimental observations of synchronization, “bursting” and reduction of apparent noise in the beating dynamics of paced cells. Thus, our analogy and theoretical approach provides robust predictions for the beating dynamics, and their biochemical and mechanical modulation.
Highlights
Contraction of adult cardiac cells in tissue is highly regulated by pacemaker cells (Huxley, 1974; Hill and Olson, 2012), which produce electrical impulses that are transmitted to cardiomyocytes, signaling them to contract (Hill and Olson, 2012)
We focus here on the unique role of RyR channels in the cytoplasmic [Ca2+] cycle, since recent studies have shown that calcium ion oscillations in pacemaker cells can occur independently of calcium entry across the surface membrane (Vinogradova et al, 2004, 2006; Maltsev and Lakatta, 2007)
We have recently shown that a minimal model that accounts only for the adaptive RyR dynamics coupled to calcium pump activity (Cohen and Safran, 2019) predicts, in a simple manner, spontaneous calcium oscillations
Summary
The pacemaker cells, unlike adult cardiomyocyte cells, show spontaneous contraction-relaxation cycles even in the absence of an external electrical signal (Vinogradova et al, 2004, 2006; Maltsev and Lakatta, 2007) These cells beat at a relatively fixed frequency, between 0.5 and 3 Hz depending on the species (Kehat et al, 2001; Yang et al, 2002; Majkut et al, 2013). When Ca2+ was rapidly increased and held constant (a “step function” increase), the opening probability showed an “adaptive” response, an initial sharp increase (overshoot) followed by an exponential relaxation to a steady-state value, with a typical time-scale of ∼ 100 ms (Valdivia et al, 1995) (see Figure 1B) This response suggests that the channel dynamics depends on the instantaneous calcium concentration, and on the rate at which it changes. The adaptive response (along with calcium pump activity) turns out to be a crucial component in the generation of spontaneous calcium oscillations (Cohen and Safran, 2019)
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