Abstract
Calcium (Ca) sparks are elementary events of biological Ca signaling. A normal Ca spark has a brief duration in the range of 10 to 100 ms, but long-lasting sparks with durations of several hundred milliseconds to seconds are also widely observed. Experiments have shown that the transition from normal to long-lasting sparks can occur when ryanodine receptor (RyR) open probability is either increased or decreased. Here, we demonstrate theoretically and computationally that long-lasting sparks emerge as a collective dynamical behavior of the network of diffusively coupled Ca release units (CRUs). We show that normal sparks occur when the CRU network is monostable and excitable, while long-lasting sparks occur when the network dynamics possesses multiple metastable attractors, each attractor corresponding to a different spatial firing pattern of sparks. We further highlight the mechanisms and conditions that produce long-lasting sparks, demonstrating the existence of an optimal range of RyR open probability favoring long-lasting sparks. We find that when CRU firings are sparse and sarcoplasmic reticulum (SR) Ca load is high, increasing RyR open probability promotes long-lasting sparks by potentiating Ca-induced Ca release (CICR). In contrast, when CICR is already strong enough to produce frequent firings, decreasing RyR open probability counter-intuitively promotes long-lasting sparks by decreasing spark frequency. The decrease in spark frequency promotes intra-SR Ca diffusion from neighboring non-firing CRUs to the firing CRUs, which helps to maintain the local SR Ca concentration of the firing CRUs above a critical level to sustain firing. In this setting, decreasing RyR open probability further suppresses long-lasting sparks by weakening CICR. Since a long-lasting spark terminates via the Kramers’ escape process over a potential barrier, its duration exhibits an exponential distribution determined by the barrier height and noise strength, which is modulated differently by different ways of altering the Ca release flux strength.
Highlights
Calcium (Ca) is a ubiquitous signaling ion in biology, regulating both normal biological pathways as well as disease processes [1,2,3]
We demonstrate theoretically and computationally that normal brief sparks are excitable transients, while long-lasting sparks are multiple metastable states emerging in the diffusively coupled Ca release unit network, as a result of cooperativity and release competition among the Ca release units
We propose a theory for the transition from normal brief sparks to long-lasting sparks based on a coupled Ca release units (CRUs) network, which unifies the seemingly contradictory experimental observations described above
Summary
Calcium (Ca) is a ubiquitous signaling ion in biology, regulating both normal biological pathways as well as disease processes [1,2,3]. IP3Rs or RyRs are clustered on the membrane of the ER/SR, forming discrete Ca release units (CRUs). CICR causes the IP3Rs or RyRs to open and close collectively in a cluster, resulting in random and discrete Ca release events, called Ca sparks [6]. Ca sparks have been considered as the dynamical elements which interact to generate sub-cellular and cellular dynamics for Ca signaling and muscle contraction, such as Ca waves and oscillations [7,8,9,10,11,12] and more complex nonlinear dynamics in the heart [5,13,14,15,16,17,18]
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