Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)


Applied Science


Localized cytosolic Ca2+ elevations known as puffs and sparks are important regulators of cellular function that arise due to the cooperative activity of Ca2+-regulated inositol 1,4,5-trisphosphate receptors (IP3Rs) or ryanodine receptors (RyRs) co-localized at Ca2+ release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. Theoretical studies have demonstrated that the cooperative gating of a cluster of Ca2+-regulated Ca 2+ channels modeled as a continuous-time discrete-state Markov chain may result in dynamics reminiscent of Ca2+ puffs and sparks. In such simulations, individual Ca2+-release channels are coupled via a mathematical representation of the local [Ca2+] and exhibit "stochastic Ca2+ excitability" where channels open and close in a concerted fashion. This dissertation uses Markov chain models of Ca 2+ release sites to advance our understanding of the biophysics connecting the microscopic parameters of IP3R and RyR gating to the collective phenomenon of puffs and sparks.;The dynamics of puffs and sparks exhibited by release site models that include both Ca2+ coupling and nearest-neighbor allosteric coupling are studied. Allosteric interactions are included in a manner that promotes the synchronous gating of channels by stabilizing neighboring closed-closed and/or open-open channel pairs. When the strength of Ca2+-mediated channel coupling is systematically varied, simulations that include allosteric interactions often exhibit more robust Ca2+ puffs and sparks. Interestingly, the changes in puff/spark duration, inter-event interval, and frequency observed upon the random removal of allosteric couplings that stabilize closed-closed channel pairs are qualitatively different than the changes observed when open-open channel pairs, or both open-open and closed-closed channel pairs are stabilized. The validity of a computationally efficient mean-field reduction applicable to the dynamics of a cluster of Ca2+-release Ca2+ channels coupled via the local [Ca2+] and allosteric interactions is also investigated.;Markov chain models of Ca2+ release sites composed of channels that are both activated and inactivated by Ca2+ are used to clarify the role of Ca2+ inactivation in the generation and termination of puffs and sparks. It is found that when the average fraction of inactivated channels is significant, puffs and sparks are often less sensitive to variations in the number of channels at release sites and the strength of Ca2+ coupling. While excessively fast Ca2+ inactivation can preclude puffs and sparks moderately fast Ca2+ inactivation often leads to time-irreversible puff/sparks whose termination is facilitated by the recruitment of inactivated channels throughout the duration of the puff/spark event. On the other hand, Ca2+ inactivation may be an important negative feedback mechanism even when its time constant is much greater than the duration of puffs and sparks. In fact, slow Ca 2+ inactivation can lead to release sites with a substantial fraction of inactivated channels that exhibit nearly time-reversible puffs and sparks that terminate without additional recruitment of inactivated channels.



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