Reduction of calcium release site models via moment fitting of phase-type distributions

Models of calcium (Ca2+) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca2+ channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca2+ puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca2+ release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca2+. Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca2+ release site models is unique in several respects and novel in this biophysical context.