title: Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release.
abstract: Population density approaches to modeling local control of Ca(2+)-induced Ca(2+) release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca(2+) signals. Unfortunately, the computational complexity of such "local/global" whole cell models scales with the number of Ca(2+) release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca(2+) concentration ([Ca(2+)]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca(2+) homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca(2+)] promotes elevated network sarcoplasmic reticulum (SR) [Ca(2+)] via SR Ca(2+)-ATPase-mediated Ca(2+) uptake. However, elevated myoplasmic [Ca(2+)] may also activate RyRs and promote stochastic SR Ca(2+) release, which can in turn decrease SR [Ca(2+)]. Increasing myoplasmic [Ca(2+)] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca(2+)] depending on whether myoplasmic [Ca(2+)] is low or high. In the later case, spontaneous release decreases SR [Ca(2+)] in a manner that maintains robust Ca(2+) sparks.
authors.affiliation: Department of Applied Science, The College of William and Mary, Williamsburg, Virginia;
authors.forename: Xiao
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Applied Science, The College of William and Mary, Williamsburg, Virginia;
authors.forename: Seth H
authors.initials: SH
authors.lastname: Weinberg
authors.affiliation: Department of Mathematics and Computer Science, The Hobart and William Smith Colleges, Geneva, New York; and.
authors.forename: Yan
authors.initials: Y
authors.lastname: Hao
authors.affiliation: Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, New York, New York.
authors.forename: Eric A
authors.initials: EA
authors.lastname: Sobie
authors.affiliation: Department of Applied Science, The College of William and Mary, Williamsburg, Virginia; greg@as.wm.edu.
authors.forename: Gregory D
authors.initials: GD
authors.lastname: Smith
mesh_terms: D000818:Animals; D002118:Calcium / Q000378:metabolism; D020013:Calcium Signaling; D006352:Heart Ventricles / Q000166:cytology / Q000378:metabolism*; D006706:Homeostasis; D008390:Markov Chains; D008955:Models, Cardiovascular; D032383:Myocytes, Cardiac / Q000378:metabolism*; D019837:Ryanodine Receptor Calcium Release Channel / Q000378:metabolism; D012519:Sarcoplasmic Reticulum / Q000378:metabolism; D053498:Sarcoplasmic Reticulum Calcium-Transporting ATPases / Q000378:metabolism
chemical_list: D019837:Ryanodine Receptor Calcium Release Channel; D053498:Sarcoplasmic Reticulum Calcium-Transporting ATPases; D002118:Calcium
keywords: Fokker-Planck equation; Langevin equation; calcium homeostasis; calcium release site; multiscale whole cell model