| Dynamics of A Three-Variable Nonlinear Model of Vasomotion: Comparison of Theory and Experiment Biophysical Journal, Volume 93, Issue 5, 1 September 2007, Pages 1534-1556 D. Parthimos, R.E. Haddock, C.E. Hill and T.M. Griffith Abstract The effects of pharmacological interventions that modulate Ca homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca] in the cytosol, [Ca] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca stores and transmembrane ion fluxes via K channels, Cl channels, and voltage-operated Ca channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables. Abstract | Full Text | PDF (1857 kb) |
| Sensing and refilling calcium stores in an excitable cell Biophysical Journal, Volume 72, Issue 3, 1 March 1997, Pages 1080-1091 Y.X. Li, S.S. Stojilković, J. Keizer and J. Rinzel Abstract Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ mobilization leads to depletion of the endoplasmic reticulum (ER) and an increase in Ca2+ entry. We show here for the gonadotroph, an excitable endocrine cell, that sensing of ER Ca2+ content can occur without the Ca2+ release-activated Ca2+ current (Icrac), but rather through the coupling of IP3-induced Ca2+ oscillations to plasma membrane voltage spikes that gate Ca2+ entry. Thus we demonstrate that capacitative Ca2+ entry is accomplished through Ca(2+)-controlled Ca2+ entry. We develop a comprehensive model, with parameter values constrained by available experimental data, to simulate the spatiotemporal behavior of agonist-induced Ca2+ signals in both the cytosol and ER lumen of gonadotrophs. The model combines two previously developed models, one for ER-mediated Ca2+ oscillations and another for plasma membrane potential-driven Ca2+ oscillations. Simulations show agreement with existing experimental records of store content, cytosolic Ca2+ concentration ([Ca2+]i), and electrical activity, and make a variety of new, experimentally testable predictions. In particular, computations with the model suggest that [Ca2+]i in the vicinity of the plasma membrane acts as a messenger for ER content via Ca(2+)-activated K+ channels and Ca2+ pumps in the plasma membrane. We conclude that, in excitable cells that do not express Icrac, [Ca2+]i profiles provide a sensitive mechanism for regulating net calcium flux through the plasma membrane during both store depletion and refilling. Abstract | PDF (2013 kb) |
| Local Calcium Signaling Biophysical Journal, Volume 94, Issue , 1 February 2008, Pages 413-418 Full Text | PDF (113 kb) |
Copyright © 1996 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 71, Issue 6, 3477-3487, 1 December 1996
doi:10.1016/S0006-3495(96)79543-7
Research Article
J. Keizer and L. Levine
Institute of Theoretical Dynamics, University of California, Davis 95616, USA. jekeizer@ucdavis.edu
A simplified mechanism that mimics "adaptation" of the ryanodine receptor (RyR) has been developed and its significance for Ca2+(-)induced Ca2+ release and Ca2+ oscillations investigated. For parameters that reproduce experimental data for the RyR from cardiac cells, adaptation of the RyR in combination with sarco/endoplasmic reticulum Ca2+ ATPase Ca2+ pumps in the internal stores can give rise to either low [Cai2+] steady states or Ca2+ oscillations coexisting with unphysiologically high [Cai2+] steady states. In this closed-cell-type model rapid, adaptation-dependent Ca2+ oscillations occur only in limited ranges of parameters. In the presence of Ca2+ influx and efflux from outside the cell (open-cell model) Ca2+ oscillations occur for a wide range of physiological parameter values and have a period that is determined by the rate of Ca2+ refilling of the stores. Although the rate of adaptation of the RyR has a role in determining the shape and the period of the Ca2+ spike, it is not essential for their existence. This is in marked contrast with what is observed for the inositol 1,4,5-trisphosphate receptor for which the biphasic activation and inhibition of its activity by Ca2+ are sufficient to produce oscillations. Results for this model are compared with those based on Ca2+(-)induced Ca2+ release alone in the bullfrog sympathetic neuron. This kinetic model should be suitable for analyzing phenomena associated with "Ca2+ sparks," including their merger into Ca2+ waves in cardiac myocytes.