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WIREs Syst Biol Med
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Calcium dynamics and signaling in vascular regulation: computational models

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Abstract Calcium is a universal signaling molecule with a central role in a number of vascular functions including in the regulation of tone and blood flow. Experimentation has provided insights into signaling pathways that lead to or affected by Ca2+ mobilization in the vasculature. Mathematical modeling offers a systematic approach to the analysis of these mechanisms and can serve as a tool for data interpretation and for guiding new experimental studies. Comprehensive models of calcium dynamics are well advanced for some systems such as the heart. This review summarizes the progress that has been made in modeling Ca2+ dynamics and signaling in vascular cells. Model simulations show how Ca2+ signaling emerges as a result of complex, nonlinear interactions that cannot be properly analyzed using only a reductionist's approach. A strategy of integrative modeling in the vasculature is outlined that will allow linking macroscale pathophysiological responses to the underlying cellular mechanisms. WIREs Syst Biol Med 2011 3 93–106 DOI: 10.1002/wsbm.97 This article is categorized under: Models of Systems Properties and Processes > Cellular Models Biological Mechanisms > Cell Signaling

Models of calcium dynamics in ECs. (a) A model introduced by Wong and Klassen.47 The model contained an internal calcium store that was divided into a superficial (sc) and deep (dc) compartments and four transmembrane currents: a sodium current (INa), a potassium current (IK), a Ca2+‐activated potassium current (IK, Ca), and a stretch‐activated calcium current (ISA). (b) A calcium dynamics model in human umbilical vein endothelial cells (HUVECS) introduced by Wiesner and coworkers.48 The model includes descriptions for CICR, CCE, kinetics for IP3 formations following thrombin receptor activation, and Ca2+ buffering. Formulations for the NCX and the PMCA pump were also included. (c) A model of endothelial cell electrophysiology presented by Schuster and coworkers (reprinted with permission from Ref 50. Copyright 2003 Springer). Model focuses on K+ currents from bradykinin‐sensitive channels (i.e., the large‐conductance BKCa channel, the apamin‐insensitive small‐conductance SKCa channel, and an NSC channel) and the apamin‐sensitive SKCa channel that is not gated by bradykinin. (d) An endothelial cell electrophysiology/ionic dynamics model introduced by Silva et al.51 Model contains several transmembrane currents from: store‐operated Ca2+ channels (SOC); nonselective cation (NSC) channels; voltage‐regulated anion channel (VRAC); Ca2+‐activated Cl channels (CACC); inward rectifier K+ channels; Ca2+‐activated K+ channels (small‐conductance SKCa, intermediate‐conductance IKCa); Na+‐K+‐ATPase (NaK) pumps; plasma membrane Ca2+‐ATPase (PMCA) pumps; Na+/Ca2+ exchanger (NCX). The model accounts for changes in membrane potential (Vm) and in the intracellular concentrations of the four main ionic species following agonist induced IP3 release.

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Models of calcium dynamics in SMCs. (a) The Wong and Klassen model of Ca2+ dynamics and membrane's electrical behavior in vascular smooth muscle (reproduced with permission from Ref 53. Copyright 1993 Elsevier). The model includes two intracellular stores. A‐store is an IP3‐sensitive store. C‐store is replenished by extracellular Ca2+. Jeff and JD are the active and passive transmembrane Ca2+ efflux; Jp is the Ca2+ uptake rate of the A‐store; ICa is the Ca2+ current through the voltage‐operated channel; Iin is the inward current through the receptor‐operated channel; IK, Ca and IK are the calcium and voltage‐dependent K+ channels. (b) Minimal model reproduced from Parthimos and coworkers.58 Model contains two independent internal stores [a ryanodine‐sensitive (CICR) and inositol 1,4,5‐trisphosphate (InsP3) sensitive]. Membrane component contains descriptions for: transmembrane currents for Cl, K+ channels; voltage‐ and receptor‐operated Ca2+ channels (VOCCs and ROCCs, respectively); Na+‐K+‐ATPase, and Ca2+‐ATPase pumps; NCX. (c) Detailed model reproduced with permission from Ref 62. Copyright 2003 Elsevier. Membrane model (upper panel) describing ionic membrane currents and transmembrane potential. Black and white indicates resistance with voltage‐dependent nonlinearity, and the all white resistor indicates linear element. Fluid compartment model (lower panel) describes ionic dynamics, Ca2+ buffering, and Ca2+ handling by sarcoplasmic reticulum (SR). The SR is divided into a ryonadine‐sensitive release compartment and an uptake compartment containing SERCA pumps that communicate. (d) Diagram of the cell model presented and reproduced from Ref 65. Copyright 2007 American Physiological Society. Model contains three intracellular compartments: bulk cytosol (cyt), microdomains (md), and sarcoplasmic reticulum (SR). Ji, diff is the electrodiffusive flux of ion i between the microdomains and the bulk cytosol.

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Multicellular models of the vascular wall. (a) The Koenigsberger model integrates on a two‐dimensional grid model equations for SMCs superposed on a two‐dimensional grid of ECs. ECs are arranged parallel and SMCs perpendicular to the vessel axis (reproduced with permission from Ref 73. Copyright 2005 Elsevier). Cell geometry is approximated by a rectangle. Each cell is connected with its nearest neighbors on the same layer (homocellular connection) and with the cells on the other layer directly superposed on it (hetero‐cellular connection). (b) A model of the SMC layer introduced by Jacobsen and coworkers (Reproduced with permission from Ref 76. Copyright 2007 American Physiological Society). Each SMC (upper panel) contains: Na+/K+‐ATPase (1), NCX (2), plasma membrane Ca2+‐ATPase (3), sarco(endo)plasmic reticulum Ca2+‐ATPase (4), SR calcium release channel (5), cytoplasmic calcium buffer (6), SR calcium buffer (7), cGMP‐sensitive calcium‐dependent chloride channel (8), calcium‐activated potassium channels (9), voltage‐sensitive calcium channel (L‐type calcium channel; 10), and gap junction (11). The SMCs are arranged into a single‐layered cell plate (lower panel). Each spindle‐shaped cell couples to neighboring cells through gap junctions (black double‐barrel structures). (c) Multicellular model of a vessel segment presented by Kapela and coworkers.78, 79 ECs and SMCs are placed in appropriate arrangement. Cells are coupled by nitric oxide (NO) and myoendothelial gap junctions permeable to Ca2+, Na+, K+, and Cl ions, and IP3. Kir—inward rectifier K+ channel; VRAC—volume‐regulated anion channel; SKCa, IKCa and BKCa—small‐, intermediate‐, and large‐conductance Ca2+‐activated K+ channels; SOC—store‐operated channel; NSC—nonselective cation channel, CaCC and ClCa—Ca2+‐activated chloride channel; NaK—Na+‐K+‐ATPase; PMCA—plasma membrane Ca2+‐ATPase; NCX—Na+/Ca2+ exchanger; NaKCl—Na+‐K+‐Cl cotransport; Kv—voltage‐dependent K+ channel; Kleak—unspecified K+ leak current; VOCC—voltage‐operated Ca2+ channels; SR/ER—sarco/endoplasmic reticulum; IP3R—IP3 receptor; RyR—ryanodine receptor; SERCA—SR/ER Ca2+‐ATPase; CSQN—calsequestrin; CM—calmodulin; R—receptor; G—G‐protein; DAG—diacylglycerol; PLC—phospholipase C; sGC—soluble guanylate cyclase; cGMP—cyclic guanosine monophosphate.

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Strategy for integrative modeling of the vasculature. (a) Genomic, proteomic and in vitro data such as electrophysiological recordings can be utilized to provide mathematical formulations for subcellular components and signaling pathways. Representative example shows the three‐dimensional folding of KIR2.1 protein and the current–voltage behavior of a KIR channel in an EC. (b) An EC model51 that integrates such formulations and incorporates membrane channels, pumps and exchangers, intracellular compartments, and signaling mechanisms. The model can simulate membrane electrophysiology, dynamic behavior of Ca2+ and other ions, and the generation of second messengers and signaling factors. (c) EC and SMCs can be coupled through gap junctions and the diffusion of species like NO and IP3.78 (d) Multicellular models of the vascular wall can be constructed by placing EC and SMCs cells in an appropriate arrangement.79 (e) Example of a biotransport model investigating the diffusion of species (i.e., NO, O2) in and around a single arteriole and incorporates RBCs and nearby capillaries.80 (f) A biomechanics model of a single arteriole presents the constriction of the vessel at the site of norepinephrine application in the absence of longitudinal signal conduction. (g) Detailed computational model investigating blood flow and O2 distribution in three‐dimensional vascular networks and mesoscale tissue volumes.95 (h) Reconstructed whole‐organ vessel network and blood flow calculations.(Reprinted with permission from Ref 96. Copyright 2002 Society for Industrial and Applied Mathematics)..

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Biological Mechanisms > Cell Signaling
Models of Systems Properties and Processes > Cellular Models

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