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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

# NaCaX

Model number: 0055

An ion channel, a sodium calcium exchanger in the surface membrane (sarcolemma) of mammalian pacemaker cells. A mathematical model for the electrophysiological responses.

## Detailed Description

A sodium calcium exchange model. Sodium calcium ion channels exist in the surface membrane (sarcolemma) of a muscle cell. At allows sodium ions to flow down the electrochemical gradient of sodium, across the plasma membrane in exchange for the countertransport of calcium ions. Thus, the maintenance of calcium contentration in cells can be maintained. In this model, it is in regard to the maintenance of calcium concentration in the sarcoplasmic reticulum of cardiac cells. This model is derived from the Demir, Clark, Murphey, and Giles model: A mathematical model of a rabbit sinoatrial node cell. The Demir et al model is a mathematical model for the electrophysiological responses of a rabbit sinoatrial node cell. It describes many ion channels causing known currents in mammalian pacemaker cells. The sodium calcium exchanger is focused on for this model.

## Figures

The following figures were all generated with JSim. They can be reproduced by downloading the project file, or running the applet (below).

Figure 1 displays the pacemaker and action potential waveforms. Figure 2 shows the first derivative (dV/dt) of the model-generated waveform. Figure three gives the total background (IB), pump (INaK and ICaP), and exchanger (INaCa) currents.

Figure 4 displays the transmembrane ionic currents (ICa,L and IK). Figure 5 gives the Current vs Voltage plots for the major ionic currents (ICa,L, IK, and INaCa).

All currents are given in picoamps, all voltages are in millivolts, and all time is given in seconds.

## Relevant Equations

A complete list of equations can be found in the source code of the project file. The following equations are for only the pump and exchanger currents, as well as the differential equation describing the membrane potential (voltage).

$\large { I_{\text{\small{NaCa}}} = k_{\text{\small{NaCa}}} \frac {[\text {Na}]_{\text{\small{i}}}^3 [\text {Ca}]_{\text{\small{c}}} e^{0.03743 V \cdot \gamma} - [\text {Na}]_{\text{\small{c}}}^3 [\text {Ca}]_{\text{\small{i}}} e^{0.03743 V \cdot (\gamma - 1)}}{1 + d_{\text{\small{NaCa}}} ([\text {Na}]_{\text{\small{i}}}^3 [\text {Ca}]_{\text{\small{c}}} + [\text {Na}]_{\text{\small{c}}}^3 [\text {Ca}]_{\text{\small{i}}})}$

$\large { I_{\text{\small{NaK}}} = I_{\text{\small{NaK max}}} ( \frac {[\text {Na}]_{\text{\small{i}}}}{[\text {Na}]_{\text{\small{i}}} + k_{\text{\small{mNa}}}})^3 (\frac {[\text {K}]_{\text{\small{c}}}}{[\text {K}]_{\text{\small{c}}} + k_{\text{\small{mK}}}})^2 ( \frac {1.6}{1.5 + e^{\small{[\frac {V + 60}{-40}]}}})$

$\large { I_{\text{\small{CaP}}} = I_{\text{\small{CaP max}}} ( \frac {[\text {Ca}]_{\text{\small{i}}}}{[\text {Ca}]_{\text{\small{i}}} + 0.0004})$

$\large { \frac {d}{dt} V(t) = - \frac {I_{\text{\small{Na}}} + I_{\text{\small{Ca,T}}} + I_{\text{\small{Ca,L}}} + I_{\text{\small{K}}} + I_{\text{\small{f}}} + I_{\text{\small{B}}} + I_{\text{\small{NaK}}} + I_{\text{\small{NaCa}}} + I_{\text{\small{CaP}}}}{C_{\text{\small{m}}}}$

## Run JSim Model

Press the “Run Applet” button to bring up the model in a separate window.

## References

S.S. Demir, J.W. Clark, C.R. Murphey, W.R. Giles, A mathematical model of a rabbit sinoatrial node cell, Modeling in Physiology, American Physiological Society C832 - C852, 1994

## Key Terms

Sodium calcium exchanger, ion channel, sarcolemma, sarcoplasmic reticulum, cardiac cell, sinoatrial, electrochemical gradient.

## JSim Tutorial

Click here to go to a JSim tutorial webpage, with an introduction to the JSim GUI, detailed usage instructions, and an accompaying video.

## Model History

Get Model history in CVS.

Copyright (C) 1999-2009 University of Washington. From the National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061. Academic use is unrestricted. Software may be copied so long as this copyright notice is included. This software was developed with support from NIH grant HL073598. Please cite this grant in any publication for which this software is used and send one reprint to the address given above.

Model development and archiving support at physiome.org provided by the following grants: NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.