Model number

Model of transmembrane resting potential due to concentration differences in K, Na, and Ca across a membrane with constant conductance for each ion.


 Calculation of steady-state resting potential, EGoldman, due to Na, K, 
 and Ca leakages, with or without the NaK ATPase (the "sodium pump"). Allows changing of 
 concentrations and temperature in order to explore the Nernst and Goldman potential relationships.

 Display is set up using log scaling on bottom two panels. Set rateo to 
 a negative rate such as -1 mv/ms to show that Em and Egoldman changes as Ki decreases.
 Note in Model Outputs table that Em and Egoldman potentials are different.
 Model accounts for two monovalent cations, K and Na, and one divalent ion, Ca, all 
 driven by their electrochem gradients. Membrane separates 2 regions containing fixed 
 concentrations of Na and Ca and varying amounts of K. Solute activities are unity. 
 Currents reach S.S. instantaneously.

 The NaKATPase, the sodium pump, creats a net efflux of positive charges, and therefore
 tends to polarize the membrane. The pump current can produce mambrane potentials
 more negative than EK. Oubain, a blocker of this ATPase, causes depolarization of 
 4 to 8 mV. The NaKATPase current changes during an action potential. To generate a
 pump current there must be K outside and Na inside. The pump reversal potential is
 highly negative, perhaps below -200 mV.

 Nernst potentials are independent of conductance. Given a
 single channel conductance about 300 pSiemens; 10^6 chan -> 300 uS.
 What would be the the current flow at the starting concentrations Ko=5 and Ki=150 mM?
 Insert suitable concentrations for Ca, e.g. 1e-4 and 2 mM, and for Na, 12 and 144 mM
 and determine the slopes.
 See Notes within this .proj file for guidance.


The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

Download JSim model project file


Help running a JSim model.

 Goldman David E. Potential, impedance, and rectification in membranes.
 J Gen Physiol 27: 37-60, 1943.

 Hodgkin AL and Katz B. The effect of sodium ions on the electrical activity
 of the giant axon of the squid. J Physiol 108: 37-77, 1949.

 Sperelakis N. Origin of the cardiac resting potential. Appendix: Physical principles, 
 derivations, and applications. In: Handbook of Physiology, Sec. 2, The Cardiovascular 
 System. Vol. 1, edited by Berne RM, Sperelakis N, and Geiger SR.
 Baltimore: Waverly Press, Inc., 1979, pp 187-267. 9

 Hille B. Ion Channels of Excitable Membranes, Third Edition.
 Sunderland, Massachusetts: Sinauer Associates, 2001, 814 pp. page 19, Figure 1.6
Key terms
Channel Nernst potential
ionic current
resting membrane potential

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, 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.