Model number

Model of Boltzmann gated channel conductance vs. transmembrane voltage for any ion. Conductance change has fixed timelag, tau.


 Provides current voltage relationships for potassium currents
 through a passive leak conductance and through a voltage-gated channel 
 in a membrane. Gives Nernst potentials. Allows changing of gate charges
 and mean Em for the gate, EKchan, as well as concentrations and temperature 
 in order to explore the Boltzmann relationships.

 Model is essentially that of Vboltzmann but to demosntrate a time lag in the 
 conformational change and the conductance, the transmembrame voltage Em is 
 changed to be a function ot time, so the independent variable is "t". The 
 lag is not in the Hille description on p19, but later in the book.
 Model for monovalent cation in water driven by electrochem gradient
 Membrane separates 2 regions of fixed concentrations, Ko and Ki
 Solute activities are unity. Currents do not reach S.S. instantaneously
 but are delayed by a single exponential lag.
 Single channel conductance about 300 pSiemens; 10^6 chan -> 300 uS.
 See Notes, section J, within this .proj file for a suggestion to create a tau(t, Em).

fig 1

Figure: Membrane current (Jelect) and conductance (gK) as a function of transmembrane potential. Current flows through passive leakage and a voltage-gated channel. Dashed lines (Jelecttau and gKlag) show the effect of conductance time lag (Current does not reach S.S. immediately).


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.

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