JSim v1.1
/*
MODEL NUMBER: 0106
MODEL NAME: VboltzmannLagged
SHORT DESCRIPTION: Model of Boltzmann gated channel conductance vs. transmembrane
voltage for any ion. Conductance change has fixed timelag, tau.
*/
import nsrunit; unit conversion on;
math VboltzmannLagged {
realDomain t msec; t.min = 0; t.max = 1000; t.delta =0.2;
//PARAMETERS are defined here, with units. // 2 slashes start comments:
real Em(t) mV, // Em , membrane potential
gKleak = 0.0003 siemens/cm^2, // Permeant bkgd leak channel
gKstep = 0.0030 siemens/cm^2, // Max Perm of gated channel; Siemen = 1/ohm
Am = 1 cm^2, // Surface area of membrane
Ko = 5 mM, Ki = 150 mM, // K concns outside and in
R = 8.31441 J*mol^(-1)*K^(-1), // gas constant
Temp = 310.16 K, // 37C
RT = R*Temp, // 19.340*10^6 mmHg*cm^3*mol^(-1)at 37C
Farad = 96485 coulomb*mol^(-1), // Faraday
qe = 1.6022e-19 coulomb, // elementary charge
//Nav = 6.0221e23, // Avagadro's #, no.molecules/mole
kB = 1.3807e-23 volt*coulomb*K^(-1), // Boltzmann's const., J*deg^-1
RToF = (1000 mV/volt)*RT/Farad, // mV, RToF=26.73 mV at 37C,
zg = 10, // # gating charges per channel, various
boltzg = (0.001 volt/mV)*zg*qe/(kB*Temp), // 1/volt, RToF = kB*Temp/qe
valence= 1, // boltcheck = qe/(kB*Temp),
RTozF = RToF/valence, // RTozF = RT/(Farad*z), mV;
loge10 = ln(10), // natural log of 10
VK = loge10*RTozF*log(Ko/Ki), // mV, ENernst for K, mV
EKchan = -40 mV; // mean Em for chan opening, mV
// VARIABLES: with units:
real Jelect(t) amp, // Jelect is electrical current as if gK change were instanteous
Jelecttau(t) amp, // Jelecttau is current when conductance change is slowed
zero(t) = 0, // zero(Em) is for plotting the zero current level
tau = 10 ms, // time constant for conformational change
gK(t) siemens/cm^2, // instantaneous conductance change (leak + channel)
gKlag(t) siemens/cm^2, // lagged conductance change
gKchannel(t) siemens/cm^2,// conductance of Boltzmann channel only, not leak
gchannellag(t) siemens/cm^2, // lagged conductance of Boltzmann channel only, not leak
rate = 1 mV/ms; // rate of change of Em
// INITIAL CONDITIONS:
when (t= t.min) {gchannellag = gKstep/(1+exp(-boltzg*(Em-EKchan))); Em = -150;}
// ODEs:
Em:t = rate;
gKchannel = gKstep/(1+exp(-boltzg*(Em-EKchan))) ; //instantaneous change
gK = gKleak + gKchannel; // instantaneous, as in VBoltzmann
Jelect = Am*(Em-VK)*gK; // instantaneous current, without lag
gchannellag:t= (1/tau)*(gKchannel-gchannellag); //the lag equation
gKlag = gKleak + gchannellag; // gchannel is lagged, not the leak
Jelecttau = Am*(Em-VK)*gKlag; // current with lagged gK change
} // END
/*
DETAILED DESCRIPTION: 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).
SHORTCOMINGS/GENERAL COMMENTS:
KEY WORDS:
Channel, Nernst potential, ionic current, gating current, conformational state,
Tutorial, membrane potential, Boltzmann, electrophysiology
REFERENCES:
Hille B. Ion Channels of Excitable Membranes, Third Edition.
Sunderland, Massachusetts: Sinauer Associates, 2001, 814 pp. page 19, Figure 1.6
REVISION HISTORY:
Written by JBB 5mar11
Revised by BEJ 8mar11 to update comments' format.
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2011 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 an email
with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
*/