#pragma rtGlobals=1 // Use modern global access method. // Procedures for performing Hodgkin Huxley simulations of excitable membrane. // The simulations are based on: // Hodgkin, A.L. & Huxley, A.F. (1952) "A quantitative description of membrane current and its // application to conduction and excitation in nerve" Journal of Physiology, vol. 117, pp. 500-544 // Created 25/9/2000 - JBF // For more information about these procedures, or to report bugs, please contact: // James.Fallon@ieee.org // Performs simulation of membrane voltage based on the Hodgkin Huxley equations. // The current waveform is supplied and should be scaled in 's' and 'A'. An appropriate form is: // make /o/n=1000 Current // setscale /p x 0, 2e-5, "s", Current // setscale d 0, 0, "A", Current // Current = ((x > 1e-3) - (x > 2e-3))*10e-6 // which is equivalent to a current pulse of 10µA for 1 ms. // The rate constants are adjusted according to the temperature, Temp, in ¡C. // The method used determines what other wavesforms are calculated: // Method 1: Voltage only (returned in current datafolder) // 2: Voltage and current wavesforms (returned in 'Hodgkin Huxley' data folder) Function SimulateHodgkinHuxley(Current, Temp, Method) Wave Current Variable Temp, Method string currentfldr = getdatafolder(1) newdatafolder /o/s root:Packages newdatafolder /o/s 'Hodgkin Huxley' make /o w_para={1,120,-115,36,12,0.3,-10.613, Temp} // Copy current wave ... duplicate /o Current, Voltage, w_Current, w_m, w_h, w_n setscale /p x 0,deltax(Current)*1000,"ms",Voltage, w_Current, w_m, w_h, w_n w_Current *= -1e6 switch (Method) case 2: // Voltage and currents ... duplicate /o Current INa, IK, Il setscale /p x 0,deltax(Current)*1000,"ms", INa, IK, Il break case 1: default: break endswitch // Initialise starting values ... w_m[0]=0.052971; w_h[0]= 0.59665; w_n[0]= 0.3179 voltage[0]= 0 // Perform simulation ... integrateODE /q=1/u=(numpnts(Voltage)) Hodgkin_Huxley, w_para, {Voltage, w_m, w_h, w_n} if (v_flag == 1) return v_flag endif // Return resulting voltage wave ... duplicate /o Voltage \$currentfldr+"Voltage" wave Voltage = \$currentfldr+"Voltage" Voltage = -(voltage+60)/1000; setscale d 0,0,"V",Voltage setscale /p x 0,deltax(Current),"s",Voltage switch (Method) case 2: // Voltage and currents ... INa = w_para[1]*(w_m^3)*w_h*(voltage-w_para[2]) IK = w_para[3]*(w_n^4)*(voltage-w_para[4]) Il = w_para[5]*(voltage-w_para[6]) break case 1: default: break endswitch setdatafolder \$currentfldr return 0 End // SimulateHodgkinHuxley(Current, Temp, Method) // Function used to solve the Hodgkin Huxley equations for an excitable membrane. // The function calculates the derivatives of V, m, h, and n. The curent value is passed // in w_Y and the resulting derivative is returned in w_dY. The order in w_Y is: // w_Y[0] = V // w_Y[1] = m // w_Y[2] = h // w_Y[3] = n // Extra parameters can be passed in w_Para and theses are: // w_para[0] = Cm // w_para[1] = GNa // w_para[2] = VNa // w_para[3] = GK // w_para[4] = VK // w_para[5] = Gl // w_para[6] = Vl // w_para[7] = Temp Function Hodgkin_Huxley(w_para, t, w_Y, w_dY) Wave w_para, w_Y, w_dY variable t // Load local variables ... variable V = w_Y[0], m= w_Y[1], h= w_Y[2], n= w_Y[3] // Reference current wave ... wave w_Current = w_Current // Calculate the derivatives ... // dV/dt w_dY[0] = (w_Current(t)- w_para[5]*(V-w_para[6]) - w_para[1]*m^3*h*(V-w_para[2]) - w_para[3]*n^4*(V-w_para[4]))/w_para[0] // dm/dt w_dY[1] = (0.1*(V+25) / (exp((V+25)/10)-1) * (1-m) - 4*exp(V/18)*m)*3^((w_para[7]-6.3)/10) // dh/dt w_dY[2] = (0.07*exp(V/20)*(1-h) - h/(exp((V+30)/10)+1))*3^((w_para[7]-6.3)/10) // dn/dt w_dY[3] = (0.01*(V+10)/(exp((V+10)/10)-1)*(1-n) - 1/8*exp(V/80)*n)*3^((w_para[7]-6.3)/10) End // Hodgkin_Huxley(w_para, t, w_Y, w_dY)