hodgkin_huxley_basic_hodgkin_huxley_源码

%% Basic Hodgkin-Huxley Implementation % This is an implementation of the basic HH equations. It allows the user % to provide a single stimulus at the time, strength, and duration of the % user's choosing. % Equations from Hodgkin, Huxley, J. Physiol (1952) 117, 500-544 % Iyad Obeid % 25 November 2015 % Version 0.0 clear; figure(1);clf; %%%%%%%%%%%%%%%%%% % DEFINE CONSTANTS %%%%%%%%%%%%%%%%%% % Nernst Potentials Ena = 115; Ek = -12; El = 10.6; % Maximum Conductances gna = 120; gk = 36; gl = 0.3; % Membrane Capacitance C = 1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DEFINE VOLTAGE-DEPENDENT GATE ACTIVATIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Likelihoods of gates opening an = @(u) (0.1-0.01*u)/(exp(1-0.1*u)-1); am = @(u) (2.5-0.1*u)/(exp(2.5-0.1*u)-1); ah = @(u) 0.07*exp(-u/20); % Likelihoods of gates closing bn = @(u) 0.125*exp(-u/80); bm = @(u) 4*exp(-u/18); bh = @(u) 1/(exp(3-0.1*u)+1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DEFINE FORMULAE FOR STEADY STATE GATE ACTIVATIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% m_inf = @(u) am(u) / ( am(u) + bm(u) ); n_inf = @(u) an(u) / ( an(u) + bn(u) ); h_inf = @(u) ah(u) / ( ah(u) + bh(u) ); %%%%%%%%%%%%% % DEFINE TIME %%%%%%%%%%%%% dt = 0.001; t = 0:dt:100; %%%%%%%%%%%%%%%%%%%%%%%%%%%% % INITIALIZE STATE VARIABLES %%%%%%%%%%%%%%%%%%%%%%%%%%%% m = 0*t + m_inf(0); n = 0*t + n_inf(0); h = 0*t + h_inf(0); v = 0*t; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DEFINE STIMULUS STRENGTH, DURATION, & DELAY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tSTIM_START = 10; tSTIM_DUR = 1; STIM_STRENGTH = 10; %%%%%%%%%%%%% % DEFINE MISC %%%%%%%%%%%%% inRange = @(x,a,b) (x>=a) & (x<b); %%%%%%%%%%% % MAIN LOOP %%%%%%%%%%% for i = 1:length(t)-1 % extract membrane voltage u = v(i); % solve for membrane currents Ik = gk * n(i)^4 * (u - Ek); Ina = gna * m(i)^3*h(i) * (u - Ena); Il = gl * (u - El); Imem = Ik + Ina + Il; % determine stimulus current, if any Istim = 20 + 10*sin(dt/10); % if inRange( t(i) , tSTIM_START , tSTIM_START+tSTIM_DUR) % Istim = STIM_STRENGTH; % end % define the state variable derivatives dv = (Istim - Imem)/C; dm = am(u) * (1-m(i)) - bm(u) * m(i); dh = ah(u) * (1-h(i)) - bh(u) * h(i); dn = an(u) * (1-n(i)) - bn(u) * n(i); % use forward euler to increment the state variables v(i+1) = v(i) + dv*dt; m(i+1) = m(i) + dm*dt; h(i+1) = h(i) + dh*dt; n(i+1) = n(i) + dn*dt; end % plot the results plot(t,v); %axis([t(1) t(end) -20 120]); xlabel('time (ms)'); ylabel('membrane voltage (mV)');