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model HodgkinHuxley
"Model of action potential in squid neurons (1952)"
parameter Real C_m =1.0 "membrane capacitance";
parameter Real g_Na =120 "conductance";
parameter Real g_K =36 "conductance";
parameter Real g_L =0.3 "conductance";
parameter Real V_Na =115 "potential";
parameter Real V_K =-12 "potential";
parameter Real V_lk =-49.387 "leak reveral potential";
parameter Real E_Na =-190 "equilibrium potential";
parameter Real E_K =-63 "equilibrium potential";
parameter Real E_lk =-85.613 "equilibrium potential";
parameter Real n =0.31768 "dimensionless; 0 to 1";
parameter Real m =0.05293 "dimensionless; 0 to 1";
parameter Real h =0.59612 "dimensionless; 0 to 1";
Real V_m "membrane voltage potential";
Real I =1.0 "membrane current";
Real alpha_n, alpha_m, alpha_h "rate constants";
Real beta_n, beta_m, beta_h "rate constants";
equation
C_m * der(V_m) = I - g_Na * m^3 * h * (V_m - E_Na) - g_K * n^4 * (V_m - E_K) - G_lk * (V_m - E_lk);
der(n) = alpha_n - n * (alpha_n + beta_n);
der(m) = alpha_m - m * (alpha_m + beta_m);
der(h) = alpha_h - h * (alpha_h + beta_h);
alpha_n = 0.01 * (V_m + 10) / (e^((V_m + 10)/10) - 1);
alpha_m = 0.1 * (V_m + 25) / (e^((V_m + 25)/10) - 1);
alpha_h = 0.07 * e^(V_m / 20);
beta_n = 0.125 * e^(V_m / 80);
beta_m = 4*e^(V_m/18);
beta_h = 1 / (e^((V_m + 30)/10) + 1);
end HodgkinHuxley;
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