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Hodgkin Huxley Python Implementation
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| import scipy as sp | |
| import pylab as plt | |
| from scipy.integrate import odeint | |
| from scipy import stats | |
| import scipy.linalg as lin | |
| ## Full Hodgkin-Huxley Model (copied from Computational Lab 2) | |
| # Constants | |
| C_m = 1.0 # membrane capacitance, in uF/cm^2 | |
| g_Na = 120.0 # maximum conducances, in mS/cm^2 | |
| g_K = 36.0 | |
| g_L = 0.3 | |
| E_Na = 50.0 # Nernst reversal potentials, in mV | |
| E_K = -77.0 | |
| E_L = -54.387 | |
| # Channel gating kinetics | |
| # Functions of membrane voltage | |
| def alpha_m(V): return 0.1*(V+40.0)/(1.0 - sp.exp(-(V+40.0) / 10.0)) | |
| def beta_m(V): return 4.0*sp.exp(-(V+65.0) / 18.0) | |
| def alpha_h(V): return 0.07*sp.exp(-(V+65.0) / 20.0) | |
| def beta_h(V): return 1.0/(1.0 + sp.exp(-(V+35.0) / 10.0)) | |
| def alpha_n(V): return 0.01*(V+55.0)/(1.0 - sp.exp(-(V+55.0) / 10.0)) | |
| def beta_n(V): return 0.125*sp.exp(-(V+65) / 80.0) | |
| # Membrane currents (in uA/cm^2) | |
| # Sodium (Na = element name) | |
| def I_Na(V,m,h):return g_Na * m**3 * h * (V - E_Na) | |
| # Potassium (K = element name) | |
| def I_K(V, n): return g_K * n**4 * (V - E_K) | |
| # Leak | |
| def I_L(V): return g_L * (V - E_L) | |
| # External current | |
| def I_inj(t): # step up 10 uA/cm^2 every 100ms for 400ms | |
| return 10*(t>100) - 10*(t>200) + 35*(t>300) | |
| #return 10*t | |
| # The time to integrate over | |
| t = sp.arange(0.0, 400.0, 0.1) | |
| # Integrate! | |
| def dALLdt(X, t): | |
| V, m, h, n = X | |
| #calculate membrane potential & activation variables | |
| dVdt = (I_inj(t) - I_Na(V, m, h) - I_K(V, n) - I_L(V)) / C_m | |
| dmdt = alpha_m(V)*(1.0-m) - beta_m(V)*m | |
| dhdt = alpha_h(V)*(1.0-h) - beta_h(V)*h | |
| dndt = alpha_n(V)*(1.0-n) - beta_n(V)*n | |
| return dVdt, dmdt, dhdt, dndt | |
| X = odeint(dALLdt, [-65, 0.05, 0.6, 0.32], t) | |
| V = X[:,0] | |
| m = X[:,1] | |
| h = X[:,2] | |
| n = X[:,3] | |
| ina = I_Na(V,m,h) | |
| ik = I_K(V, n) | |
| il = I_L(V) | |
| plt.figure() | |
| plt.subplot(4,1,1) | |
| plt.title('Hodgkin-Huxley Neuron') | |
| plt.plot(t, V, 'k') | |
| plt.ylabel('V (mV)') | |
| plt.subplot(4,1,2) | |
| plt.plot(t, ina, 'c', label='$I_{Na}$') | |
| plt.plot(t, ik, 'y', label='$I_{K}$') | |
| plt.plot(t, il, 'm', label='$I_{L}$') | |
| plt.ylabel('Current') | |
| plt.legend() | |
| plt.subplot(4,1,3) | |
| plt.plot(t, m, 'r', label='m') | |
| plt.plot(t, h, 'g', label='h') | |
| plt.plot(t, n, 'b', label='n') | |
| plt.ylabel('Gating Value') | |
| plt.legend() | |
| plt.subplot(4,1,4) | |
| plt.plot(t, I_inj(t), 'k') | |
| plt.xlabel('t (ms)') | |
| plt.ylabel('$I_{inj}$ ($\\mu{A}/cm^2$)') | |
| plt.ylim(-1, 31) | |
| plt.show() |
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