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irahulsonkarirahulsonkar
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inital commit notebook (issue #19)
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‎notebook/.ipynb_checkpoints/HHmodel-checkpoint.py‎

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import scipy as sp
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import numpy as np
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import pylab as plt
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from scipy.integrate import odeint
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class HodgkinHuxley:
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t = np.arange(0.0, 450.0, 0.01)
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def __init__(self, C_m, g_Na, g_K, g_L, E_Na, E_K, E_L, t):
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self.C_m = C_m
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self.g_Na = g_Na
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self.g_K = g_K
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self.g_L = g_L
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self.E_Na = E_Na
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self.E_K = E_K
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self.E_L = E_L
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self.t = t
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#self.tn = tn
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#self.delta_t = delta_t
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#self.t = np.arange(t0, tn, delta_t)
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#print(self.t)
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def alpha_m(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.1*(V+40.0)/(1.0 - np.exp(-(V+40.0) / 10.0))
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def beta_m(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 4.0*np.exp(-(V+65.0) / 18.0)
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def alpha_h(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.07*np.exp(-(V+65.0) / 20.0)
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def beta_h(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 1.0/(1.0 + np.exp(-(V+35.0) / 10.0))
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def alpha_n(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.01*(V+55.0)/(1.0 - np.exp(-(V+55.0) / 10.0))
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def beta_n(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.125*np.exp(-(V+65) / 80.0)
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def I_Na(self, V, m, h):
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"""
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Membrane current (in uA/cm^2)
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Sodium (Na = element name)
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| :param V:
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| :param m:
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| :param h:
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| :return:
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"""
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return self.g_Na * m**3 * h * (V - self.E_Na)
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def I_K(self, V, n):
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"""
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Membrane current (in uA/cm^2)
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Potassium (K = element name)
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| :param V:
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| :param h:
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| :return:
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"""
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return self.g_K * n**4 * (V - self.E_K)
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# Leak
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def I_L(self, V):
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"""
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Membrane current (in uA/cm^2)
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Leak
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| :param V:
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| :param h:
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| :return:
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"""
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return self.g_L * (V - self.E_L)
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def I_inj(self, t):
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"""
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External Current
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| :param t: time
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| :return: step up to 10 uA/cm^2 at t>100
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| step down to 0 uA/cm^2 at t>200
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| step up to 35 uA/cm^2 at t>300
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| step down to 0 uA/cm^2 at t>400
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"""
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return 10*(t>100) - 10*(t>200) + 35*(t>300) - 35*(t>400)
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@staticmethod
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def dALLdt(X, t, self):
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"""
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Integrate
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| :param X:
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| :param t:
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| :return: calculate membrane potential & activation variables
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"""
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V, m, h, n = X
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dVdt = (self.I_inj(t) - self.I_Na(V, m, h) - self.I_K(V, n) - self.I_L(V)) / self.C_m
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dmdt = self.alpha_m(V)*(1.0-m) - self.beta_m(V)*m
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dhdt = self.alpha_h(V)*(1.0-h) - self.beta_h(V)*h
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dndt = self.alpha_n(V)*(1.0-n) - self.beta_n(V)*n
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return dVdt, dmdt, dhdt, dndt
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def Main(self):
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"""
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Main demo for the Hodgkin Huxley neuron model
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"""
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X = odeint(self.dALLdt, [-65, 0.05, 0.6, 0.32], self.t, args=(self,))
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V = X[:,0]
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m = X[:,1]
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h = X[:,2]
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n = X[:,3]
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ina = self.I_Na(V, m, h)
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ik = self.I_K(V, n)
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il = self.I_L(V)
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plt.figure(figsize=[4,2])
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ax1 = plt.subplot(4,1,1)
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plt.title('Hodgkin-Huxley Neuron')
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plt.plot(self.t, V, 'k')
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plt.ylabel('V (mV)')
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plt.subplot(4,1,2, sharex = ax1)
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plt.plot(self.t, ina, 'c', label='$I_{Na}$')
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plt.plot(self.t, ik, 'y', label='$I_{K}$')
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plt.plot(self.t, il, 'm', label='$I_{L}$')
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plt.ylabel('Current')
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plt.legend()
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plt.subplot(4,1,3, sharex = ax1)
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plt.plot(self.t, m, 'r', label='m')
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plt.plot(self.t, h, 'g', label='h')
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plt.plot(self.t, n, 'b', label='n')
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plt.ylabel('Gating Value')
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plt.legend()
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plt.subplot(4,1,4, sharex = ax1)
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i_inj_values = [self.I_inj(t) for t in self.t]
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plt.plot(self.t, i_inj_values, 'k')
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plt.xlabel('t (ms)')
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plt.ylabel('$I_{inj}$ ($\\mu{A}/cm^2$)')
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plt.ylim(-1, 40)
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plt.tight_layout()
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plt.show()
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#plt.rcParams["figure.figsize"]=200,100
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#plt.show()

‎notebook/.ipynb_checkpoints/HodgkinHuxley-checkpoint.py‎

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import scipy as sp
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import numpy as np
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import pylab as plt
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from scipy.integrate import odeint
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class HodgkinHuxley():
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"""Full Hodgkin-Huxley Model implemented in Python"""
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C_m = 1.0
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"""membrane capacitance, in uF/cm^2"""
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g_Na = 120.0
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"""Sodium (Na) maximum conductances, in mS/cm^2"""
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g_K = 36.0
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"""Postassium (K) maximum conductances, in mS/cm^2"""
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g_L = 0.3
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"""Leak maximum conductances, in mS/cm^2"""
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E_Na = 50.0
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"""Sodium (Na) Nernst reversal potentials, in mV"""
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E_K = -77.0
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"""Postassium (K) Nernst reversal potentials, in mV"""
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E_L = -54.387
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"""Leak Nernst reversal potentials, in mV"""
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t = np.arange(0.0, 450.0, 0.01)
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""" The time to integrate over """
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def alpha_m(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.1*(V+40.0)/(1.0 - np.exp(-(V+40.0) / 10.0))
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def beta_m(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 4.0*np.exp(-(V+65.0) / 18.0)
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def alpha_h(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.07*np.exp(-(V+65.0) / 20.0)
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def beta_h(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 1.0/(1.0 + np.exp(-(V+35.0) / 10.0))
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def alpha_n(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.01*(V+55.0)/(1.0 - np.exp(-(V+55.0) / 10.0))
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def beta_n(self, V):
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"""Channel gating kinetics. Functions of membrane voltage"""
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return 0.125*np.exp(-(V+65) / 80.0)
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def I_Na(self, V, m, h):
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"""
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Membrane current (in uA/cm^2)
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Sodium (Na = element name)
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| :param V:
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| :param m:
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| :param h:
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| :return:
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"""
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return self.g_Na * m**3 * h * (V - self.E_Na)
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def I_K(self, V, n):
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"""
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Membrane current (in uA/cm^2)
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Potassium (K = element name)
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| :param V:
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| :param h:
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| :return:
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"""
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return self.g_K * n**4 * (V - self.E_K)
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# Leak
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def I_L(self, V):
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"""
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Membrane current (in uA/cm^2)
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Leak
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| :param V:
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| :param h:
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| :return:
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"""
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return self.g_L * (V - self.E_L)
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def I_inj(self, t):
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"""
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External Current
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| :param t: time
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| :return: step up to 10 uA/cm^2 at t>100
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| step down to 0 uA/cm^2 at t>200
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| step up to 35 uA/cm^2 at t>300
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| step down to 0 uA/cm^2 at t>400
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"""
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return 10*(t>100) - 10*(t>200) + 35*(t>300) - 35*(t>400)
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@staticmethod
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def dALLdt(X, t, self):
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"""
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Integrate
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| :param X:
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| :param t:
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| :return: calculate membrane potential & activation variables
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"""
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V, m, h, n = X
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dVdt = (self.I_inj(t) - self.I_Na(V, m, h) - self.I_K(V, n) - self.I_L(V)) / self.C_m
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dmdt = self.alpha_m(V)*(1.0-m) - self.beta_m(V)*m
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dhdt = self.alpha_h(V)*(1.0-h) - self.beta_h(V)*h
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dndt = self.alpha_n(V)*(1.0-n) - self.beta_n(V)*n
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return dVdt, dmdt, dhdt, dndt
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def Main(self):
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"""
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Main demo for the Hodgkin Huxley neuron model
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"""
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X = odeint(self.dALLdt, [-65, 0.05, 0.6, 0.32], self.t, args=(self,))
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V = X[:,0]
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m = X[:,1]
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h = X[:,2]
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n = X[:,3]
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ina = self.I_Na(V, m, h)
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ik = self.I_K(V, n)
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il = self.I_L(V)
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plt.figure()
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ax1 = plt.subplot(4,1,1)
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plt.title('Hodgkin-Huxley Neuron')
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plt.plot(self.t, V, 'k')
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plt.ylabel('V (mV)')
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plt.subplot(4,1,2, sharex = ax1)
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plt.plot(self.t, ina, 'c', label='$I_{Na}$')
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plt.plot(self.t, ik, 'y', label='$I_{K}$')
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plt.plot(self.t, il, 'm', label='$I_{L}$')
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plt.ylabel('Current')
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plt.legend()
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plt.subplot(4,1,3, sharex = ax1)
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plt.plot(self.t, m, 'r', label='m')
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plt.plot(self.t, h, 'g', label='h')
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plt.plot(self.t, n, 'b', label='n')
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plt.ylabel('Gating Value')
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plt.legend()
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plt.subplot(4,1,4, sharex = ax1)
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i_inj_values = [self.I_inj(t) for t in self.t]
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plt.plot(self.t, i_inj_values, 'k')
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plt.xlabel('t (ms)')
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plt.ylabel('$I_{inj}$ ($\\mu{A}/cm^2$)')
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plt.ylim(-1, 40)
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plt.tight_layout()
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plt.show()
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if __name__ == '__main__':
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runner = HodgkinHuxley()
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runner.Main()

‎notebook/.ipynb_checkpoints/equivalentCircuit-checkpoint.PNG‎

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