Can you please help me complete writing this program in Python 3.5? See the deta
ID: 3774539 • Letter: C
Question
Can you please help me complete writing this program in Python 3.5? See the details below:
Write a program in Python 3.5 that can solve the Hodgkin-Huxley first order differential equation using the Euler method and the 4^th order (see article called "A quantitative description of membrane current and its application to conduction and excitation in nerve"). This program must include functions called irange(), euler(), and rk(). The following code below is what I currently have: (Also, please see notes at the bottom, and I need to add code where it says "ADD CODE HERE! !!")| "Create a generator to iterate over the interval we wish to solve the ODE on" while startExplanation / Answer
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()
actually i got some idea so this code for that.its not exact