耦合两个HH神经元

Question

我将两个hodgkin-huxley神经元与双指数突触连接进行耦合，这种耦合似乎是正确的，突触后神经元在突触前神经元峰后出现峰。但问题是突触后神经元不会因为未知的原因停止放电

the pre-synaptic and post-synaptic voltage with pre-synaptic current

import numpy as np
import matplotlib.pyplot as plt
import time

def HHmodel(I,gSyn):
    #holders
    v = []
    m = []
    h = []
    n = []
    dt = 0.05
    t = np.linspace(0,100,len(I))
    Isyn = []
    #constants
    Cm = 1.0 #microFarad
    ENa=50 #miliVolt
    EK=-77  #miliVolt
    El=-54 #miliVolt
    g_Na=120 #mScm-2
    g_K=36 #mScm-2
    g_l=0.03 #mScm-2
    Esyn = 4 #mScm-2
    def alphaN(v):
        return 0.01*(v+50)/(1-np.exp(-(v+50)/10))

    def betaN(v):
        return 0.125*np.exp(-(v+60)/80)

    def alphaM(v):
        return 0.1*(v+35)/(1-np.exp(-(v+35)/10))

    def betaM(v):
        return 4.0*np.exp(-0.0556*(v+60))

    def alphaH(v):
        return 0.07*np.exp(-0.05*(v+60))

    def betaH(v):
        return 1/(1+np.exp(-(0.1)*(v+30)))

    #Initialize the voltage and the channels :
    v.append(-60)
    m0 = alphaM(v[0])/(alphaM(v[0])+betaM(v[0]))
    n0 = alphaN(v[0])/(alphaN(v[0])+betaN(v[0]))
    h0 = alphaH(v[0])/(alphaH(v[0])+betaH(v[0]))

    #t.append(0)
    m.append(m0)
    n.append(n0)
    h.append(h0)

    #solving ODE using Euler's method:
    for i in range(1,len(t)):
        m.append(m[i-1] + dt*((alphaM(v[i-1])*(1-m[i-1]))-betaM(v[i-1])*m[i-1]))
        n.append(n[i-1] + dt*((alphaN(v[i-1])*(1-n[i-1]))-betaN(v[i-1])*n[i-1]))
        h.append(h[i-1] + dt*((alphaH(v[i-1])*(1-h[i-1]))-betaH(v[i-1])*h[i-1]))
        gNa = g_Na * h[i-1]*(m[i-1])**3
        gK=g_K*n[i-1]**4
        gl=g_l
        INa = gNa*(v[i-1]-ENa)
        IK = gK*(v[i-1]-EK)
        Il=gl*(v[i-1]-El)
        if (gSyn.any()==0):
            v.append(v[i-1]+(dt)*((1/Cm)*(I[i-1]-(INa+IK+Il))))
            Isyn.append(0)
            #print('sucks')
        else:
            #Isyn = -gSyn*(v[i-1]-Esyn)
            Isyn.append(-gSyn[i-1]*(v[i-1]-Esyn))
            v.append(v[i-1]+(dt)*((1/Cm)*(I[i-1]-(INa+IK+Il+Isyn[i-1]))))

        #v.append(v[i-1]+(dt)*((1/Cm)*(I-(INa+IK+Il))))
    return v,t,Isyn
#function to count the spikes and generate pre-synaptic current
def synapticCurrent(voltage,time):
    spikes = []
    for i in range(len(time)):
        if (voltage[i-1]<0 and voltage[i]>0):
            spikes.append(round(time[i],3))
        else:
            spikes.append(0)
    tfinal = np.zeros(len(spikes))
    if (len(spikes)>1):
        t = np.arange(0,100,1)
        for i in range(len(spikes)):
            if (spikes[i]!= 0):
                tfinal[i:i+100] = t
    tRise = 1.5
    tDecay = 2
    gBar = 2
    gSyn = -gBar*(1/tDecay-tDecay)*(np.exp(-(tfinal)/tDecay)-np.exp(-(tfinal)/tRise))
    #Isyn = -gSyn*(voltage-Esyn)
    return gSyn,spikes

offset = 6.4
dataset = 10000
standardDeviation = 3
pulsyCurrent = np.zeros(dataset)
pulsyCurrent[2000:2500] = 8
constantCurrent = 6.2*np.ones(dataset)
voltage1,time,Isyn1 = HHmodel(pulsyCurrent,np.zeros(dataset))
synapticCurrent1,spikes1 = synapticCurrent(voltage1,time)
voltage2,time,Isyn2 = HHmodel(constantCurrent,synapticCurrent1)
synapticCurrent2,spikes2 = synapticCurrent(voltage2,time)
#plt.plot(preSynaptic1)
plt.figure(figsize=(18,8))
plt.plot(time,voltage1,'r--',label='preSynaptic voltage');
plt.plot(time,voltage2,'g-.',label='postSynaptic voltage');
plt.plot(time[1::],Isyn2,'b--',label='synapticCurrent');
#plt.plot(time,preSynaptic1,'y');
plt.eventplot(spikes1[10::],colors='red',linelengths=2,linewidths=3,lineoffsets=-10);
plt.eventplot(spikes2[10::],colors='green',linelengths=2,linewidths=3,lineoffsets=10);
plt.legend(loc='upper left')
plt.show()

如果你发现问题，请告诉我。 对我来说，一切似乎都是对的