Morris-Lecar neurons connected by a conductance-based synapse.

ml_syn.py

#!/usr/bin/env python

"""
Morris-Lecar neurons connected by a conductance-based synapse.
"""

import numpy as np
import matplotlib
matplotlib.use('agg')

from brian import *

# Parameters from Rinzel & Ermentrout: Analysis of Neural Excitability and
# Oscillations, ch.7 (pp. 251-292) in 
# Methods in Neural Modeling: From Ions to Networks, 2nd Ed., 1998.

C = 20.0*uF

VL = -60.0*mV
VCa = 120.0*mV
VK = -84.0*mV

gCa = 4.4*msiemens
gK = 8.0*msiemens
gL = 2.0*msiemens

V1 = -1.2*mV
V2 = 18.0*mV
V3 = 2.0*mV
V4 = 30.0*mV

phi = 0.04/ms

n_model = Equations("""
dV/dt=(I-gL*(V-VL)-gCa*Minf*(V-VCa)-gK*N*(V-VK))/C : volt
dN/dt=(Ninf-N)*TauN : 1
Minf=(1+tanh((V-V1)/V2))/2.0 : 1
Ninf=(1+tanh((V-V3)/V4))/2.0 : 1
TauN=phi*cosh((V-V3)/(2*V4)) : 1/second
I : amp
""")

s_model = SynapticEquations("""
gS : siemens
I = gS*(V_pre-V_post) : amp
""")

N = 2
dt = 0.1*ms
clock = Clock(dt=dt)
g = NeuronGroup(N, model=n_model, clock=clock)
s = Synapses(g, model=s_model, clock=clock)

# Define connection between first and second neuron:
s[0, 1] = True

# Initialize conductance:
s.gS = 0.5*msiemens

# Link I parameters in neuron and synapse models:
g.I = s.I

# Initial state values:
g.V = -10.0*mV
g.N = (1+tanh((g.V-V3)/V4))/2.0

# Set constant input current for first neuron:
dur = 300*ms
g[0].I = TimedArray(np.ones(int(dur/dt))*200*uamp, dt=dt)

# Execute model:
state_mon = MultiStateMonitor(g, record=True)
run(dur)

# Visualize results
subplot(211)
plot(state_mon['V'].times/ms, state_mon['V'][0]/mV)
xlabel('t (ms)')
ylabel('V (mV)')
title('Membrane Potential (neuron 0)')
subplot(212)
plot(state_mon['V'].times/ms, state_mon['V'][1]/mV)
xlabel('t (ms)')
ylabel('V (mV)')
title('Membrane Potential (neuron 1)')
tight_layout()
savefig('ml_syn.png')