Example: Wang_Buszaki_1996

Note

You can launch an interactive, editable version of this example without installing any local files using the Binder service (although note that at some times this may be slow or fail to open):

Wang-Buszaki model

J Neurosci. 1996 Oct 15;16(20):6402-13. Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. Wang XJ, Buzsaki G.

Note that implicit integration (exponential Euler) cannot be used, and therefore simulation is rather slow.

from brian2 import *

defaultclock.dt = 0.01*ms

Cm = 1*uF # /cm**2
Iapp = 2*uA
gL = 0.1*msiemens
EL = -65*mV
ENa = 55*mV
EK = -90*mV
gNa = 35*msiemens
gK = 9*msiemens

eqs = '''
dv/dt = (-gNa*m**3*h*(v-ENa)-gK*n**4*(v-EK)-gL*(v-EL)+Iapp)/Cm : volt
m = alpha_m/(alpha_m+beta_m) : 1
alpha_m = 0.1/mV*10*mV/exprel(-(v+35*mV)/(10*mV))/ms : Hz
beta_m = 4*exp(-(v+60*mV)/(18*mV))/ms : Hz
dh/dt = 5*(alpha_h*(1-h)-beta_h*h) : 1
alpha_h = 0.07*exp(-(v+58*mV)/(20*mV))/ms : Hz
beta_h = 1./(exp(-0.1/mV*(v+28*mV))+1)/ms : Hz
dn/dt = 5*(alpha_n*(1-n)-beta_n*n) : 1
alpha_n = 0.01/mV*10*mV/exprel(-(v+34*mV)/(10*mV))/ms : Hz
beta_n = 0.125*exp(-(v+44*mV)/(80*mV))/ms : Hz
'''

neuron = NeuronGroup(1, eqs, method='exponential_euler')
neuron.v = -70*mV
neuron.h = 1
M = StateMonitor(neuron, 'v', record=0)

run(100*ms, report='text')

plot(M.t/ms, M[0].v/mV)
show()