Skip to content
Permalink
master
Switch branches/tags
Go to file
 
 
Cannot retrieve contributors at this time
"""
wb_cond_exp - Wang-Buzsaki model
################################
Description
+++++++++++
wb_cond_exp is an implementation of a modified Hodkin-Huxley model.
(1) Post-synaptic currents: Incoming spike events induce a post-synaptic change
of conductance modeled by an exponential function.
(2) Spike Detection: Spike detection is done by a combined threshold-and-local-
maximum search: if there is a local maximum above a certain threshold of
the membrane potential, it is considered a spike.
References
++++++++++
.. [1] Wang, X.J. and Buzsaki, G., (1996) Gamma oscillation by synaptic
inhibition in a hippocampal interneuronal network model. Journal of
neuroscience, 16(20), pp.6402-6413.
See Also
++++++++
hh_cond_exp_traub, wb_cond_multisyn
"""
neuron wb_cond_exp:
state:
r integer = 0 # number of steps in the current refractory phase
V_m mV = E_L # Membrane potential
Inact_h real = alpha_h_init / ( alpha_h_init + beta_h_init )
Act_n real = alpha_n_init / ( alpha_n_init + beta_n_init )
end
equations:
# synapses: exponential conductance
kernel g_in = exp(-1.0 / tau_syn_in * t)
kernel g_ex = exp(-1.0 / tau_syn_ex * t)
recordable inline I_syn_exc pA = convolve(g_ex, spikeExc) * ( V_m - E_ex )
recordable inline I_syn_inh pA = convolve(g_in, spikeInh) * ( V_m - E_in )
inline I_Na pA = g_Na * _subexpr(V_m) * Inact_h * ( V_m - E_Na )
inline I_K pA = g_K * Act_n**4 * ( V_m - E_K )
inline I_L pA = g_L * ( V_m - E_L )
V_m' =( -( I_Na + I_K + I_L ) + I_e + I_stim + I_syn_inh + I_syn_exc ) / C_m
Act_n' = ( alpha_n(V_m) * ( 1 - Act_n ) - beta_n(V_m) * Act_n ) # n-variable
Inact_h' = ( alpha_h(V_m) * ( 1 - Inact_h ) - beta_h(V_m) * Inact_h ) # h-variable
end
parameters:
t_ref ms = 2.0 ms # Refractory period
g_Na nS = 3500.0 nS # Sodium peak conductance
g_K nS = 900.0 nS # Potassium peak conductance
g_L nS = 10 nS # Leak conductance
C_m pF = 100.0 pF # Membrane Capacitance
E_Na mV = 55.0 mV # Sodium reversal potential
E_K mV = -90.0 mV # Potassium reversal potentia
E_L mV = -65.0 mV # Leak reversal Potential (aka resting potential)
V_Tr mV = -55.0 mV # Spike Threshold
tau_syn_ex ms = 0.2 ms # Rise time of the excitatory synaptic alpha function i
tau_syn_in ms = 10.0 ms # Rise time of the inhibitory synaptic alpha function
E_ex mV = 0.0 mV # Excitatory synaptic reversal potential
E_in mV = -75.0 mV # Inhibitory synaptic reversal potential
# constant external input current
I_e pA = 0 pA
end
internals:
RefractoryCounts integer = steps(t_ref) # refractory time in steps
alpha_n_init 1/ms = -0.05/(ms*mV) * (E_L + 34.0 mV) / (exp(-0.1 * (E_L + 34.0 mV)) - 1.0)
beta_n_init 1/ms = 0.625/ms * exp(-(E_L + 44.0 mV) / 80.0 mV)
alpha_h_init 1/ms = 0.35/ms * exp(-(E_L + 58.0 mV) / 20.0 mV)
beta_h_init 1/ms = 5.0 / (exp(-0.1 / mV * (E_L + 28.0 mV)) + 1.0) /ms
end
input:
spikeInh nS <- inhibitory spike
spikeExc nS <- excitatory spike
I_stim pA <- continuous
end
output: spike
update:
U_old mV = V_m
integrate_odes()
# sending spikes: crossing 0 mV, pseudo-refractoriness and local maximum...
if r > 0: # is refractory?
r -= 1
elif V_m > V_Tr and U_old > V_m: # threshold && maximum
r = RefractoryCounts
emit_spike()
end
end
function _subexpr(V_m mV) real:
return alpha_m(V_m)**3 / ( alpha_m(V_m) + beta_m(V_m) )**3
end
function alpha_m(V_m mV) 1/ms:
return 0.1/(ms*mV) * (V_m + 35.0 mV) / (1.0 - exp(-0.1 mV * (V_m + 35.0 mV)))
end
function beta_m(V_m mV) 1/ms:
return 4.0/(ms) * exp(-(V_m + 60.0 mV) / 18.0 mV)
end
function alpha_n(V_m mV) 1/ms:
return -0.05/(ms*mV) * (V_m + 34.0 mV) / (exp(-0.1 * (V_m + 34.0 mV)) - 1.0)
end
function beta_n(V_m mV) 1/ms:
return 0.625/ms * exp(-(V_m + 44.0 mV) / 80.0 mV)
end
function alpha_h(V_m mV) 1/ms:
return 0.35/ms * exp(-(V_m + 58.0 mV) / 20.0 mV)
end
function beta_h(V_m mV) 1/ms:
return 5.0 / (exp(-0.1 / mV * (V_m + 28.0 mV)) + 1.0) /ms
end
end