MorrisLecar#
- class brainpy.dyn.MorrisLecar(size, sharding=None, keep_size=False, mode=None, name=None, method='exp_auto', init_var=True, V_Ca=130.0, g_Ca=4.4, V_K=-84.0, g_K=8.0, V_leak=-60.0, g_leak=2.0, C=20.0, V1=-1.2, V2=18.0, V3=2.0, V4=30.0, phi=0.04, V_th=10.0, W_initializer=OneInit(value=0.02), V_initializer=Uniform(min_val=-70.0, max_val=-60.0, rng=[3949182063 2081860855]), noise=None)[source]#
The Morris-Lecar neuron model.
Model Descriptions
The Morris-Lecar model [4] (Also known as \(I_{Ca}+I_K\)-model) is a two-dimensional “reduced” excitation model applicable to systems having two non-inactivating voltage-sensitive conductances. This model was named after Cathy Morris and Harold Lecar, who derived it in 1981. Because it is two-dimensional, the Morris-Lecar model is one of the favorite conductance-based models in computational neuroscience.
The original form of the model employed an instantaneously responding voltage-sensitive Ca2+ conductance for excitation and a delayed voltage-dependent K+ conductance for recovery. The equations of the model are:
\[\begin{split}\begin{aligned} C\frac{dV}{dt} =& - g_{Ca} M_{\infty} (V - V_{Ca})- g_{K} W(V - V_{K}) - g_{Leak} (V - V_{Leak}) + I_{ext} \\ \frac{dW}{dt} =& \frac{W_{\infty}(V) - W}{ \tau_W(V)} \end{aligned}\end{split}\]Here, \(V\) is the membrane potential, \(W\) is the “recovery variable”, which is almost invariably the normalized \(K^+\)-ion conductance, and \(I_{ext}\) is the applied current stimulus.
Model Parameters
Parameter
Init Value
Unit
Explanation
V_Ca
130
mV
Equilibrium potentials of Ca+.(mV)
g_Ca
4.4
Maximum conductance of corresponding Ca+.(mS/cm2)
V_K
-84
mV
Equilibrium potentials of K+.(mV)
g_K
8
Maximum conductance of corresponding K+.(mS/cm2)
V_Leak
-60
mV
Equilibrium potentials of leak current.(mV)
g_Leak
2
Maximum conductance of leak current.(mS/cm2)
C
20
Membrane capacitance.(uF/cm2)
V1
-1.2
Potential at which M_inf = 0.5.(mV)
V2
18
Reciprocal of slope of voltage dependence of M_inf.(mV)
V3
2
Potential at which W_inf = 0.5.(mV)
V4
30
Reciprocal of slope of voltage dependence of W_inf.(mV)
phi
0.04
A temperature factor. (1/s)
V_th
10
mV
The spike threshold.
References