MorrisLecar

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=[2459466628 2755113083]), 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

update(x=None)[source]#

The function to specify the updating rule.