Morris-Lecar Neuron
The Morris Lecar neuron model (also see this Scholarpedia article) is a 2-dimensional neuron model which models neural dynamics based on calcium and potassium conductances. A simplification of Hodgkin-Huxley dynamics without the sodium channels. Potassium and calcium can capture many of the core dynamics.
Part of a family of 2-variable neuron activation models.
As a family tree, Hodgkin-Huxley came first, then FitzHugh-Nagumo, then Morris-Lecar.
Membrane potential is what shows as activation.
Parameter descriptions are given here though it may help to simply think of these as the parameters of a complex dynamical system. More detailed description of similar parameters are in the AdEx docs.
The model tracks membrane voltage \(V\) and a potassium gating variable \(w_K\):
\[\frac{dV}{dt} = \frac{I_{bg} - I_{ion} + I_{syn} + I_{noise}}{C}\] \[\frac{dw_K}{dt} = \phi \cdot \lambda(V) \cdot \left(K_{\infty}(V) - w_K\right)\]Where:
- \(I_{ion} = I_{Ca} + I_K + I_L\) is the total ionic current.
- \[I_{Ca} = g_{Ca} \cdot m_{\infty}(V) \cdot (V - V_{Ca})\]
- \[I_K = g_K \cdot w_K \cdot (V - V_K)\]
- \[I_L = g_L \cdot (V - V_L)\]
- \[m_{\infty}(V) = 0.5 \cdot (1 + \tanh((V - V_{m1}) / V_{m2}))\]
- \[K_{\infty}(V) = 0.5 \cdot (1 + \tanh((V - V_{w1}) / V_{w2}))\]
- \[\lambda(V) = \cosh((V - V_{w1}) / 2V_{w2})\]
A spike is recorded if the membrane potential exceeds a fixed threshold.
Parameters
Ion Properties
- Ca²⁺ Conductance (µS/cm²): Maximal calcium conductance.
- K⁺ Conductance (µS/cm²): Maximal potassium conductance.
- Leak Conductance (µS/cm²): Maximal leak conductance.
- Ca²⁺ Equilibrium (mV): Reversal potential for calcium current.
- K⁺ Equilibrium (mV): Reversal potential for potassium current.
- Leak Equilibrium (mV): Reversal potential for leak current.
Membrane Properties
- Capacitance (µF/cm²): Affects the rate of membrane voltage change.
- Voltage Const. 1, 2: Shape the voltage dependence of calcium activation.
- Threshold (mV): Spike occurs when voltage exceeds this threshold.
- Background Current (nA): Constant applied input current.
Potassium Constants
- K⁺ Const. 1, 2: Shape the voltage dependence of potassium gating.
- K⁺ φ: Time constant for potassium gating variable dynamics.
For all other parameters, see common neuron properties