Hodgkin-Huxley-Model-

Hodgkin&Huxley Model in MATLAB and Simulink.

It is a first model of a cell. Huxley and Hodgkin took giant axon from a squid and they have explained ion channels mechanism.

Assuming cell as an electrical system before a biological is the fundamental part of modelling the cell membrane.

Figure. Circuit representation

Hodgkin and Huxley are found and formulated this model after series of voltage clamp experiments by altering sodium and potassium concentrations.

$$\ C_m * (dV/dt) = I - I_m $$

$$\ I_m = g_Na * m^3 * h * (V - V_Na) - g_K * n^4 * (V - V_K) - g_L * (V - V_L) $$

Leakage Current: $$\ dm/dt = α_m * (1 - m) - β_m * m $$ $$\ dn/dt = α_n * (1 - n) - β_n * n $$ $$\ dh/dt = α_h * (1 - h) - β_h * h $$

Variables: m, n, h: State variables

g: Channel conductivity

α, β : Rate coefficients

C_m : Membrane capacitance

I: Input current

V: Membrane potential

I_m : Membrane current

V_Na : Sodium equilibrium potential

V_K : Potassium equilibrium potential

V_L : Leakage equilibrium potential

Model:

Output: