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.
![image](https://private-user-images.githubusercontent.com/75501882/248479076-43afdc49-e4a2-4c93-a5c7-7e6db20d2691.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.BPpX49kiq9qjEHwzY_n2RbB7jObBs4h7dT1BZfMzj0Q)
Assuming cell as an electrical system before a biological is the fundamental part of modelling the cell membrane.
![image](https://private-user-images.githubusercontent.com/75501882/248479036-5535f66b-a4c1-4dd2-8108-b8ddc0cea100.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.t8cmLrzUuJA_hxucG_s0a_CoVp1mTynk_BJLj40AN_g)
Figure. Circuit representation
Hodgkin and Huxley are found and formulated this model after series of voltage clamp experiments by altering sodium and potassium concentrations.
Leakage Current:
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:
![image](https://private-user-images.githubusercontent.com/75501882/248479976-c7f75276-b514-447a-9628-21c146fe1bcd.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.udJm7DCjaPWE0Ax-aM_esZNZ3HHr8OnPTOuovb6PjWQ)
Output:
![image](https://private-user-images.githubusercontent.com/75501882/248479850-2d50e813-8c7f-4ec0-88a9-e6ebadcb3db9.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.6czptY7jKeVkyhe6_y8G5StXHYfZFqLc4GnR6EpbkjE)