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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.IAeiytFP2pyqq7r9v2e3fLdFBamayPogEJ7PDXCbBmE)
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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.gRJ-0Vnr0j5lCl5EO2uGninnGDtPKFEVNTtVAp0hIzE)
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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.brm8xu2c-ZtNUxX-8X6lrGz9RFVQR4j8tUHi_ZnBgag)
Output:
![image](https://private-user-images.githubusercontent.com/75501882/248479850-2d50e813-8c7f-4ec0-88a9-e6ebadcb3db9.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.nPPHzNTJIjyIp6lZiP5xUgSwTwlsT-pH9DacQyGL9f0)