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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.f3-4_v8W6MoXFv1rMektyuqrj8hb5m_vpalijMIdcXQ)
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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.F-O1lijB3XEGfuuMmWhlY2xT_nMHmCm0ukvmWQk4jx8)
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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.eifk2mDFHl29uOiEJUBUVChNDGEBc48vB8pErOdddeo)
Output:
![image](https://private-user-images.githubusercontent.com/75501882/248479850-2d50e813-8c7f-4ec0-88a9-e6ebadcb3db9.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.6guajkAuxYjA33EQUxVk935FohRfTuRNtP1jjLgMoiQ)