Team:Paris/Modeling/Others prog

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complexes

```function complexes = complexes(x,y,K,n)
% amount of complexes n*x + y = x_-_y in function of x, y

% x, y = initial amounts of binding molecules
% K = dissociation constant
% n = stoechiometric coefficient of x

syms z; % to treat z as a symbolic variable
Eqn = ( ( x - n*z )^n )*( y - z ) - K*z; % to define the equation in whose
% the amount of complexes is a root

S = eval(solve( Eqn, 'z' )); % the vector of the roots

Index = find ((0 < S) & (n*S < x) & (S < y) & (imag(S) == 0)); % determine
% which
% root is
% acceptable

complexes = S(Index(1)); % the result

end
```

hill

```function compl = hill(x,K,n)
% complexation nx + Y = x_-_Y when x is in large excess :
% gives the ratio (x_-_Y)/(Ytotal) in function of x

% x = molecule that binds to Y
% K^n = dissociation constant
% n = stoechiometric coefficient of x ; also known as 'cooperativity'

compl = x^n/(K^n + x^n);

end
```