MATLAB: I want to estimate kinetic parameters of Haldane inhibition model and find value of Ks and Ki but i dont know how to find haldane inhibition model in cftool or any other tool in matlab. please guide me to how to find these parameters .

curve fittingmodel

Haldane inhibition equation is M = (Mmax S)/Ks + S + (s(sqr)/ki) but the reason is i dont know how to implement Halnane Model in matlab and which tool help me to to easily calculate vale of Ks and Ki which are Kinetic parameters in Haldane inhibition Model.Please kindly help me i am new on Matlab.

Best Answer

I’m interested in these problems, so I decided to code this and run it. I experimented with various initial parameter estimates, and these provided the best fit:
% Parameters: mumax = b(1),  Ks = b(2),  Ki = b(3)
HaldaneInhMdl = @(b,S) b(1).*S ./ (b(2) + S + S.^2./b(3));
mu = [0.00169 0.001636 0.001387 0.001254 0.001444 0.0001631];
S = [1500 2500 3500 4500 5500 6500];
SSECF = @(b) sum((mu - HaldaneInhMdl(b,S)).^2);     % Sum-Squared-Error Cost Function
B0 = [0.004; 250; 2000];                            % Initial Parameter Estimates
[B, SSE] = fminsearch(SSECF, B0)                    % Estimate Parameters
Sp = linspace(min(S), max(S), 50);                  % ‘S’ Vector For Plot
fitmu = HaldaneInhMdl(B,Sp);                        % Calculate Fit
figure(1)
plot(S, mu, 'pg')
hold on
plot(Sp, fitmu, '-r')
hold off
grid
xlabel('Substrate [S]')
ylabel('\mu')
legend('Data', 'Fit', 'Location', 'SW')
txtlbl = sprintf('\\mu = %.3f \\times S / (%6.0f + S + s^2/%.1f)', B);
text(1500, 0.0006, txtlbl)
The call to fminsearch returns two values here, the first being ‘B’, the vector of the estimated parameters, and the second ‘SSE’ is the sum-squared-error at the convergence. The code is otherwise self-explanatory. You can make a more interesting text label with LaTeX. The one I provided here simply presents the estimated parameters in the context of the equation.
Related Question