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 .

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.

[Star Strider]

Your statement of the model is impossible to interpret. (I cannot find a definition online that seems to match it.)

Make an attempt at coding the equation, and tell us what your data are, in terms of the equation. Including some or all of your data set would also help.

We can help you with the parameter estimation, but the approach depends on whether the function turns out to be linear or nonlinear.

[UOS Ambala Tech]

Haldane Kinetic Model

Sir Value of μ are [0.00169 0.001636 0.001387 0.001254 0.001444 0.0001631] and value of S is [1500 2500 3500 4500 5500 6500] i want to calculate value of Ks Ki and μmax and show them on nonlinear curve using kinetics equation of Haldane Kinetic Model whose equation is given in picture please hel me.i am very thankful to you for your kind answer .

[UOS Ambala Tech]

Sir i use it for Modeling of the bio-degradation of phenol by Haldane inhibitory model or also known as Haldane kinetic model to estimate kinetic parameters Ks Ki and μmax on a curve.

Answer 1

[Star Strider]

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.

[UOS Ambala Tech]

Thanks Sir. you are great. :) You have solved my problem. I am jumping with excitement because i was stuck in it for 2 days and you are the one who give me relief.

[Star Strider]

My pleasure, as always!

[Star Strider]

The ‘B0’ are the initial parameter estimates (so fminsearch knows where to start looking). I probably used those values after the function converged near them, after a few attempts to fit it. (Nearly three years later, I don’t remember exactly how I arrived at them.) The ‘B’ vector are the fitted parameter estimates.

Different data sets would likely require different ‘B0’. They would likely be close to these.

[Alex Sha]

The matlab code provided by Star Strider above will lead to a local solution since the initial start-values given are not appropriate (actually, it is really hard job to guess initial start-values), the global solution should be:

Root of Mean Square Error (RMSE): 0.000333344649507014
Sum of Squared Residual: 6.66711932129723E-7
Correlation Coef. (R): 0.763906844412625
R-Square: 0.583553666940454

Parameter	Best Estimate
----------	-------------
b1	-0.0024588918013058
b2	-2415.37695742383
b3	-1712.36849656769