You can use MatLab's fit function. Let me give you an example.
Let us assume you have the following set of 50 experimental values of S and mu
S = linspace(0,10000,50);
mu = 0.1160*S./(43.53+S+(S.^2/387))-0.5*rand(size(S))/500; % I have added random noise to the measured values
Now, you can create a fittype using, let's say, the Haldane model.
fitfunc = fittype(@(mumax,KS,KI,x) mumax*x./(KS+x+x.^2/KI));
The you give initial guesses for the three parameters.
x0 = [0.1 50 300];
And eventually use fit to optimize the parameters using the experimental data.
f = fit(S',mu',fitfunc,'StartPoint',x0);
coeffvals = coeffvalues(f)
plot(f,S,mu)
As you can see, the coefficient values are slightly different from those specified in your table due to my adding of a random noise to simulate experimental data.
You can use the same procedure with the other functions listed in your table.
