The usual way to do this is by using what are called "dummy variables". I can't tell what you mean by, "I have several data sets (testI followed by a number)", so I'm going to take a guess at how to use a dummy variable in your case, you'll have to adapt it as appropriate.
I'll guess that you have two predictor variables, testC and testI, and one response, testE. Let's say you have two sets of those, with lengths n1 and n2. Create a new predictor variable
dummy = [repmat(1,n1,1); repmat(2,n2,1)]
then concatenate the two testC's together, testI's together, testE's together. Now you have one big (n1+n2)x4 set of data: the three original but concatenated variables, and dummy. Your model is chi2S(p,testConc,testI, testE), I'll guess that inside of that you compute something in the form of
sum((testE - f(p,testC,testI)).^2)
To get "stratified" estimates of a and b, and a "pooled" estimate of K, you need is to minimize
sum((testE(dummy==1) - f(p([1 3 5]),testC(dummy==1),testI(dummy==1))).^2) + sum((testE(dummy==2) - f(p([2 4 5]),testC(dummy==2),testI(dummy==1))).^2)
where p is now [a1 a2 b1 b2 K]. Pick starting values, pass this to fminsearch, and there you go. If your model really is this kind of response = f(parameters,predictors) form, I would strongly recommend that you use nlinfit, if you have access to the Statistics Toolbox, or lsqcurvefit, if you have access to the Optimization Toolbox.
Hope this helps.