5 is an advanced topic), and not precisely correctly. One may guess that other popular programs have similar characteristics, this website but I am not aware that any systematic testing has been done, so using any of them involves investing more confidence in the competence of the programmer than is wise. It is possible to decrease the dependence on assumptions about whose truth or otherwise there is little or no information,

either by using distribution-free methods (Cornish-Bowden and Eisenthal, 1974) or by using internal evidence in the data to suggest the most appropriate weighting scheme for least-squares analysis (Cornish-Bowden and Endrenyi, 1981). The former approach is easy to apply to Michaelis–Menten data, but computationally inconvenient for

equations of more than two parameters; the latter is readily generalizable. However, neither of them, as far as I know, Selleck AZD4547 has been incorporated into commercial programs in current use. I have discussed these questions in more detail elsewhere (Cornish-Bowden, 2012). For any set of observed rates v  , a program finds the parameter values for which the weighted sum of squared differences ∑w(v−v^)2 between the observed values v   and the calculated values v^ is a minimum. If the rates are known to have uniform standard deviation then each weight w   is set to 1; if they are known to have uniform coefficient of variation they should be weighted according to the true values, but as these are always unknown one must use calculated values as the best estimates, i.e., w=1/v^2. intermediate and other weighting schemes are also possible, but commercial programs usually make no provision for these. In introducing proper Branched chain aminotransferase methods of statistical analysis to enzymology, Wilkinson (1961) used the following series of (a  , v  ) pairs to illustrate the method he proposed: (0.138, 0.148); (0.220, 0.171); (0.291, 0.234); (0.560, 0.324); (0.766, 0.390); (1.46, 0.493). This example allows a simple test of whether a commercial program actually calculates what it is claimed

to calculate. For a uniform standard error it should give K^m=0.59655, V^=0.69040 and for a uniform coefficient of variation it should give K^m=0.51976, V^=0.64919 (the circumflexes indicate that these are least-squares values). SigmaPlot 11.2 gets the first calculation correct, for example, but for the second it gives K^m=0.5519, V^=0.6632 which is not correct. The discrepancy is within experimental uncertainty, of course, and has little practical importance, but it still illustrates the important point that one cannot assume that the authors of commercial programs really understand what they are trying to do. I have discussed elsewhere ( Cornish-Bowden, 2012) how they could have obtained such a result. It would be interesting to make similar studies of the results given by other widely used commercial programs, but as far as I know this has not been done.