On the dangers of adjusting the parameters values of mechanism-based mathematical models

Mechanism-based mathematical models describe systems in terms of identifiable physical processes, and the parameters are assumed to have fundamental physical significance. Ideally, the parameter values are measured independent of the system being modeled, but these values are often adjusted to give the best fit of model predictions to experimental data. A systematic investigation of the effects of such parameter adjustment was conducted by developing a model system comprising a known reaction mechanism and known rate constants. Simulations of experiments were run, and then attempts were made to model the system under a variety of problematic, but realistic, conditions. (1) When one rate constant was seriously in error, adjustment of a different rate constant gave the greatest improvement in the model fit. (2) When a contaminant was present in the experiment, the effects could be hidden by the adjustment of the rate constants. (3) When an incorrect reaction mechanism was assumed, the error could be hidden by parameter adjustment if the concentrations of only one of the reacting species were considered or if an unweighted fit was used for the optimization. (4) Parameter values adjusted for one set of experimental conditions gave a poorer fit than did the unadjusted parameter values when attempting to model a new set of experimental condition (addition of an inhibitor). These results show the potential dangers of adjusting parameter values and the importance of measuring as many variables as possible in a complex system.