Evaluation of parameter estimation methods for estimating cellulase binding constants

Four nonlinear methods were investigated, with and without weighting, to determine their abilities to estimate the cellulase binding constants of a Thermomonospora fusca cellulase, E3, using the Langmuir adsorption model. The resulting binding constants were compared to those returned by the linear least squares method on the traditional linearizations of the Langmuir model, using both ordinary and Wilkerson-weighted formats. Of the linearizations tested, the Hanes-Woolf method, without weighting, returned the most reliable results. While the nonlinear methods avoided the inherent problems associated with the linearizations, the Gauss and Box-Kanemasu methods demonstrated convergence difficulties when the initial guesses significantly deviated from their true values. The most robust method was the Complex-Box search method, which converged on the global minimum independent of the initial guesses. The weighted methods failed to yield estimates of the maximum cellulase binding level comparable with those observed experimentally. Specifically, the Eb,ms estimated by the weighted methods were 25–30% lower than those obtained experimentally. It was postulated that this phenomenon is due to the error structure associated with the measured free cellulase concentration and to the limits on the number of data point replications.