Variance reduction by simultaneous multi-exponential analysis of data sets from different experiments

The analysis of experimental data from the photocycle of bacteriorhodopsin (bR) as sums of exponentials has accumulated a large amount of information on its kinetics which is still controversial. One reason for ambiguous results can be found in the inherent instabilities connected with the fitting of noisy data by sums of exponentials. Nevertheless, there are strategies to optimize the experiments and the data analysis by a proper combination of well known techniques. This paper describes an applicable approach based on the correct weighting of the data, a separation of the linear and the non-linear parameters in the process of the least squares approximation, and a statistical analysis applying the correlation matrix, the determinant of Fisher's information matrix, and the variance of the parameters as a measure of the reliability of the results. In addition, the confidence regions for the linear approximation of the non-linear model are compared with confidence regions for the true non-linear model. Evaluation techniques and rules for an optimum experimental design are mainly exemplified by the analysis of numerically generated model data with increasing complexity. The estimation of the number of exponentials significant for the interpretation of a given set of data is demonstrated by using records from eight absorption and photocurrent experiments on the photocycle of bacteriorhodopsin. Offprint requests to: K.-H. Müller