Revisiting the Generalization of Entropy for Non-positive Distribution: Application for Exponent Spectra Analysis

Originally the maximum entropy method for exponent deconvolution was restricted to the positive exponent's amplitudes by the entropy S(f,m) definition. It limits application of the method, since many experimental kinetics show both the rise and the decay, which manifest themselves as positive and negative amplitudes in the exponent spectrum. The generalization of entropy formulation for non-negative distribution (S.F. Gull and J. Skilling) overcomes this limitation. The drawback of the approach was, that m lost the meaning of the prior distribution, since that maximum of generalized S(f,m) is independent on m and achieved at f=0. It is significant problem when there are apriori information about possible spectrum behaviour. In the present work some assumptions of the entropy generalization was relaxed and alternative entropy formulation, with non-uniform prior was used for analysis of simulated and experimental data. The new approach was applied to spectra analysis of the absorption kinetics of the bacteriorhodopsin (bR - light driven proton pump from archea Halobacterium salinarium) photocycle. It was shown that the process of the intermediate M formation is non-exponential in the wild type bR. The non-exponential process could be interpreted as result of the protein conformational changes during proton transfer from the Shiff-base of bR.