Revisiting the Generalization of Entropy for Nonpositive Distribution: Application for Exponent Spectra Analysis
Abstract
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 nonnegative 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 nonuniform 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 nonexponential in the wild type bR. The nonexponential process could be interpreted as result of the protein conformational changes during proton transfer from the Shiffbase of bR.
 Publication:

Bayesian Inference and Maximum Entropy Methods in Science and Engineering: The 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
 Pub Date:
 December 2009
 DOI:
 10.1063/1.3275618
 Bibcode:
 2009AIPC.1193..218K
 Keywords:

 entropy;
 numerical analysis;
 functional analysis;
 algorithm theory;
 proteins;
 05.70.Ln;
 02.60.Cb;
 02.30.Sa;
 02.60.Gf;
 87.14.E;
 Nonequilibrium and irreversible thermodynamics;
 Numerical simulation;
 solution of equations;
 Functional analysis;
 Algorithms for functional approximation;
 Proteins