Theory and procedures for finding a correct kinetic model for the bacteriorhodopsin photocycle

In this paper, we present the implementation and results of new methodology based on linear algebra. The theory behind these methods is covered in det ail in the Supporting Information, available electronically (Shrager and He ndler), In brief, the methods presented search through all possible forward sequential submodels in order to find candidates that can be used to const ruct a complete model for the BR-photocycle. The methodology is limited onl y to forward sequential models. If no such models are compatible with the e xperimental data, none will be found, The procedures apply objective tests and filters to eliminate possibilities that cannot be correct, thus cutting the total number of candidate sequences to be considered. In the current a pplication, which uses six exponentials, the total sequences were cut from 1950 to 49. The remaining sequences were further screened using known exper imental criteria. The approach led to a solution which consists of a pair o f sequences, one with 5 exponentials showing BR* --> L-f --> M-f --> N --> O --> BR and the other with three exponentials showing BR* --> L-s --> M-s --> BR. The deduced complete kinetic model for the BR photocycle is thus ei ther a single photocycle branched at the L intermediate or a pair of two pa rallel photocycles, Reasons for preferring the parallel photocycles are pre sented. Synthetic data constructed on the basis of the parallel photocycles were indistinguishable from the experimental data in a number of analytica l tests that were applied.