Singular Value Decomposition with Self-modeling Applied to Determine Bacteriorhodopsin Intermediate Spectra: Analysis of Simulated Data

An a priori model-independent method for the determination of accurate spectra of photocycle intermediates is developed. The method, singular value decomposition with self-modeling (SVD-SM), is tested on simulated difference spectra designed to mimic the photocycle of the Asp-96 --> Asn mutant of bacteriorhodopsin. Stoichiometric constraints, valid until the onset of the recovery of bleached bacteriorhodopsin at the end of the photocycle, guide the self-modeling procedure. The difference spectra of the intermediates are determined in eigenvector space by confining the search for their coordinates to a stoichiometric plane. In the absence of random noise, SVD-SM recovers the intermediate spectra and their time evolution nearly exactly. The recovery of input spectra and kinetics is excellent although somewhat less exact when realistic random noise is included in the input spectra. The difference between recovered and input kinetics is now visually discernible, but the same reaction scheme with nearly identical rate constants to those assumed in the simulation fits the output kinetics well. SVD-SM relegates the selection of a photocycle model to the late stage of the analysis. It thus avoids derivation of erroneous model-specific spectra that result from global model-fitting approaches that assume a model at the outset.