Evaluation of intrinsic chemical kinetics and transient product spectra from time-resolved spectroscopic data

Abstract

This communication is devoted to the evaluation of true spectra and intrinsic (microscopic) rate constants from apparent kinetics measured in time-resolved spectroscopic experiments monitoring complex relaxation dynamics of multi-intermediate systems. Retinal proteins, cytochrom c oxidase, phytochrome, hemoglobin, and photoactive yellow protein are examples of natural systems in which several transient states (intermediates) overlap so strongly, both in time and spectral domains, that their isolation and full characterization by classical biochemical methods is impossible, and mathematical evaluation of their true spectra and microscopic kinetic constants is required. Most of the popular methods for analysis of kinetic data, global fitting (GF), singular value decomposition (SVD), principal component analysis (PCA) and factor analysis (FA), are applicable to two-dimensional (2D, in time and spectral domains) arrays of data. All these methods produce only a phenomenological description of data, that approximates the measured data only with apparent kinetics. A fundamental limitation, namely, insufficient information in 2D data, does not allow any of these methods to reach the final goal: to recalculate from apparent to intrinsic values in any but the most trivial cases. A strategy was proposed (J.F. Nagle, Biophys. J.. 59 (1991) 476–487) to include an additional (third) information-rich dimension, temperature, into the simultaneous computer analysis. A simultaneous direct fitting of 3D data arrays to systems of differential rate equations allows recalculation of apparent kinetics into true spectra and intrinsic rate constants. In spite of its evident theoretical advantages, this strategy has not been successful on real data. Here we describe another custom-built program, SCHEMEFIT, developed for the same purpose: to fit measured kinetics directly to the system of coupled differential rate equations describing the photochrome's relaxation dynamics. Though sharing the main strategy with the previous approach, SCHEMEFIT is based on a different set of numeric algorithms, and its application requires different tactics. Its performance is illustrated on synthetic data, and compared with GF and SVD. An example of applying SCHEMEFIT to the photocycle of halorhodopsin is also reported.