ANALYSIS OF FLASH PHOTOLYSIS DATA BY A GLOBAL FIT WITH MULTI-EXPONENTIALS–I. DETERMINATION OF THE MINIMAL NUMBER OF INTERMEDIATES IN THE PHOTOCYCLE OF BACTERIORHODOPSIN BY THE ‘STABILITY CRITERION’

Two bathointermediates of the bacteriorhodopsin photocycle, from time-resolved nanosecond spectra in the visible

Time-resolved measurements were performed on wild-type bacteriorhodopsin with an optical multichannel analyzer in the spectral range 350-735 nm, from 100 ns to the photocycle completion, at four temperatures in the 5-30 degrees C range. The intent was to examine the possibility of two K-like bathochromic intermediates and to obtain their spectra and kinetics in the visible. The existence of a second K-like intermediate, termed KL, had been postulated (Shichida et al., Biochim. Biophys. Acta 1983, 723, 240-246) to reconcile inconsistencies in data in the pico- and microsecond time domains. However, introduction of KL led to a controversy, since neither its visible spectrum nor its kinetics could be confirmed. Infrared data (Dioumaev and Braiman, J. Phys. Chem. B 1997, 101, 1655-1662) revealed a state which might have been considered a homologue to KL, but it had a kinetic pattern different from that of the earlier proposed KL. Here, we characterize two distinct K-like intermediates, K(E) ("early") and K(L) ("late"), by their spectra and kinetics in the visible as revealed by global kinetic analysis. The K(E)-to-K(L) transition has a time constant of approximately 250 ns at 20 degrees C, and describes a shift from K(E) with lambda(max) at approximately 600 nm and extinction of approximately 56,000 M(-1) x cm(-1) to K(L) with lambda(max) at approximately 590 nm and extinction of approximately 50,000 M(-1) x cm(-1). The temperature dependence of this transition is characterized by an enthalpy of activation of DeltaH(++) approximately 40 kJ/mol and a positive entropy of activation of DeltaS(++)/R approximately 4. The consequences of multiple K-like states for interpreting the spectral evolution in the early stages of the photocycle are discussed.

Bayesian maximum entropy (two-dimensional) lifetime distribution reconstruction from time-resolved spectroscopic data

Time-resolved spectroscopy is often used to monitor the relaxation processes (or reactions) of physical, chemical, and biochemical systems after some fast physical or chemical perturbation. Time-resolved spectra contain information about the relaxation kinetics, in the form of macroscopic time constants of decay and their decay associated spectra. In the present paper we show how the Bayesian maximum entropy inversion of the Laplace transform (MaxEnt-iLT) can provide a lifetime distribution without sign-restrictions (or two-dimensional (2D)-lifetime distribution), representing the most probable inference given the data. From the reconstructed (2D) lifetime distribution it is possible to obtain the number of exponentials decays, macroscopic rate constants, and exponential amplitudes (or their decay associated spectra) present in the data. More importantly, the obtained (2D) lifetime distribution is obtained free from pre-conditioned ideas about the number of exponential decays present in the data. In contrast to the standard regularized maximum entropy method, the Bayesian MaxEnt approach automatically estimates the regularization parameter, providing an unsupervised and more objective analysis. We also show that the regularization parameter can be automatically determined by the L-curve and generalized cross-validation methods, providing (2D) lifetime reconstructions relatively close to the Bayesian best inference. Finally, we propose the use of MaxEnt-iLT for a more objective discrimination between data-supported and data-unsupported quantitative kinetic models, which takes both the data and the analysis limitations into account. All these aspects are illustrated with realistic time-resolved Fourier transform infrared (FT-IR) synthetic spectra of the bacteriorhodopsin photocycle.

Bacteriorhodopsin

Bacteriorhodopsin is a seven-transmembrane helical protein that contains all-trans retinal. In this light-driven pump, a reaction cycle initiated by photoisomerization to 13-cis causes translocation of a proton across the membrane. Local changes in the geometry of the protonated Schiff base and the proton acceptor Asp85, and the proton conductivities of the half channels that lead from this active site to the two membrane surfaces, interact so as to allow timely proton transfers that result in proton release on the extracellular side and proton uptake on the cytoplasmic one. The details of the steps in this photocycle, and the underlying principles that ensure unidirectionality of the movement of a proton across the protein, provide strong clues to how ion pumps function.

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

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.

The photocycle of bacteriorhodopsin at high pH and ionic strength. I. Effects of pH and buffer on the absorption kinetics

A fitting analysis resolved the kinetics in the microsecond to second time range of the absorption changes in the bacteriorhodopsin photocycle at pH = 8.0-9.5 in 3 M KCl into seven exponential components. The time constants and/or amplitudes of all components are strongly pH-dependent. In the pH range studied, the logarithms of the pH-dependent time constants varied linearly with pH. The maximum absolute value of the corresponding slopes was 0.4, in contrast with the theoretically expected value of 1 for unidirectional reactions coupled directly to proton exchange with the bulk phase. This indicates that the extracted macroscopic rate constants are not identical to the microscopic rate constants for the elementary photocycle reaction steps. Unexpected differences were found in the kinetic parameters in CHES and borate buffers.

Proton translocation mechanism and energetics in the light-driven pump bacteriorhodopsin

In spite of many still unsolved problems, the mechanism and energetics of the light-driven proton transport are now basically understood. Energy captured during photoexcitation, and retained in the form of bond rotations and strains of the retinal, is transformed into directed changes in the pKa values of vectorially arranged proton transfer groups. The framework for the spatial and temporal organization of these changes is provided by the protein near the retinal Schiff base. The transport is completed by proton transfer among three essential groups in three domains lying roughly parallel with the membrane plane (Fig. 1): (a) the anionic D85 that is included in a complex of residues on the extracellular side containing also R82, D212, Y57 and bound water; (b) the protonated Schiff base; and (c) the protonated D96 that is included in a complex of residues on the cytoplasmic side containing also R227, T46, S226, and bound water. Other neighboring polar groups and water bound elsewhere which play a role in the transport do so either by further influencing the pKa values of the three protonable groups, or by providing passive pathways for proton transfer. The Schiff base proton, destabilized after photoexcitation, is transferred to the low pKa group D85 located on the extracellular side. The access of the deprotonated Schiff base then changes to the cytoplasmic side (the 'reprotonation switch') and its proton affinity increases. Finally, the proton of the high pKa group D96, with access to the cytoplasmic side, is destabilized by a protein conformational change through rearrangement of R227, T46, S226 and bound water, and becomes transferred to the Schiff base. As shown schematically in Fig. 3, these internal events are coupled to proton release and uptake at the two aqueous surfaces. The charge of the extracellular hydrogen-bonded complex is redistributed upon protonation of D85, and if the pH is above the pKa of the complex a proton is released to the bulk. After reprotonation of the Schiff base the pKa of the cytoplasmic hydrogen-bonded complex is raised well above the pH, and D96 regains a proton from the bulk. If the pH is lower than the pKa of the extracellular complex the proton release is delayed until the end of the photocycle. In either sequence there is net transfer of a proton from the cytoplasmic to the extracellular phase. The transfer of excess free energy from the chromophore to the protein, and finally to the transported proton, is described by a characteristic thermodynamic cycle.(ABSTRACT TRUNCATED AT 400 WORDS)

Proton transfer and energy coupling in the bacteriorhodopsin photocycle

A description of the rate constants and the energetics of the elementary reaction steps of the photocycle of bacteriorhodopsin has been helpful in understanding the mechanism of proton transport in this light-driven pump. The evidence suggests a single unbranched reaction sequence, BR-hv----K in equilibrium with L in equilibrium with M1----M2 in equilibrium with N in equilibrium with O----BR, where coupling to the proton-motive force is at the energetically and mechanistically important M1----M2 step. The consequences of site-specific mutations expressed homologously in Halobacterium halobium have revealed characteristics of the Schiff base deprotonation in the L----M1 reaction, the reorientation of the Schiff base from the extracellular to the cytoplasmic side in the M1----M2 reaction, and the reprotonation of the Schiff base in the M2----N reaction.

Effects of detergent environments on the photocycle of purified monomeric bacteriorhodopsin

Time-resolved difference spectra have been obtained for the photocycle of delipidated bacteriorhodopsin monomers (d-BR) in six different detergent micelle environments that were prepared by two new detergent-exchange techniques. A global kinetic analysis of the photocycle spectra for d-BR in each detergent environment was performed. Comparison of these results with those obtained for the photocycle of bacteriorhodopsin in purple membrane (PM) shows that there is one fewer kinetically distinguishable process for monomeric BR between the decay of the K intermediate and the rise of the M intermediate. Assuming a sequential pathway occurs in the photocycle, it appears that the equilibrium between the L and M intermediates is reached much more rapidly in the detergent micelles. This is attributed to a more direct interaction between Asp-85 and the proton on the nitrogen of the Schiff base of retinal for BR in the detergents. Equilibrium concentrations of late photocycle intermediates are also altered in detergents. The later steps of the photocycle, including the decay of the M intermediate, are slowed in detergents with rings in their hydrocarbon region. This is attributed to effects on conformational changes occurring during the decay of M and/or other later photocycle intermediates. The lifetime of dark adaptation of light-adapted d-BR in different detergent environments increases in environments where the lifetime of the M intermediate increases. These results suggest that the high percentage of either unsaturated or methyl-branched lipids in PM and the membranes of other retinal proteins may be important for their effective functioning.

Pathways of the rise and decay of the M photointermediate(s) of bacteriorhodopsin

The photocycle of bacteriorhodopsin (BR) was studied at alkaline pH with a gated multichannel analyzer, in order to understand the origins of kinetic complexities in the rise and decay of the M intermediate. The results indicate that the biphasic rise and decay kinetics are unrelated to a photoreaction of the N intermediate of the BR photocycle, proposed earlier by others [Kouyama et al. (1988) Biochemistry 27, 5855-5863]. Rather, under conditions where N did not accumulate in appreciable amounts (high pH, low salt concentration), they were accounted for by conventional kinetic schemes. These contained reversible interconversions, either M in equilibrium with N in one of two parallel photocycles or L in equilibrium with as well as M in equilibrium with N in a single photocycle. Monomeric BR also showed these kinetic complications. Conditions were then created where N accumulated in a photo steady state (high pH, high salt concentration, background illumination). The apparent increase in the proportion of the slow M decay component by the background illumination could be quantitatively accounted for with the single photocycle model, by the mixing of the relaxation of the background light induced photo steady state with the inherent kinetics of the photocycle. Postulating a new M intermediate which is produced by the photoreaction of N was neither necessary nor warranted by the data. The difference spectra suggested instead that absorption of light by N generates only one intermediate, observable between 100 ns and 1 ms, which absorbs near 610 nm. Thus, the photoreaction of N resembles in some respects that of BR containing 13-cis-retinal.