Thermal equilibration between the M and N intermediates in the photocycle of bacteriorhodopsin

Machine-learning model selection and parameter estimation from kinetic data of complex first-order reaction systems

Dealing with a system of first-order reactions is a recurrent issue in chemometrics, especially in the analysis of data obtained by spectroscopic methods applied on complex biological systems. We argue that global multiexponential fitting, the still common way to solve such problems, has serious weaknesses compared to contemporary methods of sparse modeling. Combining the advantages of group lasso and elastic net-the statistical methods proven to be very powerful in other areas-we created an optimization problem tunable from very sparse to very dense distribution over a large pre-defined grid of time constants, fitting both simulated and experimental multiwavelength spectroscopic data with high computational efficiency. We found that the optimal values of the tuning hyperparameters can be selected by a machine-learning algorithm based on a Bayesian optimization procedure, utilizing widely used or novel versions of cross-validation. The derived algorithm accurately recovered the true sparse kinetic parameters of an extremely complex simulated model of the bacteriorhodopsin photocycle, as well as the wide peak of hypothetical distributed kinetics in the presence of different noise levels. It also performed well in the analysis of the ultrafast experimental fluorescence kinetics data detected on the coenzyme FAD in a very wide logarithmic time window. We conclude that the primary application of the presented algorithms-implemented in available software-covers a wide area of studies on light-induced physical, chemical, and biological processes carried out with different spectroscopic methods. The demand for this kind of analysis is expected to soar due to the emerging ultrafast multidimensional infrared and electronic spectroscopic techniques that provide very large and complex datasets. In addition, simulations based on our methods could help in designing the technical parameters of future experiments for the verification of particular hypothetical models.

Ultrafast Photoinduced Deactivation Dynamics of Proteorhodopsin

We report femtosecond time-resolved absorption change measurements of the photoinduced deactivation dynamics of a microbial rhodopsin in the ultraviolet-visible and mid-infrared range. The blue light quenching process is recorded in green proteorhodopsin's (GPR) primary proton donor mutant E108Q from the deprotonated 13-cis photointermediate. The return of GPR to the dark state occurs in two steps, starting with the photoinduced 13-cis to all-trans reisomerization of the retinal. The subsequent Schiff base reprotonation via the primary proton acceptor (D97) occurs on a nanosecond time scale. This step is two orders of magnitude faster than that in bacteriorhodopsin, potentially because of the very high pK_A of the GPR primary proton acceptor.

Photocycle and photoreversal of photoactive yellow protein at alkaline pH: kinetics, intermediates, and equilibria

Since the habitat of Halorhodospira halophila is distinctly alkaline, we investigated the kinetics and intermediates of the photocycle and photoreversal of the photoreceptor photoactive yellow protein (PYP) from pH 8 to 11. SVD analysis of the transient absorption time traces in a broad wavelength range (330-510 nm) shows the presence of three spectrally distinct species (I1, I1', and I2') at pH 10. The spectrum of I1' was obtained in two different ways. The maximal absorption is at 425 nm. I1' probably has a deprotonated chromophore and may be regarded as the alkaline form of I2'. At pH 10, the I1 intermediate decays in approximately 330 micros in part to I1' before I1 and I1' decay further to I2' in approximately 1 ms. From the rise of I2' (approximately 1 ms) to the end of the photocycle, the three intermediates (I1, I1', and I2') remain in equilibrium and decay together to P in approximately 830 ms. Assuming that the spectra of I1, I1', and I2' are pH-independent, their time courses were determined. On the millisecond to second time scale, they are in a pH-dependent equilibrium with a pKa of approximately 9.9. With an increase in pH, the I1 and I1' populations increase at the expense of the amount of I2'. The apparent rate constant for the recovery of P slows with an increase in pH with a pKa of approximately 9.7. The equal pH dependence of this rate and the equilibrium concentrations follows, if we assume that the equilibration rates between the intermediates are much faster than the recovery rate and that the recovery occurs from I2'. The pKa of approximately 9.9 is assigned to the deprotonation of the phenol of the surface-exposed chromophore in the I1'-I2' equilibrium. The I1-I1' equilibrium is pH-independent. Photoreversal experiments at pH 10 with the second flash at 355 nm indicate the presence of only one I2-like intermediate, which we assign on the basis of its lambda(max) value to I2'. After the rapid unresolved photoisomerization to I2'(trans), the reversal pathway back to P involves two sequential steps (60 micros and 3 ms). The amplitude spectra show that I1'(trans) and I1(trans) intermediates participate in this reversal.

Photoexcitation of the O-intermediate in bacteriorhodopsin mutant L93A

During the extended lifetime of the O-state in bacteriorhodopsin (bR) mutant L93A, two substates have been distinguished. The first O-intermediate (OI) is in rapid equilibrium with N and apparently still has a 13-cis chromophore. OI undergoes a photoreaction with a small absorbance change, positive charge transport in the pumping direction, and proton release and uptake. None of these effects was detected after photoexcitation of the late O (OII). The most likely interpretation of the effects seen is an accelerated return of the molecule from the OI- to the bR-state. However, with a lifetime approximately 140 ms, the reaction cannot account for the observed high pumping efficiency of the mutant under continuous illumination. We suggest that OII corresponds to the O-intermediate with a twisted all-trans chromophore seen in the photocycle of wild-type bR, where the 13-cis OI-intermediate under the usual conditions does not accumulate in easily detectable amounts and, therefore, has generally been overlooked. Both the OI- and OII-decays are apparently strongly inhibited in the mutant.

Origins of deuterium kinetic isotope effects on the proton transfers of the bacteriorhodopsin photocycle

Deuterium kinetic isotope effects (KIE) were measured, and proton inventory plots were constructed, for the rates of reactions in the photocycles of wild-type bacteriorhodopsin and several site-specific mutants. Consistent with earlier reports from many groups, very large KIEs were observed for the third (and largest) rise component for the M state and for the decay of the O state, processes both linked to proton transfers in the extracellular region. The proton inventory plots (ratio of reaction rates in mixtures of H(2)O and D(2)O to that in H(2)O vs mole fraction of D(2)O) were approximately linear for the first and second M rise components and for M decay, as well as for O decay, indicating that the rates of these reactions are limited by simple proton transfer. Uniquely, the third rise component of M (and in the D96N mutant also a fourth rise component) exhibited a strongly curved proton inventory plot, suggesting that its rate, which largely accounts for the rate of deprotonation of the retinal Schiff base, depends on a complex multiproton process. This curvature is observed also in the E194Q, E204Q, and Y57F mutants but not in the R82A mutant. From these findings, and from the locations of bound water in the extracellular region in the crystal structure of the protein [Luecke, Schobert, Richter, Cartailler, and Lanyi (1999) J. Mol. Biol. 291, 899-911], we suspect that the effects of deuterium substitution on the formation of the M state originate from cooperative rearrangements of the extensively hydrogen-bonded water molecules 401, 402, and 406 near Asp-85 and Arg-82.

Photoelectric response of the N intermediate of bacteriorhodopsin and its mutant T46V

Double flash experiments were performed in order to gain information about the characteristics of the N intermediates of the photocycle of bacteriorhodopsin. The N intermediates of wild-type bacteriorhodopsin and mutant T46V were excited at different delay times after the first laser flash which induced the photocycle and the electric responses were registered. These electric signals revealed that charge motions occurred in both cases, though charge translocation, i.e. H(+) pumping, could not be observed. The delay time dependence of the electric signals is characterized by two distinct processes corresponding to two substates of the N intermediates.

Time-resolved step-scan Fourier transform infrared spectroscopy reveals differences between early and late M intermediates of bacteriorhodopsin

In this report, from time-resolved step-scan Fourier transform infrared investigations from 15 ns to 160 ms, we provide evidence for the subsequent rise of three different M states that differ in their structures. The first state rises with approximately 3 microseconds to only a small percentage. Its structure as judged from amide I/II bands differs in small but well-defined aspects from the L state. The next M state, which appears in approximately 40 microseconds, has almost all of the characteristics of the "late" M state, i.e., it differs considerably from the first one. Here, the L left arrow over right arrow M equilibrium is shifted toward M, although some percentage of L still persists. In the last M state (rise time approximately 130 microseconds), the equilibrium is shifted toward full deprotonation of the Schiff base, and only small additional structural changes take place. In addition to these results obtained for unbuffered conditions or at pH 7, experiments performed at lower and higher pH are presented. These results are discussed in terms of the molecular changes postulated to occur in the M intermediate to allow the shift of the L/M equilibrium toward M and possibly to regulate the change of the accessibility of the Schiff base necessary for effective proton pumping.

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.

Understanding structure and function in the light-driven proton pump bacteriorhodopsin

The atomic structure of bacteriorhodopsin and the outlines of its proton transport mechanism are now available. Photoisomerization of the retinal in the chromophore creates a steric and electrostatic conflict at the retinal binding site. The free energy gain sets off a sequence of reactions in which directed proton transfers take place between the protonated retinal Schiff base, Asp-85, and Asp-96. These internal steps, and other proton transfers at and near the two aqueous interfaces, add up to the translocation of a proton from the cytoplasmic to the extracellular side of the membrane. Bound water plays a crucial role in proton conduction in both extracellular and cytoplasmic regions, but the means by which the protons move from site to site differ. Proton release to the extracellular surface is through interaction of a hydrogen-bonded chain of identified aspartic acid, arginine, water, and glutamic acid residues with Asp-85, while proton uptake from the cytoplasmic surface utilizes a single aspartic acid, Asp-96, whose protonation state appears to be regulated by the protein conformation dependent hydration of this region. The directionality of the translocation is ensured by the accessibility of the Schiff base to the extracellular and cytoplasmic directions after the retinal is photoisomerized, as well as the changing proton affinities of the acceptor Asp-85 and donor Asp-96.

Kinetic and thermodynamic study of the bacteriorhodopsin photocycle over a wide pH range

The photocycle of bacteriorhodopsin and its thermodynamic parameters were studied in the pH range of 4.5-9. Measurements were performed at five different wavelengths (410, 500, 570, 610, and 650 nm), in the time interval 300 ns to 0.5 s, at six temperatures between 5 and 30 degreesC. Data were fitted to different photocycle models. The sequential model with reversible reactions gave a good fit, and the linear character of the Eyring plots was fulfilled. The parallel model with unidirectional reactions gave a poor fit, and the Eyring plot of the rate constants did not follow the expected linear behavior. When a parallel model with reversible reactions, which has twice as many free parameters as the sequential model, was considered, the quality of the fit did not improve and the Eyring plots were not linear. The sequential model was used to determine the thermodynamic activation parameters (activation enthalpy, entropy, and free energy) of the transitions and the free energy levels of the intermediates. pH dependence of the parameters revealed details of the transitions between the intermediates: the transitions M1 to M2 and N to O disclosed a large entropy increase, which could be interpreted as a loosening of the protein structure. The pH dependence of the energy levels explains the disappearance of intermediate O at high pH. A hypothesis is proposed to interpret the relation between the observed pKa of the photocycle energetics and the role of several amino acids in the protein.

Electric signals during the bacteriorhodopsin photocycle, determined over a wide pH range

From the electric signals measured after photoexcitation, the electrogenicity of the photocycle intermediates of bacteriorhodopsin were determined in a pH range of 4.5-9. Current measurements and absorption kinetic signals at five wavelengths were recorded in the time interval from 300 ns to 0.5 s. To fit the data, the model containing sequential intermediates connected by reversible first-order reactions was used. The electrogenicities were calculated from the integral of the current signal, by using the time-dependent concentrations of the intermediates, obtained from the fits. Almost all of the calculated electrogenicities were pH independent, suggesting that the charge motions occur inside the protein. Only the N intermediate exhibited pH-dependent electrogenicity, implying that the protonation of Asp96, from the intracellular part of the protein, is not from a well-determined proton donor. The calculated electrogenicities gave good approximations of all of the details of the measured electric signals.

Connectivity of the retinal Schiff base to Asp85 and Asp96 during the bacteriorhodopsin photocycle: the local-access model

In the recently proposed local-access model for proton transfers in the bacteriorhodopsin transport cycle (Brown et al. 1998. Biochemistry. 37:3982-3993), connection between the retinal Schiff base and Asp85 (in the extracellular direction) and Asp96 (in the cytoplasmic direction)is maintained as long as the retinal is in its photoisomerized state. The directionality of the proton translocation is determined by influences in the protein that make Asp85 a proton acceptor and, subsequently, Asp96 a proton donor. The idea of concurrent local access of the Schiff base in the two directions is now put to a test in the photocycle of the D115N/D96N mutant. The kinetics had suggested that there is a single sequence of intermediates, L<-->M1<-->M2<-->N, and the M2-->M1 reaction depends on whether a proton is released to the extracellular surface. This is now confirmed. We find that at pH 5, where proton release does not occur, but not at higher pH, the photostationary state created by illumination with yellow light contains not only the M1 and M2 states, but also the L and the N intermediates. Because the L and M1 states decay rapidly, they can be present only if they are in equilibrium with later intermediates of the photocycle. Perturbation of this mixture with a blue flash caused depletion of the M intermediate, followed by its partial recovery at the expense of the L state. The change in the amplitude of the C=O stretch band at 1759 cm-1 demonstrated protonation of Asp85 in this process. Thus, during the reequilibration the Schiff base lost its proton to Asp85. Because the N state, also present in the mixture, arises by protonation of the Schiff base from the cytoplasmic surface, these results fulfill the expectation that under the conditions tested the extracellular access of the Schiff base would not be lost at the time when there is access in the cytoplasmic direction. Instead, the connectivity of the Schiff base flickers rapidly (with the time constant of the M1<-->M2 equilibration) between the two directions during the entire L-to-N segment of the photocycle.

Early and late M intermediates in the bacteriorhodopsin photocycle: a solid-state NMR study

To enforce vectorial proton transport in bacteriorhodopsin (bR), it is necessary that there be a change in molecular structure between deprotonation and reprotonation of the chromophore-i.e., there must be at least two different M intermediates in the functional photocycle. We present here the first detection of multiple M intermediates in native wild-type bacteriorhodopsin by solid-state NMR. Illumination of light-adapted [zeta-15N-Lys]-bR at low temperatures shifts the 15N signal of the retinal Schiff base (SB) downfield by about 150 ppm, indicating a deprotonated chromophore. In 0.3 M Gdn-HCl at pH 10.0, two different M states are obtained, depending on the temperature during illumination. The M state routinely prepared at the lower temperature, Mo, decays to the newly observed M state, Mn, and the N intermediate, as the temperature is increased. Both relax to bR568 at 0 degreesC. A unique reaction sequence is derived: bR568-->Mo-->(Mn+N)-->bR568. Mo and Mn have similar chemical shifts at [12-13C]ret, [14-13C]ret, and [epsilon-13C]Lys216, indicating that Mn, like Mo, has a 13-cis and C=N anti chromophore. However, a small splitting in the [14-13C]ret signal of Mo reveals that it has at least two substates. The 7 ppm greater shielding of the SB nitrogen in Mn compared to Mo suggests an increase in basicity and/or hydrogen bonding. Probing the peptide backbone of the protein, via [1-13C]Val labeling, reveals a substantial structural change between Mo and Mn including the relaxation of perturbations at some sites and the development of new perturbations at other sites. The combination of the change in the protein structure and the increase in the pKa of the SB suggests that the demonstrated Mo-->Mn transition may function as the "reprotonation switch" required for vectorial proton transport.

Fourier transform infrared double-flash experiments resolve bacteriorhodopsin's M1 to M2 transition

The orientation of the central proton-binding site, the protonated Schiff base, away from the proton release side to the proton uptake side is crucial for the directionality of the proton pump bacteriorhodopsin. It has been proposed that this movement, called the reprotonation switch, takes place in the M1 to M2 transition. To resolve the molecular events in this M1 to M2 transition, we performed double-flash experiments. In these experiments a first pulse initiates the photocycle and a second pulse selectively drives bR molecules in the M intermediate back into the BR ground state. For short delay times between initiating and resetting pulses, most of the M molecules being reset are in the M1 intermediate, and for longer delay times most of the reset M molecules are in the M2 intermediate. The BR-M1 and BR-M2 difference spectra are monitored with nanosecond step-scan Fourier transform infrared spectroscopy. Because the Schiff base reprotonation rate is kM1 = 0.8 x 10(7) s(-1) in the light-induced M1 back-reaction and kM2 = 0.36 x 10(7) s(-1) in the M2 back-reaction, the two different M intermediates represent two different proton accessibility configurations of the Schiff base. The results show only a minute movement of one or two peptide bonds in the M1 to M2 transition that changes the interaction of the Schiff base with Y185. This backbone movement is distinct from the larger one in the subsequent M to N transition. No evidence of a chromophore isomerization is seen in the M1 to M2 transition. Furthermore, the results show time-resolved reprotonation of the Schiff base from D85 in the M photo-back-reaction, instead of from D96, as in the conventional cycle.

Spectrally silent transitions in the bacteriorhodopsin photocycle

The photocycle kinetics of bacteriorhodopsin were analyzed from 0 to 40 degrees C at 101 wavelengths (330-730 nm). The data can be satisfactorily approximated by eight exponents. The slowest component (half-time 20 ms at 20 degrees C) belongs to the 13-cis cycle. The residual seven exponentials that are sufficient to describe the all-trans photocycle indicate that at least seven intermediates of the all-trans cycle must exist, although only five spectrally distinct species (K, L, M, N, and O) have been identified. These seven exponentials and their spectra at different temperatures provide the basis for the discussion of various kinetic schemes of the relaxation. The simplest model of irreversible sequential transitions includes after the first K--> L step the quasiequilibria of L<-->M, M<-->N, and N<-->O intermediates. These quasiequilibria are controlled by rate-limiting dynamics of the protein and/or proton transfer steps outside the chromophore region. Thus there exists an apparent kinetic paradox (i.e., why is the number of exponents of relaxation (at least seven) higher than the number of distinct spectral intermediates (only five)), which can be explained by assuming that some of the transitions correspond to changes in the quasiequilibria between spectrally distinct intermediates (i.e., are spectrally silent).

Arginine-82 regulates the pKa of the group responsible for the light-driven proton release in bacteriorhodopsin

In wild-type bacteriorhodopsin light-induced proton release occurs before uptake at neutral pH. In contrast, in mutants in which R82 is replaced by a neutral residue (as in R82A and R82Q), only a small fraction of the protons is released before proton uptake at neutral pH; the major fraction is released after uptake. In R82Q the relative amounts of the two types of proton release, "early" (preceding proton uptake) and "late" (following proton uptake), are pH dependent. The main conclusions are that 1) R82 is not the normal light-driven proton release group; early proton release can be observed in the R82Q mutant at higher pH values, suggesting that the proton release group has not been eliminated. 2) R82 affects the pKa of the proton release group both in the unphotolyzed state of the pigment and during the photocycle. In the wild type (in 150 mM salt) the pKa of this group decreases from approximately 9.5 in the unphotolyzed pigment to approximately 5.8 in the M intermediate, leading to early proton release at neutral pH. In the R82 mutants the respective values of pKa of the proton release group in the unphotolyzed pigment and in M are approximately 8 and 7.5 in R82Q (in 1 M salt) and approximately 8 and 6.5 in R82K (in 150 mM KCl). Thus in R82Q the pKa of the proton release group does not decrease enough in the photocycle to allow early proton release from this group at neutral pH. 3) Early proton release in R82Q can be detected as a photocurrent signal that is kinetically distinct from those photocurrents that are due to proton movements from the Schiff base to D85 during M formation and from D96 to the Schiff base during the M-->N transition. 4) In R82Q, at neutral pH, proton uptake from the medium occurs during the formation of O. The proton is released during the O-->bacteriorhodopsin transition, probably from D85 because the normal proton release group cannot deprotonate at this pH. 5) The time constant of early proton release is increased from 85 microseconds in the wild type to 1 ms in R82Q (in 150 mM salt). This can be directly attributed to the increase in the pKa of the proton release group and also explains the uncoupling of proton release from M formation. 6) In the E204Q mutant only late proton release is observed at both neutral and alkaline pH, consistent with the idea that E204 is the proton release group. The proton release is concurrent with the O-->bacteriorhodopsin transition, as in R82Q at neutral pH.

Determination of the transiently lowered pKa of the retinal Schiff base during the photocycle of bacteriorhodopsin

Reprotonation of the transiently deprotonated retinal Schiff base in the bacteriorhodopsin photocycle is greatly slowed when the proton donor Asp-96 is removed with site-specific mutagenesis, but its rate is restored upon adding azide or other weak acids such as formate and cyanate. As expected, between pH 3 and 7 the rate of Schiff base protonation in the photocycle of the D96N mutant correlates with the concentrations of the acid forms of these agents. Dissection of the rates in the biexponential reprotonation kinetics of the Schiff base between pH 7 and 9 yielded calculated rate constants for the protonation equilibrium. Their dependencies on pH and azide or cyanate concentrations are consistent with both earlier suggested mechanisms: (i) azide and other weak acids may function as proton carriers in the protonation equilibrium of the Schiff base, or (ii) the binding of their anionic forms may catalyze proton conduction to and from the Schiff base. The measured rate constants allow the calculation of the pKa of the Schiff base during its reprotonation in the photocycle of D96N. It is 8.2-8.3, a value much below the pKa determined earlier in unphotolyzed bacteriorhodopsin.

Effects of hydrostatic pressure on the kinetics reveal a volume increase during the bacteriorhodopsin photocycle

A protein structural change in the photocycle of the proton pump, bacteriorhodopsin, detected earlier in the M photointermediate by diffraction, consists mainly of changes at the cytoplasmic surface that include an outward tilt of the cytoplasmic end of helix F. Such a conformational rearrangement would result in greater exposure of the interhelical cavity to the medium, increased binding of water, and thus an increase in volume. In order to correlate the structural change with the kinetics of the photoreaction cycle, we measured the effects of hydrostatic pressure between 1 bar and 1 kbar on the rate constants of the photocycles of wild type bacteriorhodopsin and the D96N mutant. Combining the results provided all of the activation volumes and, therefore, the changes of volume in the various states after the K photointermediate is formed. There is an approximately 32 mL/mol volume increase after deprotonation of the retinal Schiff base to the extracellular side, during the M1 --> M2 reaction, that is not reversed until well after its reprotonation from the cytoplasmic side. The magnitude of this volume increase is about as predicted by the increase of the lattice constant in the M state. It occurs in the photocycle at the proposed reprotonation switch, supporting the idea that this conformation change is what alters the accessibility of the Schiff base from one membrane side to the other. Additionally, we observe a large positive (approximately 50 mL/mol) activation volume for proton exchange between D96 and the Schiff base of the wild type protein.(ABSTRACT TRUNCATED AT 250 WORDS)