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

Photophysics-informed two-photon voltage imaging using FRET-opsin voltage indicators

Microbial rhodopsin-derived genetically encoded voltage indicators (GEVIs) are powerful tools for mapping bioelectrical dynamics in cell culture and in live animals. Förster resonance energy transfer (FRET)-opsin GEVIs use voltage-dependent changes in opsin absorption to modulate the fluorescence of an attached fluorophore, achieving high brightness, speed, and voltage sensitivity. However, the voltage sensitivity of most FRET-opsin GEVIs has been reported to decrease or vanish under two-photon (2P) excitation. Here we investigated the photophysics of the FRET-opsin GEVIs Voltron1 and 2. We found that the voltage sensitivity came from a photocycle intermediate, not from the opsin ground state. The voltage sensitivities of both GEVIs were nonlinear functions of illumination intensity; for Voltron1, the sensitivity reversed sign under low-intensity illumination. Using photocycle-optimized 2P illumination protocols, we demonstrate 2P voltage imaging with Voltron2 in barrel cortex of a live mouse. These results open the door to high-speed 2P voltage imaging of FRET-opsin GEVIs in vivo.

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.

Infrared Difference Spectroscopy of Proteins: From Bands to Bonds

Infrared difference spectroscopy probes vibrational changes of proteins upon their perturbation. Compared with other spectroscopic methods, it stands out by its sensitivity to the protonation state, H-bonding, and the conformation of different groups in proteins, including the peptide backbone, amino acid side chains, internal water molecules, or cofactors. In particular, the detection of protonation and H-bonding changes in a time-resolved manner, not easily obtained by other techniques, is one of the most successful applications of IR difference spectroscopy. The present review deals with the use of perturbations designed to specifically change the protein between two (or more) functionally relevant states, a strategy often referred to as reaction-induced IR difference spectroscopy. In the first half of this contribution, I review the technique of reaction-induced IR difference spectroscopy of proteins, with special emphasis given to the preparation of suitable samples and their characterization, strategies for the perturbation of proteins, and methodologies for time-resolved measurements (from nanoseconds to minutes). The second half of this contribution focuses on the spectral interpretation. It starts by reviewing how changes in H-bonding, medium polarity, and vibrational coupling affect vibrational frequencies, intensities, and bandwidths. It is followed by band assignments, a crucial aspect mostly performed with the help of isotopic labeling and site-directed mutagenesis, and complemented by integration and interpretation of the results in the context of the studied protein, an aspect increasingly supported by spectral calculations. Selected examples from the literature, predominately but not exclusively from retinal proteins, are used to illustrate the topics covered in this review.

The Grateful Infrared: Sequential Protein Structural Changes Resolved by Infrared Difference Spectroscopy

The catalytic activity of proteins is a function of structural changes. Very often these are as minute as protonation changes, hydrogen bonding changes, and amino acid side chain reorientations. To resolve these, a methodology is afforded that not only provides the molecular sensitivity but allows for tracing the sequence of these hierarchical reactions at the same time. This feature article showcases results from time-resolved IR spectroscopy on channelrhodopsin (ChR), light-oxygen-voltage (LOV) domain protein, and cryptochrome (CRY). All three proteins are activated by blue light, but their biological role is drastically different. Channelrhodopsin is a transmembrane retinylidene protein which represents the first light-activated ion channel of its kind and which is involved in primitive vision (phototaxis) of algae. LOV and CRY are flavin-binding proteins acting as photoreceptors in a variety of signal transduction mechanisms in all kingdoms of life. Beyond their biological relevance, these proteins are employed in exciting optogenetic applications. We show here how IR difference absorption resolves crucial structural changes of the protein after photonic activation of the chromophore. Time-resolved techniques are introduced that cover the time range from nanoseconds to minutes along with some technical considerations. Finally, we provide an outlook toward novel experimental approaches that are currently developed in our laboratories or are just in our minds ("Gedankenexperimente"). We believe that some of them have the potential to provide new science.

Further studies with isolated absolute infrared spectra of bacteriorhodopsin photocycle intermediates: conformational changes and possible role of a new proton-binding center

We recently published procedures describing the isolation of absolute infrared spectra for the intermediates of the bacteriorhodopsin (BR) photocycle and from these, obtaining transitional difference spectra between consecutive intermediates. In that work, we concentrated mainly on proton-binding centers and the route of proton transport across the membrane. In the current study, we used isolated spectra for the amide I, amide II, and amide III envelopes to obtain quantitative information on the extent of conformational change accompanying each transition in the photocycle. Our main finding was that most of the conformational changes occur in the conversion of the M(F) intermediate to N. In our earlier publication, a new proton acceptor, absorbing at 1650 cm(-1) was identified, which appeared to accept a proton from Asp96COOH during the transformation of BR† to L. Below, we present evidence that supports this interpretation and propose a possible role for this new component.

Probing specific molecular processes and intermediates by time-resolved Fourier transform infrared spectroscopy: application to the bacteriorhodopsin photocycle

We present a general approach for probing the kinetics of specific molecular processes in proteins by time-resolved Fourier transform infrared (IR) spectroscopy. Using bacteriorhodopsin (bR) as a model we demonstrate that by appropriately monitoring some selected IR bands it is possible obtaining the kinetics of the most important events occurring in the photocycle, namely changes in the chromophore and the protein backbone conformation, and changes in the protonation state of the key residues implicated in the proton transfers. Besides confirming widely accepted views of the bR photocycle, our analysis also sheds light into some disputed issues: the degree of retinal torsion in the L intermediate to respect the ground state; the possibility of a proton transfer from Asp85 to Asp212; the relationship between the protonation/deprotonation of Asp85 and the proton release complex; and the timing of the protein backbone dynamics. By providing a direct way to estimate the kinetics of photocycle intermediates the present approach opens new prospects for a robust quantitative kinetic analysis of the bR photocycle, which could also benefit the study of other proteins involved in photosynthesis, in phototaxis, or in respiratory chains.

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.

Volume and enthalpy changes of proton transfers in the bacteriorhodopsin photocycle studied by millisecond time-resolved photopressure measurements

The volume and enthalpy changes associated with proton translocation steps during the bacteriorhodopsin (BR) photocycle were determined by time-resolved photopressure measurements. The data at 25 degrees C show a prompt increase in volume followed by two further increases and one decrease to the original state to complete the cycle. These volume changes are decomposed into enthalpy and inherent volume changes. The positive enthalpy changes support the argument for inherent entropy-driven late steps in the BR photocycle [Ort, D. R., and Parson, W. M. (1979) Enthalpy changes during the photochemical cycle of bacteriorhodopsin. Biophys. J. 25, 355-364]. The volume change data can be interpreted by the electrostriction effect as charges are canceled and formed during the proton transfers. A simple glutamic acid-glutamate ion model or a diglutamate-arginine-protonated water charge-delocalized model for the proton-release complex (PRC) fit the data. A conformational change with a large positive volume change is required in the slower rise (M --> N of the optical cycle) step and is reversed in the decay (N --> O --> BR) steps. The large variation in the published values for both the volume and enthalpy changes is greatly ameliorated if the values are presented per absorbed photon instead of per mole of BR. Thus, it is the highly differing assumptions about the quantum or reaction yields that cause the variations in the published results.

The ability of actinic light to modify the bacteriorhodopsin photocycle revisited: heterogeneity vs photocooperativity

In 1995, evidence both for photocooperativity and for heterogeneity as possible explanations for the ability of actinic light to modify the kinetics and pathways of the bacteriorhodopsin (BR) photocycle was reviewed ( Shrager, R. I., Hendler, R. W., and Bose, S. (1995) Eur. J. Biochem. 229, 589-595 ). Because both concepts could be successfully modeled to experimental data and there was suggestive published evidence for both, it was concluded that both photocooperativity and heterogeneity may be involved in the adaptation of the BR photocycle to different levels of actinic light. Since that time, more information has become available and it seemed appropriate to revisit the original question. In addition to the traditional models based on all intermediates in strict linear sequences, we have considered both homogeneous and heterogeneous models with branches. It is concluded that an explanation based on heterogeneity is more likely to be the true basis for the variation of the properties of the photocycle caused by changes in actinic light intensity. On the basis of new information presented here, it seems that a heterogeneous branched model is more likely than one with separate linear sequences.

Electrogenic proton-pumping capabilities of the m-fast and m-slow photocycles of bacteriorhodopsin

The parallel model for the bacteriorhodopsin (BR) photocycle at neutral pH and a temperature near 20 degrees C contains an M-fast cycle with steps BR-->K-->L-->Mf-->N-->O-->BR and an M-slow cycle which contains steps BR-->K-->L-->Ms-->BR. With increasing actinic laser strength, the M-fast cycle at first rises faster than the M-slow cycle, but reaches saturation sooner and at a lower level than the M-slow cycle. The O-intermediate shows the same saturation behavior as Mf. In this paper, we show that the peak current of proton flux and the apparent voltages developed by this flux show the same saturation behavior as Ms, which is very different from that of both M f and O. It is further shown that most of the proton-charge displacement is connected with the step Ms-->BR. The optical and electrical data in these studies were collected simultaneously by a newly designed and built spectrometer which is described separately.

Simultaneous measurements of fast optical and proton current kinetics in the bacteriorhodopsin photocycle using an enhanced spectrophotometer

A one-of-a-kind high speed optical multichannel spectrometer was designed and built at NIH and described in this journal in 1997 [J.W. Cole, R.W. Hendler, P.D. Smith, H.A. Fredrickson, T.J. Pohida, W.S. Friauf. A high speed optical multichannel analyzer. J Biochem Biophys Methods 1997;35:16-174.]. The most unique aspect of this instrument was the ability to follow an entire time course from a single activation using a single sample. The instrument has been used to study rapid kinetic processes in the photon-driven bacteriorhodopsin photocycle and electron transport from cytochrome c to cytochrome aa3 and from cytochrome aa3 to oxygen. The present paper describes a second generation instrument with a number of important enhancements which significantly improve its capabilities for multichannel kinetic studies. An example application is presented in which the kinetics of photon-induced proton flow across the biological membrane is measured simultaneously with the individual steps of the photocycle determined optically. Matching the time constants for the two processes indicates which molecular transformations are associated with major proton movements.

An apparent general solution for the kinetic models of the bacteriorhodopsin photocycles

For the past decade, the field of Bacteriorhodopsin (BR) research has been influenced by a kinetic view of the photocycle as a reversible, homogeneous, model (RHM) with a linear sequence of intermediates. More recently, we proposed a much different model which consists of essentially unidirectional, parallel (i.e., heterogeneous) cycles (UPM) (Hendler, R. W.; Shrager, R. I.; Bose, S. J. Phys. Chem. B 2001, 105, 3319-3328). It is important to try to resolve which of the two models is more likely to be correct, because models influence and provide a basis for further experimentation. Therefore, in this communication, we reexamine the basis for the RHM with a focus on the most recent and complete description of this model (van Stokkum, I., H., M.; Lozier, R. J. Phys. Chem. B 2002, 106, 3477-3485) vis a vis the UPM in an in-depth study. We show that (i) the tested RHM does not really work for the data of van Stokkum and Lozier nor ours; (ii) no previously published RHM model has been shown to work for data under any conditions; (iii) there are many published observations that are difficult if not impossible to explain by RHM, but are readily explained by parallel cycles. It is also shown that either a UPM or a parallel cycle model with limited reversibility correctly describes photocycle data collected at pH 5, 7, and 9 and at 10, 20, and 30 degrees and is consistent with all known experimental observations.

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.

The protonation-deprotonation kinetics of the protonated Schiff base in bicelle bacteriorhodopsin crystals

In the recently published x-ray crystal structure of the "bicelle" bacteriorhodopsin (bbR) crystal, the protein has quite a different structure from the native and the in cubo bacteriorhodopsin (cbR) crystal. Instead of packing in parallel trimers as do the native membrane and the cbR crystals, in the bbR crystal the protein packs as antiparallel monomers. To date, no functional studies have been performed, to our knowledge, to investigate if the photocycle is observed in this novel protein packing structure. In this study, both Raman and time-resolved transient absorption spectroscopy are used to both confirm the presence of the photocycle and investigate the deprotonation-reprotonation kinetics of the Schiff base proton in the bbR crystal. The observed rates of deprotonation and reprotonation processes of its Schiff base have been compared to those observed for native bR under the same conditions. Unlike the previously observed similarity of the rates of these processes for cbR crystals and those for native bacteriorhodopsin (bR), in bbR crystals the rate of deprotonation has increased by 300%, and the rate of reprotonation has decreased by nearly 700%. These results are discussed in light of the changes observed when native bR is delipidated or monomerized by detergents. Both the change of the hydrophobicity of the environment around the protonated Schiff base and Asp85 and Asp96 (which could change the pKa values of proton donor-acceptor pairs) and the water structure in the bbR crystal are offered as possible explanations for the different observations.

Bacteriorhodopsin photocycle kinetics analyzed by the maximum entropy method

A maximum entropy method (MEM) was developed for the study of the bacteriorhodopsin photocycle kinetics. The method can be applied directly to experimental kinetic absorption data without any assumption for the number of the intermediate states taking part in the photocycle. Though this method does not give a specific kinetics, its result is very useful for selection between possible photocycle kinetics. Using simulated data, it is shown that MEM gives correct results for the number of the intermediate states and the amplitude distributions around the characteristic lifetimes. Analyzing experimental absorption data at five different wavelengths, MEM gives seven or eight characteristic lifetimes, which means that at least so many distinct intermediate states exist during the photocycle. Many possible photocycle kinetic models were studied and compared with the MEM result. The best agreement was found with a branching photocycle model of eight intermediate states (K, L, M(1), M(2), M(3), M(4), N, O). The branching occurs at the L intermediate state (M(1) and M(2) being in one branch and M(3) and M(4) in the other branch), but at high pH it occurs already at the K state.

Global and target analysis of time-resolved spectra

In biological/bioenergetics research the response of a complex system to an externally applied perturbation is often studied. Spectroscopic measurements at multiple wavelengths are used to monitor the kinetics. These time-resolved spectra are considered as an example of multiway data. In this paper, the methodology for global and target analysis of time-resolved spectra is reviewed. To fully extract the information from the overwhelming amount of data, a model-based analysis is mandatory. This analysis is based upon assumptions regarding the measurement process and upon a physicochemical model for the complex system. This model is composed of building blocks representing scientific knowledge and assumptions. Building blocks are the instrument response function (IRF), the components of the system connected in a kinetic scheme, and anisotropy properties of the components. The combination of a model for the kinetics and for the spectra of the components results in a more powerful spectrotemporal model. The model parameters, like rate constants and spectra, can be estimated from the data, thus providing a concise description of the complex system dynamics. This spectrotemporal modeling approach is illustrated with an elaborate case study of the ultrafast dynamics of the photoactive yellow protein.

Photosynthetic models with maximum entropy production in irreversible charge transfer steps

Steady-state bacterial photosynthesis is modelled as cyclic chemical reaction and is examined with respect to overall efficiency, power transfer efficiency, and entropy production. A nonlinear flux-force relationship is assumed. The simplest two-state kinetic model bears complete analogy with the performance of an ideal (zero ohmic resistance of the P-N junction) solar cell. In both cases power transfer to external load is much higher than the 50% allowed by the impedance matching theorem for the linear flux-force relationship. When maximum entropy production is required in the transition with a load, one obtains high optimal photochemical yield of 97% and power transfer efficiency of 91%. In more complex photosynthetic models, entropy production is maximized in all irreversible electron/proton (non-slip) transitions in an iterative procedure. The resulting steady-state is stable with respect to an extremely wide range of initial values for forward rate constants. Optimal proton current increases proportionally to light intensity and decreases with an increase in the proton-motive force (the backpressure effect). Optimal affinity transfer efficiency is very high and nearly perfectly constant for different light absorption rates and for different electrochemical proton gradients. Optimal overall efficiency (of solar into proton-motive power) ranges from 10% (bacteriorhodopsin) to 19% (chlorophyll-based bacterial photosynthesis). Optimal time constants in a photocycle span a wide range from nanoseconds to milliseconds, just as corresponding experimental constants do. We conclude that photosynthetic proton pumps operate close to the maximum entropy production mode, connecting biological to thermodynamic evolution in a coupled self-amplifying process.

Interconversions among four M-intermediates in the bacteriorhodopsin photocycle

Halobacterium salinarum displays four distinct kinetic forms of M-intermediate in its bacteriorhodopsin photocycle. In wild-type, there are mainly two species with time constants near 2 and 5 ms. Under various kinds of stress, two other species arise with time constants near 10 and 70 ms. We show that these four species are interconvertible. Increases in membrane hydrophobicity convert the slower to faster forms. Perturbations caused by Triton X-100 or mutations convert faster to slower forms. The fastest form requires a hydrophobic membrane environment near a ring of four charged aspartate residues in the trimer, namely Asp36, Asp38, Asp102, and Asp104 in the cytoplasmic loop regions. Interconversions of the 2-ms and 5-ms species of the wild-type are accomplished by pH-changes. The potential significance of these findings is discussed.

Proton transfer reactions in native and deionized bacteriorhodopsin upon delipidation and monomerization

We have investigated the role of the native lipids on bacteriorhodopsin (bR) proton transfer and their connection with the cation-binding role. We observe that both the efficiency of M formation and the kinetics of M rise and decay depend on the lipids and lattice but, as the lipids are removed, the cation binding is a much less important factor for the proton pumping function. Upon 75% delipidation using 3-[(cholamidopropyl)dimethylammonio]-propanesulfonate (CHAPS), the M formation and decay kinetics are much slower than the native, and the efficiency of M formation is approximately 30%-40% that of the native. Upon monomerization of bR by Trition X-100, the efficiency of M recovers close to that of the native (depending on pH), M formation is approximately 10 times faster, and M decay kinetics are comparable to native at pH 7. The same results on the M intermediate are observed if deionized blue bR (deI bbR) is treated with these detergents (with or without pH buffers present), even though deionized blue bR containing all the lipids has no photocycle. This suggests that the cation(s) has a role in native bR that is different than in delipidated or monomerized bR, even so far as to suggest that the cation(s) becomes unimportant to the function as the lipids are removed.

Purple membrane lipid control of bacteriorhodopsin conformational flexibility and photocycle activity

Specific lipids of the purple membrane of Halobacteria are required for normal bacteriorhodopsin structure, function, and photocycle kinetics [Hendler, R.W. & Dracheva, S. (2001) Biochemistry (Moscow)66, 1623-1627]. The decay of the M-fast intermediate through a path including the O intermediate requires the presence of a hydrophobic environment near four charged aspartic acid residues within the cytoplasmic loop region of the protein (R. W. Hendler & S. Bose, unpublished results). On the basis of the unique ability of squalene, the most hydrophobic purple membrane lipid, to induce recovery of M-fast activity in Triton-treated purple membrane, we proposed that this uncharged lipid modulates an electrostatic repulsion between the membrane surface of the inner trimer space and the nearby charged aspartic acids of the cytoplasmic loop region to promote transmembrane alpha-helical mobility with a concomitant increase in the speed of the photocycle. We examined Triton-treated purple membranes in various stages of reconstitution with native lipid suspensions using infrared spectroscopic techniques. We demonstrate a correlation between the vibrational half-width parameter of the protein alpha-helical amide I mode at 1660 cm-1, reflecting the motional characteristics of the transmembrane helices, and the lipid-induced recovery of native bacteriorhodopsin properties in terms of the visible absorbance maxima of ground state bacteriorhodopsin and the mean decay times of the photocycle M-state intermediates.