Analysis of the Bacteriorhodopsin Photocycle by Singular Value Decomposition with Self-Modeling: A Critical Evaluation Using Realistic Simulated Data

KINNTREX: a neural network to unveil protein mechanisms from time-resolved X-ray crystallography

Here, a machine-learning method based on a kinetically informed neural network (NN) is introduced. The proposed method is designed to analyze a time series of difference electron-density maps from a time-resolved X-ray crystallographic experiment. The method is named KINNTREX (kinetics-informed NN for time-resolved X-ray crystallography). To validate KINNTREX, multiple realistic scenarios were simulated with increasing levels of complexity. For the simulations, time-resolved X-ray data were generated that mimic data collected from the photocycle of the photoactive yellow protein. KINNTREX only requires the number of intermediates and approximate relaxation times (both obtained from a singular valued decomposition) and does not require an assumption of a candidate mechanism. It successfully predicts a consistent chemical kinetic mechanism, together with difference electron-density maps of the intermediates that appear during the reaction. These features make KINNTREX attractive for tackling a wide range of biomolecular questions. In addition, the versatility of KINNTREX can inspire more NN-based applications to time-resolved data from biological macromolecules obtained by other methods.

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.

Quantifying kinetics from time series of single-molecule Förster resonance energy transfer efficiency histograms

Single-molecule fluorescence spectroscopy is a powerful approach for probing biomolecular structure and dynamics, including protein folding. For the investigation of nonequilibrium kinetics, Förster resonance energy transfer combined with confocal multiparameter detection has proven particularly versatile, owing to the large number of observables and the broad range of accessible timescales, especially in combination with rapid microfluidic mixing. However, a comprehensive kinetic analysis of the resulting time series of transfer efficiency histograms and complementary observables can be challenging owing to the complexity of the data. Here we present and compare three different methods for the analysis of such kinetic data: singular value decomposition, multivariate curve resolution with alternating least square fitting, and model-based peak fitting, where an explicit model of both the transfer efficiency histogram of each species and the kinetic mechanism of the process is employed. While each of these methods has its merits for specific applications, we conclude that model-based peak fitting is most suitable for a quantitative analysis and comparison of kinetic mechanisms.

Effect of Hofmeister cosolutes on the photocycle of photoactive yellow protein at moderately alkaline pH

The photocycle of photoactive yellow protein was studied by kinetic absorption spectroscopy from below 100ns to seconds, at moderately alkaline pH, in the presence of high concentrations of various salts. Chemometric analysis combined with multiexponential fit of the flash-induced difference spectra provided evidence for five intermediates, including a spectrally silent form before the final recovery of the parent state, but only three with significantly distinct spectra. The calculated intermediate spectra constituted the input for the following spectrotemporal model fit using a sufficiently complex photocycle scheme with reversible transitions. This yielded the rate coefficients of the molecular transitions, the final spectra and the kinetics of the intermediates. Except for the transition between the two red shifted (early) intermediates (pR1 and pR2) and the final photocycle step, all reactions appeared to be reversible. Kosmotropic and chaotropic cosolutes had a systematic effect on the molecular rate coefficients. The largest effect, associated presumably with the exposure of the hydrophobic interior of the protein, accompanies the transition between the second red-shifted and the first blue-shifted intermediate (pR2 and pB1, respectively), i.e. it coincides with the chromophore protonation. The dependence of the rate coefficients on the Hofmeister cosolutes suggests that the conformational change of photoactive yellow protein leading eventually to the most unfolded signaling state takes place in several steps, and starts already with the relaxation after the chromophore isomerization in the microsecond time domain.

Monitoring intermediate states of bacteriorhodopsin monolayers using near-field optical microscopy

We demonstrate single-molecule-level features using near-field optical microscopy on bacteriorhodopsin (bR), a membrane protein that functions as a light-driven proton pump. The photophysical properties of bR are utilized in this imaging technique, using a combination of photoexcitation sources, to accurately identify the active regions and quantify the optical parameters. The studies of bR monolayers are carried out on inert quartz substrates as well as active conducting polymer (polyaniline) substrates. The substrate also plays an important role in the photocycle quantum efficiencies. We speculate on mechanisms governing the higher near-field absorption strength of bR molecules.

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.

A priori resolution of the intermediate spectra in the bacteriorhodopsin photocycle: the time evolution of the L spectrum revealed

Resolution of the spectra of the intermediates in the photocycle of wild-type bacteriorhodopsin (BR) was achieved by singular value decomposition with exponential-fit-assisted self-modeling (SVD-EFASM) treatment of multichannel difference spectra measured at 5 degrees C during the course of the photocycle. New is the finding that two spectrally distinct L intermediates, L(1) and L(2), form sequentially. Our conclusion is that the photocycle is more complex than most published schemes. The dissection of the spectrally different L forms eliminates stoichiometric discrepancies usually appearing as systematically varying total intermediate concentrations before the onset of BR recovery. In addition, our analysis reveals that the red tails in the spectra of K and L(1) are more substantial than those of L(2) and BR. We suggest that these subtle differences in the shapes of the spectra reflect torsional and/or environmental differences in the retinyl chromophore.

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.

Transformation of time-resolved spectra to lifetime-resolved spectra by maximum entropy inversion of the laplace transform

We present a method for the analysis of time-resolved spectroscopic data following first-order kinetics. The time traces at all the available spectroscopic channels (e.g., wavelength or wavenumber) are inverse Laplace transformed. The transformation is stabilized by the maximum entropy method generalized for solutions without sign-restriction. In this way, time-resolved spectra can be converted to lifetime-resolved spectra, where bands appear at coordinates corresponding to their spectroscopic maxima and time constant of appearance (negative amplitude) or disappearance (positive amplitude). From the lifetime-resolved spectra, the number of exponentially decaying components, their time constants, and their decay-associated spectra are readily available. Moreover, since bands are spread in two dimensions extra band-resolution is possible. We named this method of transforming time-resolved spectra into lifetime-resolved spectra multi-spectroscopic channel maximum entropy inversion of the Laplace transform (M-MaxEnt-iLT). The basis of M-MaxEnt-iLT is presented in detail and its properties and limitations are thoroughly discussed. We also show how the combination of M-MaxEnt-iLT with spectral smoothing or deconvolution can improve the appearance and/or band resolution of the obtained lifetime-resolved spectra.