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

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.

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.

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.

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.