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.

Electron transfer within and between proteins is a fundamental biological phenomenon, in which efficiency depends on several physical parameters. We have engineered a number of horse heart cytochrome c single-point mutants with cysteine substitutions at various positions of the protein surface. To these cysteines, as well as to several native lysine side chains, the photoinduced redox label 8-thiouredopyrene-1,3,6-trisulfonate (TUPS) was covalently attached. The long-lived, low potential triplet excited state of TUPS, generated with high quantum efficiency, serves as an electron donor to the oxidized heme c. The rates of the forward (from the label to the heme) and the reverse (from the reduced heme back to the oxidized label) electron transfer reactions were obtained from multichannel and single wavelength flash photolysis absorption kinetic experiments. The electronic coupling term and the reorganization energy for electron transfer in this system were estimated from temperature-dependent experiments and compared with calculated parameters using the crystal and the solution NMR structure of the protein. These results together with the observation of multiexponential kinetics strongly support earlier conclusions that the flexible arm connecting TUPS to the protein allows several shortcut routes for the electron involving through space jumps between the label and the protein surface.

Dealing with a system of first-order reactions is a recurrent problem in chemometrics, especially in the analysis of data obtained by spectroscopic methods. Here we argue that global multiexponential fitting, the still common way to solve this kind of problems has serious weaknesses, in contrast to the available 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 obtained an optimization problem tunable to result in 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 very high performance. Moreover, it was found that the optimal values of the tuning hyperparameters can be selected by a machine-learning algorithm based on a Bayesian optimization procedure, utilizing a widely used and a novel version of cross-validation. The applied algorithm recovered very exactly 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 levels of noise. 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.

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