Hierarchical organization of human physical activity.

Human physical activity (HPA), a fundamental physiological signal characteristic of bodily motion is of rapidly growing interest in multidisciplinary research. Here we report the existence of hitherto unidentified hierarchical levels in the temporal organization of HPA on the ultradian scale: on the minute's scale, passive periods are followed by activity bursts of similar intensity ('quanta') that are organized into superstructures on the hours- and on the daily scale. The time course of HPA can be considered a stochastic, quasi-binary process, where quanta, assigned to task-oriented actions are organized into work packages on higher levels of hierarchy. In order to grasp the essence of this complex dynamic behaviour, we established a stochastic mathematical model which could reproduce the main statistical features of real activity time series. The results are expected to provide important data for developing novel behavioural models and advancing the diagnostics of neurological or psychiatric diseases.

Kinetics and Energetics of Intramolecular Electron Transfer in Single-Point Labeled TUPS-Cytochrome c Derivatives.

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.

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.

Kinetics of Light-Induced Intramolecular Energy Transfer in Different Conformational States of NADH.

When bound to a protein, the coenzyme NAD+/NADH typically exists in an extended conformation, while in aqueous solutions it can be characterized by an equilibrium of folded and unfolded structures. It was recognized long ago that in the folded conformation light absorption at the adenine ring initiates an effective energy transfer (ET) toward the nicotinamide group, but the mechanism of this process is still unexplored. Here we apply ultrafast transient absorption measurements on NADH combined with compartmental model analysis for following the kinetics of the ET. We find that the actual ET is extremely rapid (∼70 fs). The high rate can be well described by a Förster-type mechanism, promoted by both the special photophysical properties of adenine and the subnanometer inter-ring distance. The rapid ET creates a vibrationally hot excited state on nicotinamide, the vibrational and electronic relaxation of which is characterized by 1.7 and 650 ps, respectively.

Vibrational motions associated with primary processes in bacteriorhodopsin studied by coherent infrared emission spectroscopy.

The primary energetic processes driving the functional proton pump of bacteriorhodopsin take place in the form of complex molecular dynamic events after excitation of the retinal chromophore into the Franck-Condon state. These early events include a strong electronic polarization, skeletal stretching, and all-trans-to-13-cis isomerization upon formation of the J intermediate. The effectiveness of the photoreaction is ensured by a conical intersection between the electronic excited and ground states, providing highly nonadiabatic coupling to nuclear motions. Here, we study real-time vibrational coherences associated with these motions by analyzing light-induced infrared emission from oriented purple membranes in the 750-1400 cm(-)(1) region. The experimental technique applied is based on second-order femtosecond difference frequency generation on macroscopically ordered samples that also yield information on phase and direction of the underlying motions. Concerted use of several analysis methods resulted in the isolation and characterization of seven different vibrational modes, assigned as C-C stretches, out-of-plane methyl rocks, and hydrogen out-of-plane wags, whereas no in-plane H rock was found. Based on their lifetimes and several other criteria, we deduce that the majority of the observed modes take place on the potential energy surface of the excited electronic state. In particular, the direction sensitivity provides experimental evidence for large intermediate distortions of the retinal plane during the excited-state isomerization process.

Quantification of sudden light-induced polarization in bacteriorhodopsin by optical rectification.

Upon population of its excited state, the retinal chromophore in the membrane protein bacteriorhodopsin (bR) undergoes a sudden (less than approximately 10 fs) change in dipole moment, Deltamu, that can be visualized in a direct way by optical rectification of a broadband visible femtosecond light pulse to the infrared but has not been quantified in this way. Here we show that a transparent thick AgGaS2 crystal delivers infrared radiation with the same spectral profile as bR and is a suitable reference for quantifying conversion efficiency. Using this reference, we estimate the projection of Deltamu on the membrane normal at 11 D, corresponding to the displacement of a full charge over approximately half the length of the retinal chromophore. This result may help to evaluate models describing the interplay between the initial polarization change and the subsequent isomerization of the retinal.

Phase-synchronization of daily motor activities can reveal differential circadian patterns.

The aim of the study was to determine any alteration of the 24 h motor activity pattern of a bipolar patient in different mood states. Actigraphic records were collected on an outpatient basis for a total of 387 days. The daily actograms were synchronized in phase to the time of morning awakening before averaging, which significantly enhanced the structure of the averaged traces. The actograms were divided into three groups based on total daily count. The daily motor activity patterns of the low- and high-activity days have a different circadian pattern. We propose it may have a relevance to the different mood states. The phase-synchronization of the 24h actograms to the patient's sleep-wake cycle, specifically to the time of awaking from the nighttime sleep, may help reveal differences in the daily temporal patterns of motor activity.

Resonant optical rectification in bacteriorhodopsin.

The relative role of retinal isomerization and microscopic polarization in the phototransduction process of bacteriorhodopsin is still an open question. It is known that both processes occur on an ultrafast time scale. The retinal trans-->cis photoisomerization takes place on the time scale of a few hundred femtoseconds. On the other hand, it has been proposed that the primary light-induced event is a sudden polarization of the retinal environment, although there is no direct experimental evidence for femtosecond charge displacements, because photovoltaic techniques cannot be used to detect charge movements faster than picoseconds. Making use of the known high second-order susceptibility chi(2) of retinal in proteins, we have used a nonlinear technique, interferometric detection of coherent infrared emission, to study macroscopically oriented bacteriorhodopsin-containing purple membranes. We report and characterize impulsive macroscopic polarization of these films by optical rectification of an 11-fs visible light pulse in resonance with the optical transition. This finding provides direct evidence for charge separation as a precursor event for subsequent functional processes. A simple two-level model incorporating the resonant second-order optical properties of retinal, which are known to be a requirement for functioning of bacteriorhodopsin, is used to describe the observations. In addition to the electronic response, long-lived infrared emission at specific frequencies was observed, reflecting charge movements associated with vibrational motions. The simultaneous and phase-sensitive observation of both the electronic and vibrational signals opens the way to study the transduction of the initial polarization into structural dynamics.

Characterization of the azide-dependent bacteriorhodopsin-like photocycle of salinarum halorhodopsin.

The photocycle of salinarum halorhodopsin was investigated in the presence of azide. The azide binds to the halorhodopsin with 150 mM binding constant in the absence of chloride and with 250 mM binding constant in the presence of 1 M chloride. We demonstrate that the azide-binding site is different from that of chloride, and the influence of chloride on the binding constant is indirect. The analysis of the absorption kinetic signals indicates the existence of two parallel photocycles. One belongs to the 13-cis retinal containing protein and contains a single red shifted intermediate. The other photocycle, of the all-trans retinal containing halorhodopsin, resembles the cycle of bacteriorhodopsin and contains a long-living M intermediate. With time-resolved spectroscopy, the spectra of intermediates were determined. Intermediates L, N, and O were not detected. The multiexponential rise and decay of the M intermediate could be explained by the introduction of the "spectrally silent" intermediates M1, M2, and HR', HR, respectively. The electric signal measurements revealed the existence of a component equivalent with a proton motion toward the extracellular side of the membrane, which appears during the M1 to M2 transition. The differences between the azide-dependent photocycle of salinarum halorhodopsin and pharaonis halorhodopsin are discussed.