Excited state charge-transfer dynamics study of poplar plastocyanin by ultrafast pump-probe spectroscopy and molecular dynamics simulation

We have applied ultrafast pump-probe spectroscopy to investigate the excited state dynamics of the blue copper protein poplar plastocyanin, by exciting in the blue side of its 600-nm absorption band. The decay of the charge-transfer excited state occurs exponentially with a time constant of approximately 280 fs and is modulated by well visible oscillations. The Fourier transform of the oscillatory component, besides providing most of the vibrational modes found by conventional resonance Raman, presents additional bands in the low frequency region modes, which are reminiscent of collective motions of biological relevance. Notably, a high frequency mode at approximately 508 cm(-1), whose dynamics are consistent with that of the excited state and already observed for other blue copper proteins, is shown to be present also in poplar plastocyanin. This vibrational mode is reproduced by a molecular dynamics simulation involving the excited state of the copper site.     

Electromagnetic Radiation Influence on Nonlinear Charge and Energy Transport in Biosystems

The influence of electromagnetic radiation (EMR) on charge and energy transport processes in biological systems is studied in the light of the soliton model. It is shown that in the spectrum of biological effects of EMR there are two frequency resonances corresponding to qualitatively different frequency dependent effects of EMR on solitons. One of them is connected with the quasiresonance dynamic response of solitons to the EMR. At EMR frequencies close to the dynamic resonance frequency the solitons absorb energy from the field and generate intensive vibrational modes in the macromolecule. The second EMR resonance is connected with soliton decay due to the quantum mechanical transition of the system from the bound soliton state into the excited unbound states.     

The physical and radiobiological basis of the local effect model: a response to the commentary by R. Katz

The physical and biological basis of our model to calculate the biological effects of charged particles, termed the local effect model (LEM), has recently been questioned in a commentary by R. Katz. Major objections were related to the definition of the target size and the use of the term cross section. Here we show that the objections raised against our approach are unjustified and are largely based on serious misunderstandings of the conceptual basis of the local effect model. Furthermore, we show that the approach developed by Katz and coworkers itself suffers from exactly those deficiencies for which Katz criticizes our model. The essential conceptual differences between the two models are discussed by means of some illustrative examples, based on a comparison with experimental data. For these examples, the predictions of the local effect model are fully consistent with the experimental data. In contrast, e.g. for very heavy ions, there are significant discrepancies observed for the Katz approach. These discrepancies can be attributed to the inadequate definition of the target size in this model. Experimental data are thus clearly in favor of the definition of the target as used in the local effect model. Agreement with experimental data is achieved for protons within the Katz approach but at the cost of questionable approximations in combination with the violation of the fundamental physical principle of energy conservation.     

Real-time vibrational dynamics in chlorophyll a studied with a few-cycle pulse laser

We use a 6.8-fs laser as the light source for broad-band femtosecond pump-probe real-time vibrational spectroscopy to investigate both electronic relaxation and vibrational dynamics of the Q_y-band of Chl-a at 293 K. More than 25 vibrational modes coupled to the Q_y transition are observed. Eleven of them have been clarified predominantly due to the excited state, and six of them are concluded to be nearly exclusively resulting from the ground-state wave-packet motion. Moreover, thanks to the broad-band detection over 5000 cm⁻¹, the modulated signals due to the excited state vibrational coherence are observed on both sides of the 0-0 transition with equal separation. The corresponding nonlinear process has been studied using a three-level model, from which the probe wavelength dependence of the phase of the periodic modulation can be calculated. The probe wavelength dependence of the vibrational amplitude is interpreted in terms of the interaction between the “pump” or “laser,” Stokes, and anti-Stokes field intermediated by the molecular vibrations. In addition, an excited state absorption peak at ∼709 nm has been observed. To the best of our knowledge, this is the first study of broad-band real-time vibrational spectroscopy in Chl-a.     

Femtosecond and picosecond fluorescence of native bacteriorhodopsin and a nonisomerizing analog

The spectrally and temporally resolved fluorescence properties of native bacteriorhodopsin (bR) and bR reconstituted with a nonisomerizing analog of the retinal Schiff base (bR5.12) are examined. The first attempt to experimentally monitor the excited state relaxation processes in both type of pigments using ultrafast fluorescence spectroscopy is reported. The fluorescence is emitted from retinal molecules in an all-trans configuration. Substantial energy relaxation involves very fast intramolecular and intermolecular vibrational modes and these are shown to occur on a time scale faster than isomerization. The possible contribution of dielectric interaction between the retinal Schiff base and the protein environment for the excited state energy relaxation is discussed.     

Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or “site.” Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment–proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment–protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna–Mathews–Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.     

In defence of the high energy phosphate bond

The concept of the “high energy phosphate bond” has recently been strongly criticised by Banks &; Vernon. The criticisms were: (i) energy cannot be stored in molecules; let alone in bonds; (ii) a muscle is an open system, so that the free energy of hydrolysis of ATP is irrelevant; (iii) biological reactions cannot be at equilibrium, therefore they must be inefficient. It is argued that all of these criticisms arise because the timescale appropriate to molecular events has been left out; in particular “stored energy” needs to be defined relative to the machine which uses that energy. The criticisms may be answered using a conceptual framework which overcomes this deficiency and which was developed previously to extend classical thermodynamics to the molecular level. Criticism (i) is refuted by discussing in detail the chemiluminescent reaction of rubrene oxide, which can only be described as liberating internal energy stored in a single molecule; while it is true that entropy cannot be retained in a single molecule for long enough to do useful work with it, there is nothing which forbids internal energy from being so stored. Criticism (ii) would be true if, and only if, a muscle uses the same kind of mechanism as do the ordinary chemical machines with which we are familiar (batteries, etc). But this assumption is shown to be false; a muscle cannot use this type of mechanism. Criticism (iii) is answered by finding the conditions under which a biological machine could in fact approach 100% efficiency. These conditions are: (i) in metabolism ΔF = 0; the steps are in thermal equilibrium; (ii) in the molecular machines themselves ΔS = 0, so that ΔF = ΔH; the machines are mechanical. It is also shown that not only are these conditions perfectly conceivable, but also that there is good evidence that, over the course of evolution, they have actually been attained.     

Electron temperature in nitrogen afterglow: Dependence of theoretical results on the adopted set of cross sections and on the type of molecular distribution over vibrational levels

The electron energy distribution function in nitrogen afterglow is simulated using different available sets of cross sections for electron scattering by vibrationally excited molecules. The calculations are performed for two types of molecular distribution over vibrational levels, namely, for the Boltzmann and Treanor-Gordiets distributions. It is shown that the calculated values of the electron temperature in nitrogen afterglow depend strongly on the set of cross sections used and on the type of molecular distribution over vibrational levels. The validity of comparison between theoretical and experimental results is discussed.     

Single molecule thermodynamics in biological motors

Biological molecular machines use thermal activation energy to carry out various functions. The process of thermal activation has the stochastic nature of output events that can be described according to the laws of thermodynamics. Recently developed single molecule detection techniques have allowed each distinct enzymatic event of single biological machines to be characterized providing clues to the underlying thermodynamics. In this study, the thermodynamic properties in the stepping movement of a biological molecular motor have been examined. A single molecule detection technique was used to measure the stepping movements at various loads and temperatures and a range of thermodynamic parameters associated with the production of each forward and backward step including free energy, enthalpy, entropy and characteristic distance were obtained. The results show that an asymmetry in entropy is a primary factor that controls the direction in which the motor will step. The investigation on single molecule thermodynamics has the potential to reveal dynamic properties underlying the mechanisms of how biological molecular machines work.     

Application of electrochemical kinetics to photosynthesis and oxidative phosphorylation: The redox element hypothesis and the principle of parametric energy coupling

It is suggested that the transfer of electrons within the biological electron transfer chain is subject to the laws of electrochemical kinetics, when membrane-bound electron carriers are involved. Consequently, small tightly bound molecular complexes of two or more electron transfer proteins of different redox potential within an energy transducing membrane, which accept electrons from a donor at one membrane surface and donate it to an acceptor at the other, may be regarded as real and functioning molecular redox elements, which convert the free energy of electrons into electrochemical energy. Especially, the transfer of an electron from excited chlorophyll to an electron acceptor can be looked upon as an electrochemical oxidation of excited chlorophyll at such a complex. In this reaction the electron acceptor complex behaves like a polarized electrode, in which the electrochemical potential gradient is provided by a gradient of redox potential of its constituents.Calculations and qualitative considerations show that this concept leads to a consistent understanding of both primary and secondary reactions in photosynthesis (electron capture, delayed light emission, ion transfer, energy conversion) and can also be applied to oxidative phosphorylation. Within the proposed concept, ion transfer and the development of ion gradients have to be considered as results of electrochemical activity—not as intermediates for energy conversion. For energetic reasons, a non steady state, periodic energy coupling mechanism is postulated which functions by periodic changes of the capacity of the (electrochemically) charged energy transducing membrane, during which capacitive surplus energy is released as chemical energy. Energy transducing membranes may thus be considered as electrochemical parametric energy transformers. This concept explains active periodic conformation changes and mechanochemical processes of energy transducing membranes as energetically essential events, which trigger energy conversion according to the principle of variable parameter energy transformers.The electrochemical approach presented here has been suggested and is supported by the observation, that with respect to electron capture and conversion of excitation energy into electrochemical energy, the behaviour of excited chlorophyll at suitable solid state (semiconductor) electrodes is very similar to that of chlorophyll in photosynthetic reaction centers.     

A physical analysis of the ion parametric resonance model

We show, in elementary terms, using for the most part only elementary mathematics, the physical bases for the ion parametric resonance model so as to clarify the assumptions and consequences of the model. The analysis shows why, contrary to earlier conclusions, no combination of weak DC and AC magnetic fields can modify the transition rate to the ground state of excited ions. Although reinterpretations of the biological consequences of the motion of the excited ions circumvent that particular objection to the model, those changes introduce other difficulties. Also, other objections to the mechanism still stand; hence the model cannot account for any purported biological effects of weak extremely low frequency magnetic fields. Bioelectromagnetics 19:181–191, 1998. © 1998 Wiley-Liss, Inc.     

Classical molecular dynamics simulation of the photoinduced electron transfer dynamics of plastocyanin.

Classical molecular dynamics simulations are used to investigate the nuclear motions associated with photoinduced electron transfer in plastocyanin. The blue copper protein is modeled using a molecular mechanics potential; potential parameters for the copper-protein interactions are determined using an x-ray crystallographic structure and absorption and resonance Raman spectra. Molecular dynamics simulations yield a variety of information about the ground (oxidized) and optically excited (charge-transfer) states: 1) The probability distribution of the potential difference between the states, which is used to determine the coordinate and energy displacements, places the states well within the Marcus inverted region. 2) The two-time autocorrelation function of the difference potential in the ground state and the average of the difference potential after instantaneous excitation to the excited state are very similar (confirming linear response in this system); their decay indicates that vibrational relaxation occurs in about 1 ps in both states. 3) The spectral densities of various internal coordinates begin to identify the vibrations that affect the optical transition; the spectral density of the difference potential correlation function should also prove useful in quantum simulations of the back electron transfer. 4) Correlation functions of the protein atomic motions with the difference potential show that the nuclear motions are correlated over a distance of more than 20 A, especially along proposed electron transport paths.     

Possibility of revealing the role of nonresonant energy exchange between electrons and CO molecules at high vibrational levels

An experimental method providing information about the interaction of electrons with excited CO molecules at high vibrational levels is proposed and justified theoretically. The suggested experimental scheme is based on the use of two successive discharge pulses under the conditions prevailing in an electroionization CO laser. The first pulse should ensure a sufficiently high energy input in order for a nonequilibrium vibrational distribution function to form. The second pulse serves to study the effect of the electric current on the vibrational distribution function of excited molecules at high vibrational levels. The theoretical analysis is based on the simultaneous solution of the Boltzmann equation for the electron energy distribution function and the vibrational kinetic equations realistically describing the multiquantum vibrational-vibrational exchange processes. The calculated results show that the sensitivity of the proposed measurement technique promises to be high.     

Ab initio calculations of molecular properties of low–lying electronic states of 2–cyclopenten–1–one – link with biological activity

Geometries, vibrational frequencies, vertical and adiabatic excitation energies, dipole moments and dipole polarizabilities of the ground and the three lowest electronic excited states, S(1)(n, π (*)), T(1)(n, π (*)), and T(2)(π, π (*)) of the 2-cyclopenten-1-one molecule (2CP) were calculated at the CCSD and CCSD(T) levels of approximation. Our results indicate that two triplets T(1)(n, π (*)) and T(2)(π, π (*)) are lying very close each to other, while the singlet S(1)(n, π (*)) is well above them. There are dramatic changes in dipole moments for (n, π (*)) excited states in respect to the ground state. On the other hand the T(2)(π, π (*)) state has a similar dipole moment as the ground state. These changes can be interpreted within the MO picture using electrostatic potential maps and changes in model IR spectra. Our CCSD(T) dipole moment data for the ground state and almost isoenergetic triplets T(1)(n, π (*)) and T(2)(π, π (*)) are 1.469?a.u., 0.551?a.u., and 1.124?a.u., respectively. Dipole polarizabilities of investigated excited states are much less affected by electron excitations than dipole moments. These are the first dipole moment and polarizability data of 2CP in the literature. The changes of molecular properties upon excitation to S(1)(n, π (*)) and T(1)(n, π (*)) correlate with the experimental data on the biological activity of 2CP related to the α, β-unsaturated carbonyl group.     

Fluctuation as a tool of biological molecular machines

The mechanism for biological molecular machines is different from that of man-made ones. Recently single molecule measurements and other experiments have revealed unique operations where biological molecular machines exploit thermal fluctuation in response to small inputs of energy or signals to achieve their function. Understanding and applying this mechanism to engineering offers new artificial machine designs.     

Femtosecond relaxation processes in <Emphasis Type="Italic">Rhodobacter sphaeroides</Emphasis> reaction centers

Energy relaxation was studied with difference femtosecond spectroscopy in reaction centers of the YM210L mutant of the purple photosynthetic bacterium Rhodobacter sphaeroides at low temperature (90 K). A dynamical long-wavelength shift of stimulated emission of the excited state of the bacteriochlorophyll dimer P was found, which starts simultaneously with P* formation and is accompanied by a change in the spectral shape of this emission. The characteristic value of this shift was about 30 nm, and the characteristic time about 200 fs. Difference kinetics ΔA measured at fixed wavelengths demonstrate the femtosecond shift of the P* stimulated emission appearing as a dependence of these kinetics on wavelength. We found that the reported long-wavelength shift can be explained in terms of electron-vibrational relaxation of the P* excited state with time constants of vibrational and electronic relaxation of 100 and 50 fs, respectively. Alternative mechanisms of the dynamical shift of the P* stimulated emission spectrum are also discussed in terms of energy redistribution between vibrational modes or coherent excitation of the modes.     

Vibrational spectroscopy in the ultraviolet via Gd3+ fluorescence: application to biological systems

Coupling of the narrow 311-nm Gd3+ fluorescence transition with the vibrational transitions of its inner-sphere ligands gives rise to the emission of vibronic photons between 320 and 350 nm. The energy difference between the fluorescence and vibronic transitions is equal to that of the vibrational transitions of the molecular group coordinated to Gd3+; thus the ir spectrum of the ligand can be measured in the uv spectral region the presence of other molecules absorbing in the ir. The vibronic spectra of several biological, organic, and inorganic molecules are shown to accurately report the vibrational spectrum of the ligand.     

70% efficiency of bistate molecular machines explained by information theory,high dimensional geometry and evolutionary convergence

The relationship between information and energy is key to understanding biological systems. We can display the information in DNA sequences specifically bound by proteins by using sequence logos, and we can measure the corresponding binding energy. These can be compared by noting that one of the forms of the second law of thermodynamics defines the minimum energy dissipation required to gain one bit of information. Under the isothermal conditions that molecular machines function this is joules per bit ( is Boltzmann''s constant and T is the absolute temperature). Then an efficiency of binding can be computed by dividing the information in a logo by the free energy of binding after it has been converted to bits. The isothermal efficiencies of not only genetic control systems, but also visual pigments are near 70%. From information and coding theory, the theoretical efficiency limit for bistate molecular machines is ln 2 = 0.6931. Evolutionary convergence to maximum efficiency is limited by the constraint that molecular states must be distinct from each other. The result indicates that natural molecular machines operate close to their information processing maximum (the channel capacity), and implies that nanotechnology can attain this goal.     

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Understanding the basis for intracellular motion is critical as the field moves toward a deeper understanding of the relation between Brownian forces, molecular crowding, and anisotropic (or isotropic) energetic forcing. Effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study discusses limitations in currently popular analysis methods (e.g., mean square displacement-based analyses) and how new techniques can be used to systematically analyze Single Particle Tracking (SPT) data experiencing abrupt state changes in time or space. The approach is to track GFP tagged chromatids in metaphase in live yeast cells and quantitatively probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes can be induced by various sources including: microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, and DNA-based molecular machines including polymerases and protein exchange complexes such as chaperones and chromatin remodeling complexes. Simulations aiming to show the relevance of the approach to more general SPT data analyses are also studied. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for “ground-truth” and/or subjective information.