A stochastic model of protein conformational dynamics and electronic–conformational coupling in biological energy transduction

Protein dynamics control of electron transfer in photosynthetic reaction centers from Rps. sulfoviridis

In the cycle of photosynthetic reaction centers, the initially oxidized special pair of bacteriochlorophyll molecules is subsequently reduced by an electron transferred over a chain of four hemes of the complex. Here, we examine the kinetics of electron transfer between the proximal heme c-559 of the chain and the oxidized special pair in the reaction center from Rps. sulfoviridis in the range of temperatures from 294 to 40 K. The experimental data were obtained for three redox states of the reaction center, in which one, two, or three nearest hemes of the chain are reduced prior to special pair oxidation. The experimental kinetic data are analyzed in terms of a Sumi-Marcus-type model developed in our previous paper,1 in which similar measurements were reported on the reaction centers from Rps. viridis. The model allows us to establish a connection between the observed nonexponential electron-transfer kinetics and the local structural relaxation dynamics of the reaction center protein on the microsecond time scale. The activation energy for relaxation dynamics of the protein medium has been found to be around 0.1 eV for all three redox states, which is in contrast to a value around 0.4-0.6 eV in Rps. viridis.1 The possible nature of the difference between the reaction centers from Rps. viridis and Rps. sulfoviridis, which are believed to be very similar, is discussed. The role of the protein glass transition at low temperatures and that of internal water molecules in the process are analyzed.

Rate processes with non-Markovian dynamical disorder

Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasistatic disorder. This transition occurs at the conformational mean residence time intervals fixed much less than the inverse of the corresponding ET rates. An explanation of this paradoxical effect is provided. Moreover, its presence is also manifested for the simplest, exactly solvable non-Markovian model with a biexponential distribution of the residence times in one of the conformations. The nontrivial conditions for this phenomenon to occur are found.

Hole Transfer in a C-Shaped Molecule: Conformational Freedom versus Solvent-Mediated Coupling

The electronic coupling matrix elements attending the charge separation reactions of a C-shaped molecule containing an excited pyrene as the electron acceptor and a dimethylaniline as the donor are determined in aromatic, ether, and ester solvents. Band shape analyses of the charge-transfer emission spectra (CT --> S(0)) provide values of the reaction free energy, the solvent reorganization energy, and the vibrational reorganization energy in each solvent. The free energy for charge separation in benzene and toluene solvents is independently determined from the excited state equilibrium established between the locally excited pyrene S(1) state and the charge-transfer state. Analyses of the charge separation kinetics using the spectroscopically determined reorganization energies and reaction free energies indicate that the electronic coupling is solvent independent, despite the presence of a cleft between the donor and acceptor. Hence, solvent molecules are not involved in the coupling pathway. The orientations of the donor and acceptor units, relative to the spacer, are not rigidly constrained, and their torsional motions decrease solvent access to the cleft. Generalized Mulliken-Hush calculations show that rotation of the pyrene group about the bond connecting it to the spacer greatly modulates the magnitude of through-space coupling between the S(1) and CT states. The relationship between the torsional dynamics and the electron-transfer dynamics is discussed.

Correlated conformational fluctuations during enzymatic catalysis: Implications for catalytic rate enhancement

Correlated enzymatic conformational fluctuations are shown to contribute to the rate of enhancement achieved during catalysis. Cytidine deaminase serves as a model system. Crystallographic temperature factor data for this enzyme complexed with substrate analog, transition-state analog, and product are available, thereby establishing a measure of atomic scale conformational fluctuations along the (approximate) reaction coordinate. First, a neural network-based algorithm is used to visualize the decreased conformational fluctuations at the transition state. Second, a dynamic diffusion equation along the reaction coordinate is solved and shows that the flux velocity through the associated enzymatic conformation space is greatest at the transition state. These results suggest (1) that there are both dynamic and energetic restrictions to conformational fluctuations at the transition state, (2) that enzymatic catalysis occurs on a fluctuating potential energy surface, and (3) a form for the potential energy. The Michaelis-Menten equations are modified to describe catalysis on this fluctuating potential energy profile, leading to enhanced catalytic rates when fluctuations along the reaction coordinate are appropriately correlated. This represents a dynamic tuning of the enzyme for maximally effective transformation of the ES complex into EP.

A synthetic picture of intramolecular dynamics of proteins. Towards a contemporary statistical theory of biochemical processes

An increasing body of experimental evidence indicates the slow character of internal dynamics of native proteins. The important consequence of this is that theories of chemical reactions, used hitherto, appear inadequate for description of most biochemical reactions. Construction of a contemporary, truly advanced statistical theory of biochemical processes will need simple but realistic models of microscopic dynamics of biomolecules. In this review, intended to be a contribution towards this direction, three topics are considered. First, an intentionally simplified picture of dynamics of native proteins which emerges from recent investigations is presented. Fast vibrational modes of motion, of periods varying from 10(-14) to 10(-11) s, are contrasted with purely stochastic conformational transitions. Significant evidence is adduced that the relaxation time spectrum of the latter spreads in the whole range from 10(-11) to 10(5) s or longer, and up to 10(-7) s it is practically quasi-continuous. Next, the essential ideas of the theory of reaction rates based on stochastic models of intramolecular dynamics are outlined. Special attention is paid to reactions involving molecules in the initial conformational substrates confirmed to the transition state, which is realized in actual experimental situations. And finally, the two best experimentally justified classes of models of conformational transition dynamics, symbolically referred to as "protein glass" and "protein machine", are described and applied to the interpretation of a few simple biochemical processes, perhaps the most important result reported is the demonstration of the possibility of predominance of the short initial condition-dependent stage of protein involved reactions over the main stage described by the standard kinetics. This initial stage, and not the latter, is expected to be responsible for the coupling of component reactions in the complete enzymatic cycles as well as more complex processes of biological free energy transduction.

Protein machine model of enzymatic reactions gated by enzyme internal dynamics

The slow character of conformational transition dynamics in native proteins, recently becoming more and more apparent, makes conventional theories of chemical reactions inapplicable for the description of enzymatic reactions. Any contemporary statistical theory of biochemical processes has to be based on a possibly simple but realistic model of microscopic dynamics of participating biomolecules. In a model considered in this paper the dynamics of enzymatic protein is approximated by a quasi-continuous diffusive motion of its solid-like structural elements relative to each other. The enzymatic reaction is assumed to involve three steps (a covalent tranformation preceded and followed by association-dissociation processes with the substrate and the product), each step being gated by conformational diffusion. In general, the reaction proceeds in three stages: initial, transient and steady-state. Carefully approximated analytical formulae describing the kinetics in each stage are derived. In the limit of the fast internal dynamics of the enzyme, when compared to the local chemical transformations, the initial stage of reaction, dependent on the initial distribution of enzyme conformations, is absent and all the formulae describing the remaining two stages simplify to those provided by the classical theory of Haldane. However, following recent studies, the rule seems to be that it is the conformational dynamics of the enzyme, and not the details of chemical mechanism, that affects the rate of enzymatic reaction. Apart from the possibility of the initial inhomogeneous kinetics, the important result obtained in the limit of slow conformational dynamics is that the kinetic mechanisms of a reaction differ in general between the transient and steady-state stages. Possibilities of carrying out an experimentum crucis directly discrediting the conventional approach are considered.

Interaction between cytochrome c and the photosynthetic reaction center of purple bacteria: behaviour at low temperature

In purple photosynthetic bacteria the electron donor to the special pair, after its oxidation by a light-induced reaction, is a c-type cytochrome: either a soluble monoheme cytochrome which forms a transitory complex with the reaction center, or a tetraheme cytochrome which remains permanently bound to the reaction center. The effects of low temperatures on electron transfer in the complex are presented and discussed. They provide estimates for the reorganization energy. The most prominent effect of low temperature is that a dominant fast phase of electron transfer becomes impossible at a temperature of around 250 K (monoheme cytochrome) or located between 250 K and 80 K according to the redox state (tetraheme cytochrome). This inhibition is attributed to a freezing-like transition of pools of water molecules which blocks structural changes of the protein which are normally associated with the cytochrome oxidation.