Quantum and classical dynamics in biochemical reactions

The classic experiment of deVault and Chance touched off a long series of theoretical and experimental studies of the interplay between quantum and classical dynamics in photosynthetic electron transfer. More recently these issues have also been addressed in experiments on ligand binding reactions in heme proteins and through the study of kinetic isotope effects in enzymatic proton transfer. Theoretical effort has focused on a class of relatively simple models which display a surprisingly rich spectrum of dynamical behavior. Much less attention has been paid to a very important issue: Why are we allowed to use such simple models to describe such obviously complex molecules? Here we provide some tentative answers to this question, contrasting the cases of electron and proton transfer. We suggest that ideas based on simple models can inspire novel strategies for ‘realistic’ simulations, and that we can begin to think about the general problems of enzymatic catalysis in terms of dynamical pictures that previously have been applied only to the simpler case of electron transfer.     

Regulation levels of photosynthesis processes

The basic mechanisms of kinetic regulation of photosynthetic processes are considered, which provide a strict light regulation of electron transfer in photosynthetic reaction centers and a more flexible regulation at the level of interaction of photosystems, transmembrane ion fluxes and coupling with dark reactions of the Calvin cycle. A generalized model was developed, which integrates the modern knowledge about photosynthetic processes of higher plants. The general principles of multilevel regulation in photosynthetic systems are discussed.     

Entropy production in chiral symmetry breaking transitions

It is now well known that nonequilibrium chemical systems may reach conditions that spontaneously generate chiral asymmetry. One can find a host of model reactions that exhibit such behavior in the literature. Among these, models based on one originally devised by Frank have been studied extensively. Though the kinetic aspects of such model reactions have been discussed in great detail, the behavior of entropy in such systems is rarely discussed. In this article, the rate of entropy production per unit volume, sigma, in a modified Frank model is discussed. It is shown that the slope of sigma changes at the point at which the asymmetric states appear, behavior similar to that observed in second-order phase transitions.     

Electron transfer in quinoproteins

Soluble quinoprotein dehydrogenases oxidize a wide range of sugar, alcohol, amine, and aldehyde substrates. The physiological electron acceptors for these enzymes are not pyridine nucleotides but are other soluble redox proteins. This makes these enzymes and their electron acceptors excellent systems with which to study mechanisms of long-range interprotein electron transfer reactions. The tryptophan tryptophylquinone (TTQ)-dependent methylamine dehydrogenase (MADH) transfers electrons to a blue copper protein, amicyanin. It has been possible to alter the rate of electron transfer by using different redox forms of MADH, varying reaction conditions, and performing site-directed mutagenesis on these proteins. From kinetic and thermodynamic analyses of the reaction rates, it was possible to determine whether a change in rate is due a change in Delta G(0), electronic coupling, reorganization energy or kinetic mechanism. Examples of each of these cases are discussed in the context of the known crystal structures of the electron transfer protein complexes. The pyrroloquinoline quinone (PQQ)-dependent methanol dehydrogenase transfers electrons to a c-type cytochrome. Kinetic and thermodynamic analyses of this reaction indicated that this electron transfer reaction was conformationally coupled. Quinohemoproteins possess a quinone cofactor as well as one or more c-type hemes within the same protein. The structures of a PQQ-dependent quinohemoprotein alcohol dehydrogenase and a TTQ-dependent quinohemoprotein amine dehydrogenase are described with respect to their roles in intramolecular and intermolecular protein electron transfer reactions.     

Understanding the cytochrome bc complexes by what they don't do. The Q-cycle at 30

The cytochrome (cyt) bc(1), b(6)f and related complexes are central components of the respiratory and photosynthetic electron transport chains. These complexes carry out an extraordinary sequence of electron and proton transfer reactions that conserve redox energy in the form of a trans-membrane proton motive force for use in synthesizing ATP and other processes. Thirty years ago, Peter Mitchell proposed a general turnover mechanism for these complexes, which he called the Q-cycle. Since that time, many opposing schemes have challenged the Q-cycle but, with the accumulation of large amounts of biochemical, kinetic, thermodynamic and high-resolution structural data, the Q-cycle has triumphed as the accepted model, although some of the intermediate steps are poorly understood and still controversial. One of the major research questions concerning the cyt bc(1) and b(6)f complexes is how these enzymes suppress deleterious and dissipative side reactions. In particular, most Q-cycle models involve reactive semiquinone radical intermediates that can reduce O(2) to superoxide and lead to cellular oxidative stress. Current models to explain the avoidance of side reactions involve unprecedented or unusual enzyme mechanisms, the testing of which will involve new theoretical and experimental approaches.     

Modeling the electron transport chain of purple non‐sulfur bacteria

Purple non‐sulfur bacteria (Rhodospirillaceae) have been extensively employed for studying principles of photosynthetic and respiratory electron transport phosphorylation and for investigating the regulation of gene expression in response to redox signals. Here, we use mathematical modeling to evaluate the steady‐state behavior of the electron transport chain (ETC) in these bacteria under different environmental conditions. Elementary‐modes analysis of a stoichiometric ETC model reveals nine operational modes. Most of them represent well‐known functional states, however, two modes constitute reverse electron flow under respiratory conditions, which has been barely considered so far. We further present and analyze a kinetic model of the ETC in which rate laws of electron transfer steps are based on redox potential differences. Our model reproduces well‐known phenomena of respiratory and photosynthetic operation of the ETC and also provides non‐intuitive predictions. As one key result, model simulations demonstrate a stronger reduction of ubiquinone when switching from high‐light to low‐light conditions. This result is parameter insensitive and supports the hypothesis that the redox state of ubiquinone is a suitable signal for controlling photosynthetic gene expression.     

Pathways,pathway tubes,pathway docking,and propagators in electron transfer proteins

The simplest views of long-range electron transfer utilize flat one-dimensional barrier tunneling models, neglecting structural details of the protein medium. The pathway model of protein electron transfer reintroduces structure by distinguishing between covalent bonds, hydrogen bonds, and van der Waals contacts. These three kinds of interactions in a tunneling pathway each have distinctive decay factors associated with them. The distribution and arrangement of these bonded and nonbonded contacts in a folded protein varies tremendously between structures, adding a richness to the tunneling problem that is absent in simpler views. We review the pathway model and the predictions that it makes for protein electron transfer rates in small proteins, docked proteins, and the photosynthetic reactions center. We also review the formulation of the protein electron transfer problem as an effective two-level system. New multi-pathway approaches and improved electronic Hamiltonians are described briefly as well.     

Kinetic modeling of light limitation and sulfur deprivation effects in the induction of hydrogen production with Chlamydomonas reinhardtii: Part I. Model development and parameter identification

Chlamydomonas reinhardtii is a green microalga capable of turning its metabolism towards H2 production under specific conditions. However this H2 production, narrowly linked to the photosynthetic process, results from complex metabolic reactions highly dependent on the environmental conditions of the cells. A kinetic model has been developed to relate culture evolution from standard photosynthetic growth to H2 producing cells. It represents transition in sulfur-deprived conditions, known to lead to H2 production in Chlamydomonas reinhardtii, and the two main processes then induced which are an over-accumulation of intracellular starch and a progressive reduction of PSII activity for anoxia achievement. Because these phenomena are directly linked to the photosynthetic growth, two kinetic models were associated, the first (one) introducing light dependency (Haldane type model associated to a radiative light transfer model), the second (one) making growth a function of available sulfur amount under extracellular and intracellular forms (Droop formulation). The model parameters identification was realized from experimental data obtained with especially designed experiments and a sensitivity analysis of the model to its parameters was also conducted. Model behavior was finally studied showing interdependency between light transfer conditions, photosynthetic growth, sulfate uptake, photosynthetic activity and O2 release, during transition from oxygenic growth to anoxic H2 production conditions.     

Electron transfer through the acceptor side of photosystem I: Interaction with exogenous acceptors and molecular oxygen

This review considers the state-of-the-art on mechanisms and alternative pathways of electron transfer in photosynthetic electron transport chains of chloroplasts and cyanobacteria. The mechanisms of electron transport control between photosystems (PS) I and II and the Calvin–Benson cycle are considered. The redistribution of electron fluxes between the noncyclic, cyclic, and pseudocyclic pathways plays an important role in the regulation of photosynthesis. Mathematical modeling of light-induced electron transport processes is considered. Particular attention is given to the electron transfer reactions on the acceptor side of PS I and to interactions of PS I with exogenous acceptors, including molecular oxygen. A kinetic model of PS I and its interaction with exogenous electron acceptors has been developed. This model is based on experimental kinetics of charge recombination in isolated PS I. Kinetic and thermodynamic parameters of the electron transfer reactions in PS I are scrutinized. The free energies of electron transfer between quinone acceptors A_1A/A_1B in the symmetric redox cofactor branches of PS I and iron–sulfur clusters F_X, F_A, and F_B have been estimated. The second-order rate constants of electron transfer from PS I to external acceptors have been determined. The data suggest that byproduct formation of superoxide radical in PS I due to the reduction of molecular oxygen in the A1 site (Mehler reaction) can exceed 0.3% of the total electron flux in PS I.     

Electron tunneling through proteins

Electron transfer processes are vital elements of energy transduction pathways in living cells. More than a half century of research has produced a remarkably detailed understanding of the factors that regulate these 'currents of life'. We review investigations of Ru-modified proteins that have delineated the distance- and driving-force dependences of intra-protein electron-transfer rates. We also discuss electron transfer across protein-protein interfaces that has been probed both in solution and in structurally characterized crystals. It is now clear that electrons tunnel between sites in biological redox chains, and that protein structures tune thermodynamic properties and electronic coupling interactions to facilitate these reactions. Our work has produced an experimentally validated timetable for electron tunneling across specified distances in proteins. Many electron tunneling rates in cytochrome c oxidase and photosynthetic reaction centers agree well with timetable predictions, indicating that the natural reactions are highly optimized, both in terms of thermodynamics and electronic coupling. The rates of some reactions, however, significantly exceed timetable predictions: it is likely that multistep tunneling is responsible for these anomalously rapid charge transfer events.     

Proton and hydrogen currents in photosynthetic water oxidation

The photosynthetic processes that lead to water oxidation involve an evolution in time from photon dynamics to photochemically-driven electron transfer to coupled electron/proton chemistry. The redox-active tyrosine, Y(Z), is the component at which the proton currents necessary for water oxidation are switched on. The thermodynamic and kinetic implications of this function for Y(Z) are discussed. These considerations also provide insight into the related roles of Y(Z) in preserving the high photochemical quantum efficiency in Photosystem II (PSII) and of conserving the highly oxidizing conditions generated by the photochemistry in the PSII reaction center. The oxidation of Y(Z) by P(680)(+) can be described well by a treatment that invokes proton coupling within the context of non-adiabatic electron transfer. The reduction of Y(.)(Z), however, appears to proceed by an adiabatic process that may have hydrogen-atom transfer character.     

The effects of Tubulin denaturation on the characterization of its polymerization behavior

We report here upon a simulation study examining the effect of a dynamic mode of tubulin denaturation upon the kinetic and thermodynamic characterisation of the polymer formed for two idealized models of a tubulin polymerization reaction: (i) an irreversibly polymerizing system; and (ii) a reversibly polymerizing system. The effects of each denaturation mode upon the two model systems behavior are highlighted by interpretation of the data in terms of the classical Oosawa reversible condensation polymerization model. We reveal here findings which suggest that the measurement strategy in concert with Tubulin's instability over the time course of the experiment may bias the results obtained so as to make an irreversible system's behavior conform to the equilibrium model or alternatively distort the results obtained from a truly reversible system to produce values of the critical concentration quite seriously in error. It was also found that Tubulin denaturation may seriously distort parameter estimates gained from a kinetic characterization of the system (e.g. nucleus size and growth rate constant).     

Removal of covalent heterogeneity reveals simple folding behavior for P4-P6 RNA

RNA folding landscapes have been described alternately as simple and as complex. The limited diversity of RNA residues and the ability of RNA to form stable secondary structures prior to adoption of a tertiary structure would appear to simplify folding relative to proteins. Nevertheless, there is considerable evidence for long-lived misfolded RNA states, and these observations have suggested rugged energy landscapes. Recently, single molecule fluorescence resonance energy transfer (smFRET) studies have exposed heterogeneity in many RNAs, consistent with deeply furrowed rugged landscapes. We turned to an RNA of intermediate complexity, the P4-P6 domain from the Tetrahymena group I intron, to address basic questions in RNA folding. P4-P6 exhibited long-lived heterogeneity in smFRET experiments, but the inability to observe exchange in the behavior of individual molecules led us to probe whether there was a non-conformational origin to this heterogeneity. We determined that routine protocols in RNA preparation and purification, including UV shadowing and heat annealing, cause covalent modifications that alter folding behavior. By taking measures to avoid these treatments and by purifying away damaged P4-P6 molecules, we obtained a population of P4-P6 that gave near-uniform behavior in single molecule studies. Thus, the folding landscape of P4-P6 lacks multiple deep furrows that would trap different P4-P6 molecules in different conformations and contrasts with the molecular heterogeneity that has been seen in many smFRET studies of structured RNAs. The simplicity of P4-P6 allowed us to reliably determine the thermodynamic and kinetic effects of metal ions on folding and to now begin to build more detailed models for RNA folding behavior.     

Protein-film voltammetry: a theoretical study of the temperature effect using square-wave voltammetry

Square-wave voltammetry of surface redox reactions is considered as an adequate model for a protein-film voltammetric setup. Here we develop a theoretical approach to analyze the effects of temperature on square-wave voltammograms. The performed simulations address the surface redox reactions featuring slow, modest and fast electron transfer. The theoretical calculations show that the temperature affects the square-wave voltammetric responses in a complex way resulting in a variety of peak shapes. Temperature effects on the phenomena known as "quasireversible maximum" and "split SW peaks" are also analyzed. The simulated results can be used to analyze the redox mechanisms and kinetic parameters of electron transfer reactions in protein-film criovoltammetry and other surface-confined redox systems. Our analysis also shows how "abnormal" features present in some square-wave voltammetric studies can easily be misinterpreted by postulating "multiple species", "stable radicals", or additional processes. Finally we provide a simple algorithm to use the "quasireversible maximum" to determine the activation energy of electron transfer reactions by surface redox systems.     

Theoretical studies of proton-coupled electron transfer reactions

A theoretical formulation for proton-coupled electron transfer (PCET) is described. This theory allows the calculation of rates and kinetic isotope effects and provides insight into the underlying fundamental principles of PCET reactions. Applications of this theory to PCET reactions in iron bi-imidazoline complexes, oxoruthenium polypyridyl complexes, osmium-benzoquinone systems, amidinium-carboxylate salt bridges, DNA-acrylamide complexes, and ruthenium polypyridyl-tyrosine systems are summarized. The mechanistic insight gained from theoretical calculations on these model systems is relevant to PCET in more complex biological processes such as photosynthesis and respiration.     

Modelling of the electron transfer reactions in Photosystem I by electron tunnelling theory: the phylloquinones bound to the PsaA and the PsaB reaction centre subunits of PS I are almost isoenergetic to the iron-sulfur cluster F(X)

Photosystem I is a large macromolecular complex located in the thylakoid membranes of chloroplasts and in cyanobacteria that catalyses the light driven reduction of ferredoxin and oxidation of plastocyanin. Due to the very negative redox potential of the primary electron transfer cofactors accepting electrons, direct estimation by redox titration of the energetics of the system is hampered. However, the rates of electron transfer reactions are related to the thermodynamic properties of the system. Hence, several spectroscopic and biochemical techniques have been employed, in combination with the classical Marcus theory for electron transfer tunnelling, in order to access these parameters. Nevertheless, the values which have been presented are very variable. In particular, for the case of the tightly bound phylloquinone molecule A(1), the values of the redox potentials reported in the literature vary over a range of about 350 mV. Previous models of Photosystem I have assumed a unidirectional electron transfer model. In the present study, experimental evidence obtained by means of time resolved absorption, photovoltage, and electron paramagnetic resonance measurements are reviewed and analysed in terms of a bi-directional kinetic model for electron transfer reactions. This model takes into consideration the thermodynamic equilibrium between the iron-sulfur centre F(X) and the phylloquinone bound to either the PsaA (A(1A)) or the PsaB (A(1B)) subunit of the reaction centre and the equilibrium between the iron-sulfur centres F(A) and F(B). The experimentally determined decay lifetimes in the range of sub-picosecond to the microsecond time domains can be satisfactorily simulated, taking into consideration the edge-to-edge distances between redox cofactors and driving forces reported in the literature. The only exception to this general behaviour is the case of phylloquinone (A(1)) reoxidation. In order to describe the reported rates of the biphasic decay, of about 20 and 200 ns, associated with this electron transfer step, the redox potentials of the quinones are estimated to be almost isoenergetic with that of the iron sulfur centre F(X). A driving force in the range of 5 to 15 meV is estimated for these reactions, being slightly exergonic in the case of the A(1B) quinone and slightly endergonic, in the case of the A(1A) quinone. The simulation presented in this analysis not only describes the kinetic data obtained for the wild type samples at room temperature and is consistent with estimates of activation energy by the analysis of temperature dependence, but can also explain the effect of the mutations around the PsaB quinone binding pocket. A model of the overall energetics of the system is derived, which suggests that the only substantially irreversible electron transfer reactions are the reoxidation of A(0) on both electron transfer branches and the reduction of F(A) by F(X).     

On the Emergence of Biological Complexity: Life as a Kinetic State of Matter

A kinetic model that attempts to further clarify the nature of biological complexification is presented. Its essence: reactions of replicating systems and those of regular chemical systems follow different selection rules leading to different patterns of chemical behavior. For regular chemical systems selection is fundamentally thermodynamic, whereas for replicating chemical systems selection is effectively kinetic. Building on an extension of the kinetic stability concept it is shown that complex replicators tend to be kinetically more stable than simple ones, leading to an on-going process of kinetically-directed complexification. The high kinetic stability of simple replicating assemblies such as phages, compared to the low kinetic stability of the assembly components, illustrates the complexification principle. The analysis suggests that living systems constitute a kinetic state of matter, as opposed to the traditional thermodynamic states that dominate the inanimate world, and reaffirms our view that life is a particular manifestation of replicative chemistry.     

The reduction potential of the beta-carotene.+ /beta-carotene couple in an aqueous micro-heterogeneous environment

There is a resurgence of interest in the role of electron transfer reactions involving beta-carotene in photosynthesis. There is also current debate on the health benefits of dietary carotenoids and the possible deleterious effects on certain sub-populations such as smokers. The impact of dietary carotenoids on health may well be also related to radical reactions. A key parameter in biological systems is therefore the one-electron reduction potential of the carotenoid radical cation, now reported for the first time in a model biological aqueous environment. The value obtained is 1.06+/-0. 01 V and is sufficiently high to oxidise cell membrane proteins, but is low enough to repair P(680).+ in the photosynthetic reaction centre.