Chromophore-protein interactions and the function of the photosynthetic reaction center: a molecular dynamics study.

The coupling between electron transfer and protein structure and dynamics in the photosynthetic reaction center of Rhodopseudomonas viridis is investigated. For this purpose molecular dynamics simulations of the essential portions (a segment of 5797 atoms) of this protein complex have been carried out. Electron transfer in the primary event is modeled by altering the charge distributions of the chromophores according to quantum chemical calculations. The simulations show (i) that fluctuations of the protein matrix, which are coupled electrostatically to electron transfer, play an important role in controlling the electron transfer rates and (ii) that the protein matrix stabilizes the separated electron pair state through rapid (200 fs) and temperature-independent dielectric relaxation. The photosynthetic reaction center resembles a polar liquid in that the internal motions of the whole protein complex, rather than only those of specific side groups, contribute to i and ii. The solvent reorganization energy is about 4.5 kcal/mol. The simulations indicate that rather small structural rearrangements and changes in motional amplitudes accompany the primary electron transfer.     

Dynamics and dissipation in enzyme catalysis

We use quantized molecular dynamics simulations to characterize the role of enzyme vibrations in facilitating dihydrofolate reductase hydride transfer. By sampling the full ensemble of reactive trajectories, we are able to quantify and distinguish between statistical and dynamical correlations in the enzyme motion. We demonstrate the existence of nonequilibrium dynamical coupling between protein residues and the hydride tunneling reaction, and we characterize the spatial and temporal extent of these dynamical effects. Unlike statistical correlations, which give rise to nanometer-scale coupling between distal protein residues and the intrinsic reaction, dynamical correlations vanish at distances beyond 4–6 Å from the transferring hydride. This work finds a minimal role for nonlocal vibrational dynamics in enzyme catalysis, and it supports a model in which nanometer-scale protein fluctuations statistically modulate—or gate—the barrier for the intrinsic reaction.     

Interprotein electron transfer from cytochrome c2 to photosynthetic reaction center: tunneling across an aqueous interface

Interprotein electron transfer (ET) reactions play an important role in biological energy conversion processes. One of these reactions, the ET between cytochrome c(2) (cyt) and reaction center from photosynthetic bacteria, is the focus of this theoretical study. The changes in the ET rate constant at fixed distances during the association process were calculated as the cyt moved from the electrostatically stabilized encounter complex to the bound state having short range van der Waals contacts in the tunneling region. Multiple conformations of the protein were generated by molecular dynamics simulations including explicit water molecules. For each of these conformations, the ET rate was calculated by using the Pathways model. The ET rate increased smoothly as the cyt approached from the encounter complex to the bound state, with a tunneling decay factor beta = 1.1 A(-1). This relatively efficient coupling between redox centers is due to the ability of interfacial water molecules to form multiple strong hydrogen bonding pathways connecting tunneling pathways on the surfaces of the two proteins. The ET rate determined for the encounter complex ensemble of states is only about a factor of 100 slower than that of the bound state (tau = 100 micros, compared with 1 micros), because of fluctuations of the cyt within the encounter complex ensemble through configurations having strong tunneling pathways. The ET rate for the encounter complex is in agreement with rates observed in mutant reaction centers modified to remove shortrange hydrophobic interactions, suggesting that in this case, ET occurs within the solvent-separated, electrostatically stabilized encounter complex.     

Electron tunneling in protein crystals

The current understanding of electron tunneling through proteins has come from work on systems where donors and acceptors are held at fixed distances and orientations. The factors that control electron flow between proteins are less well understood, owing to uncertainties in the relative orientations and structures of the reactants during the very short time that tunneling occurs. As we report here, the way around such structural ambiguity is to examine oxidation-reduction reactions in protein crystals. Accordingly, we have measured and analyzed the kinetics of electron transfer between native and Zn-substituted tuna cytochrome c (cyt c) molecules in crystals of known structure. Electron transfer rates [(320 s(-1) for *Zn-cyt c --> Fe(III)-cyt c; 2000 s(-1) for Fe(II)-cyt c --> Zn-cyt c(+))] over a Zn-Fe distance of 24.1 A closely match those for intraprotein electron tunneling over similar donor-acceptor separations. Our results indicate that van der Waals interactions and water-mediated hydrogen bonds are effective coupling elements for tunneling across a protein-protein interface.     

Donor-bridge-acceptor energetics determine the distance dependence of electron tunneling in DNA

Electron transfer (ET) processes in DNA are of current interest because of their involvement in oxidative strand cleavage reactions and their relevance to the development of molecular electronics. Two mechanisms have been identified for ET in DNA, a single-step tunneling process and a multistep charge-hopping process. The dynamics of tunneling reactions depend on both the distance between the electron donor and acceptor and the nature of the molecular bridge separating the donor and acceptor. In the case of protein and alkane bridges, the distance dependence is not strongly dependent on the properties of the donor and acceptor. In contrast, we show here that the distance decay of DNA ET rates varies markedly with the energetics of the donor and acceptor relative to the bridge. Specifically, we find that an increase in the energy of the bridge states by 0.25 eV (1 eV = 1.602 x 10(-19) J) relative to the donor and acceptor energies for photochemical oxidation of nucleotides, without changing the reaction free energy, results in an increase in the characteristic exponential distance decay constant for the ET rates from 0.71 to 1.1 A(-1). These results show that, in the small tunneling energy gap regime of DNA ET, the distance dependence is not universal; it varies strongly with the tunneling energy gap. These DNA ET reactions fill a "missing link" or transition regime between the large barrier (rapidly decaying) tunneling regime and the (slowly decaying) hopping regime in the general theory of bridge-mediated ET processes.     

Protein dynamics and electron transfer: electronic decoherence and non-Condon effects

We compute the autocorrelation function of the donor-acceptor tunneling matrix element for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor {computed by Rossky and coworkers [Lockwood, D. M., Cheng, Y.-K. & Rossky, P. J. (2001) Chem. Phys. Lett. 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate. is studied as a function of donor-acceptor distance, tunneling pathway structure, tunneling energy, and temperature to explore the structural and dynamical origins of non-Condon effects. For azurin, the correlation function is remarkably insensitive to tunneling pathway structure. The decay time is only slightly shorter than it is for solvent-mediated electron transfer in small organic molecules and originates, largely, from fluctuations of valence angles rather than bond lengths.     

Coordinated effects of distal mutations on environmentally coupled tunneling in dihydrofolate reductase

One of the most intriguing questions in modern enzymology is whether enzyme dynamics evolved to enhance the catalyzed chemical transformation. In this study, dihydrofolate reductase, a small monomeric protein that catalyzes a single C-H-C transfer, is used as a model system to address this question. Experimental and computational studies have proposed a dynamic network that includes two residues remote from the active site (G121 and M42). The current study compares the nature of the H-transfer step of the WT enzyme, two single mutants, and their double mutant. The contribution of quantum mechanical tunneling and enzyme dynamics to the H-transfer step was examined by determining intrinsic kinetic isotope effects, their temperature dependence, and activation parameters. Different patterns of environmentally coupled tunneling were found for these four enzymes. The findings indicate that the naturally evolved WT dihydrofolate reductase requires no donor-acceptor distance fluctuations (no gating). Both single mutations affect the rearrangement of the system before tunneling, so some gating is required, but the overall nature of the environmentally coupled tunneling appears similar to that of the WT enzyme. The double mutation, on the other hand, seems to cause a major change in the nature of H transfer, leading to poor reorganization and substantial gating. These findings support the suggestion that these distal residues synergistically affect the H transfer at the active site of the enzyme. This observation is in accordance with the notion that these remote residues are part of a dynamic network that is coupled to the catalyzed chemistry.     

Gaussian fluctuations and linear response in an electron transfer protein

In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. Molecular dynamics simulations are presented that establish a linear dielectric response of both protein and surrounding solvent over the course of a biologically relevant electron transfer reaction: oxido-reduction of yeast cytochrome c in solution. Using an umbrella-sampling free energy approach with long simulations, an accurate treatment of long-range electrostatics and both classical and quantum models of the heme, good agreement is obtained with experiment for the redox potential relative to a heme-octapeptide complex. We obtain a reorganization free energy that is only half that for heme-octapeptide and is reproduced with a dielectric continuum model where the heme vicinity has a dielectric constant of only 1.1. This value implies that the contribution of protein reorganization to the electron transfer free energy barrier is reduced almost to the theoretical limit (a dielectric of one), and that the fluctuations of the electrostatic potential on the heme have a simple harmonic form, in accord with Marcus theory, even though the fluctuations of many individual protein groups (especially at the protein surface) are anharmonic.     

Internal and interfacial dielectric properties of cytochrome c from molecular dynamics in aqueous solution.

The dielectric properties of proteins are central to their stability and activity. We use the Fröhlich-Kirkwood theory of dielectrics to analyze two 1-ns molecular dynamics simulations of ferro- and ferricytochrome c in spherical droplets of 1400 water molecules. Protein and solvent are idealized as a series of concentric, spherical, dielectric media. Analysis results depend strongly on the treatment of the charged protein side chains at the protein/solvent interface. If charged side chains are viewed as part of the protein medium, then the protein dipole fluctuations are dominated by large, mutually uncorrelated, anisotropic, motions of the charged side chains. It is then incorrect to view the protein region as a single, homogeneous dielectric material. If one does take this view, estimates of the protein "dielectric constant" vary from 16 to 37, depending on the exact choice of model parameters. In contrast, if the charged portions of the charged side chains are viewed as part of the solvent medium, then theory and simulation are consistent: the protein dipole fluctuations excluding charged side chains are roughly those of a homogeneous, isotropic dielectric medium, with a dielectric constant of 4.7 +/- 1.0 (ferro) or 3.4 +/- 1.0 (ferri), in agreement with powder experiments. Statistical uncertainty and sensitivity to model parameters are small. Analysis of the radial dependence of the dipole fluctuations suggests that the inner half of the protein has a somewhat lower dielectric constant of 1.5-2, consistent with its biological function in electron transfer. These results suggest that Poisson-Boltzmann models could treat the protein bulk as a low-dielectric medium and the charged surface groups as part of the solvent region.     

Electron tunneling in respiratory complex I

NADH:ubiquinone oxidoreductase (complex I) plays a central role in the respiratory electron transport chain by coupling the transfer of electrons from NADH to ubiquinone to the creation of the proton gradient across the membrane necessary for ATP synthesis. Here the atomistic details of electronic wiring of all Fe/S clusters in complex I are revealed by using the tunneling current theory and computer simulations; both density functional theory and semiempirical electronic structure methods were used to examine antiferromagnetically coupled spin states and corresponding tunneling wave functions. Distinct electron tunneling pathways between neighboring Fe/S clusters are identified; the pathways primarily consist of two cysteine ligands and one additional key residue. Internal water between protein subunits is identified as an essential mediator enhancing the overall electron transfer rate by almost three orders of magnitude to achieve a physiologically significant value. The identified key residues are further characterized by sensitivity of electron transfer rates to their mutations, examined in simulations, and their conservation among complex I homologues. The unusual electronic structure properties of Fe(4)S(4) clusters in complex I explain their remarkable efficiency of electron transfer.     

Dissection of complex protein dynamics in human thioredoxin

We report our direct study of complex protein dynamics in human thioredoxin by dissecting into elementary processes and determining their relevant time scales. By combining site-directed mutagenesis with femtosecond spectroscopy, we have distinguished four partly time-overlapped dynamical processes at the active site of thioredoxin. Using intrinsic tryptophan as a molecular probe and from mutation studies, we ascertained the negligible contribution to solvation by protein sidechains and observed that the hydration dynamics at the active site occur in 0.47-0.67 and 10.8-13.2 ps. With reduced and oxidized states, we determined the electron-transfer quenching dynamics between excited tryptophan and a nearby disulfide bond in 10-17.5 ps for three mutants. A robust dynamical process in 95-114 ps, present in both redox states and all mutants regardless of neighboring charged, polar, and hydrophobic residues around the probe, is attributed to the charge transfer reaction with its adjacent peptide bond. Site-directed mutations also revealed the electronic quenching dynamics by an aspartate residue at a hydrogen bond distance in 275-615 ps. The local rotational dynamics determined by the measurement of anisotropy changes with time unraveled a relatively rigid local configuration but implies that the protein fluctuates on the time scale of longer than nanoseconds. These results elucidate the temporal evolution of hydrating water motions, electron-transfer reactions, and local protein fluctuations at the active site, and show continuously synergistic dynamics of biological function over wide time scales.     

Coupling of hydrogenic tunneling to active-site motion in the hydrogen radical transfer catalyzed by a coenzyme B12-dependent mutase

Hydrogen transfer reactions catalyzed by coenzyme B(12)-dependent methylmalonyl-CoA mutase have very large kinetic isotope effects, indicating that they proceed by a highly quantal tunneling mechanism. We explain the kinetic isotope effect by using a combined quantum mechanical/molecular mechanical potential and semiclassical quantum dynamics calculations. Multidimensional tunneling increases the magnitude of the calculated intrinsic hydrogen kinetic isotope effect by a factor of 3.6 from 14 to 51, in excellent agreement with experimental results. These calculations confirm that tunneling contributions can be large enough to explain even a kinetic isotope effect >50, not because the barrier is unusually thin but because corner-cutting tunneling decreases the distance over which the system tunnels without a comparable increase in either the effective potential barrier or the effective mass for tunneling.     

Charge conductivity in peptides: dynamic simulations of a bifunctional model supporting experimental data

Our previous finding and the given mechanism of charge and electron transfer in polypeptides are here integrated in a bifunctional model involving electronic charge transfer coupled to special internal rotations. Present molecular dynamics simulations that describe these motions in the chain result in the mean first passage times for the hopping process of an individual step. This "rest and fire" mechanism is formulated in detail-i.e., individual amino acids are weakly coupled and must first undergo alignment to reach the special strong coupling. This bifunctional model contains the essential features demanded by our prior experiments. The molecular dynamics results yield a mean first passage time distribution peaked at about 140 fs, in close agreement with our direct femtosecond measurements. In logic gate language this is a strongly conducting ON state resulting from small firing energies, the system otherwise being a quiescent OFF state. The observed time scale of about 200 fs provides confirmation of our simulations of transport, a model of extreme transduction efficiency. It explains the high efficiency of charge transport observed in polypeptides. We contend that the moderate speed of weak coupling is required in our model by the bifunctionality of peptides. This bifunctional mechanism agrees with our data and contains valuable features for a general model of long-range conductivity, final reactivity, and binding at a long distance.     

Polarizable molecules in the vibrational spectroscopy of water

We examine the role of electronic polarizability in water on short (tens of femtoseconds), intermediate (hundreds of femtoseconds), and long (approximately 1 ps) time scales by comparing molecular dynamics results to experimental data for vibrational spectroscopy of HOD in liquid D2O. Because the OH absorption frequency is sensitive to the details of the atomic forces experienced in the liquid, our results provide important quantitative comparisons for several popular empirical water potentials. When compared with their fixed-charge counterparts, the polarizable models give similar slower long time constants for the decay of vibrational correlations and re-orientational motion that is in better agreement with experiments. Polarizable potentials yield qualitatively dissimilar predictions for frequency fluctuations and transition dipole moment fluctuations at equilibrium. Models that confine the polarizability to the plane of the molecule (i.e., TIP4P-FQ) overestimate the width of the distribution describing frequency fluctuations by more than a factor of two. These models also underestimate the amplitude of the hydrogen-bond stretch at 170 cm(-1). A potential that has both an out-of-plane polarization and fluctuating charges, POL5-TZ, compares best with experiments. We interpret our findings in terms of microscopic dynamics and make suggestions that may improve the quality of emerging polarizable force fields for water.     

Femtosecond dynamics of flavoproteins: charge separation and recombination in riboflavine (vitamin B2)-binding protein and in glucose oxidase enzyme

Flavoproteins can function as hydrophobic sites for vitamin B(2) (riboflavin) or, in other structures, with cofactors for catalytic reactions such as glucose oxidation. In this contribution, we report direct observation of charge separation and recombination in two flavoproteins: riboflavin-binding protein and glucose oxidase. With femtosecond resolution, we observed the ultrafast electron transfer from tryptophan(s) to riboflavin in the riboflavin-binding protein, with two reaction times: approximately 100 fs (86% component) and 700 fs (14%). The charge recombination was observed to take place in 8 ps, as probed by the decay of the charge-separated state and the recovery of the ground state. The time scale for charge separation and recombination indicates the local structural tightness for the dynamics to occur that fast and with efficiency of more than 99%. In contrast, in glucose oxidase, electron transfer between flavin-adenine-dinucleotide and tryptophan(s)/tyrosine(s) takes much longer times, 1.8 ps (75%) and 10 ps (25%); the corresponding charge recombination occurs on two time scales, 30 ps and nanoseconds, and the efficiency is still more than 97%. The contrast in time scales for the two structurally different proteins (of the same family) correlates with the distinction in function: hydrophobic recognition of the vitamin in the former requires a tightly bound structure (ultrafast dynamics), and oxidation-reduction reactions in the latter prefer the formation of a charge-separated state that lives long enough for chemistry to occur efficiently. Finally, we also studied the influence on the dynamics of protein conformations at different ionic strengths and denaturant concentrations and observed the sharp collapse of the hydrophobic cleft and, in contrast, the gradual change of glucose oxidase.     

Biological charge transfer via flickering resonance

Biological electron-transfer (ET) reactions are typically described in the framework of coherent two-state electron tunneling or multistep hopping. However, these ET reactions may involve multiple redox cofactors in van der Waals contact with each other and with vibronic broadenings on the same scale as the energy gaps among the species. In this regime, fluctuations of the molecular structures and of the medium can produce transient energy level matching among multiple electronic states. This transient degeneracy, or flickering electronic resonance among states, is found to support coherent (ballistic) charge transfer. Importantly, ET rates arising from a flickering resonance (FR) mechanism will decay exponentially with distance because the probability of energy matching multiple states is multiplicative. The distance dependence of FR transport thus mimics the exponential decay that is usually associated with electron tunneling, although FR transport involves real carrier population on the bridge and is not a tunneling phenomenon. Likely candidates for FR transport are macromolecules with ET groups in van der Waals contact: DNA, bacterial nanowires, multiheme proteins, strongly coupled porphyrin arrays, and proteins with closely packed redox-active residues. The theory developed here is used to analyze DNA charge-transfer kinetics, and we find that charge-transfer distances up to three to four bases may be accounted for with this mechanism. Thus, the observed rapid (exponential) distance dependence of DNA ET rates over distances of ≲15 Å does not necessarily prove a tunneling mechanism.Chemical structure and, importantly, structural fluctuations determine the mechanism and kinetics of charge transfer. Redox energy fluctuations are of particular significance when transport barrier heights and the energy fluctuations are of similar magnitude. Indeed, the sensitivity of biological electron-transfer (ET) rates to conformational fluctuations and consequent (transient) delocalization is the topic of intense interest (1–3). Resonant enhancement of biological ET rates is consistent with a growing body of physical and structural data found in DNA ET through stacked nucleobases (4), extended delocalized structures of bacterial photosynthesis (including the special pair, bridging chlorophyll and pheophytin) (5), the polaronic states of oxidized porphyrin arrays up to seven porphyrin diameters in spatial extent (6), micrometer-scale bacterial nanowires (7, 8), multiheme oxidoreductases (9, 10), amino acid side chains in ribonucleotide reductase (11), engineered protein-based hopping-chains (12), and centimeter-scale charge-transport chains in filamentous bacteria (13). Here, we describe a transient or flickering resonance (FR) mechanism for ET. The FR mechanism arises when thermal fluctuations produce geometries that enable charge delocalization across the entire structure by bringing the donor (D), bridge (B), and acceptor (A) levels into energetic degeneracy. An electron or hole that is spatially localized at a starting D may move ballistically (i.e., with near constant velocity) through these fleeting structures to A. Because the probability of bringing multiple sites into energetic degeneracy is multiplicative and decays approximately exponentially with the number of sites (i.e., with distance), this transport mechanism could be mistaken for electron tunneling because of its distance dependence.     

Dynamics, transition states, and timing of bond formation in Diels-Alder reactions

The time-resolved mechanisms for eight Diels–Alder reactions have been studied by quasiclassical trajectories at 298 K, with energies and derivatives computed by UB3LYP/6-31G(d). Three of these reactions were also simulated at high temperature to compare with experimental results. The reaction trajectories require 50–150 fs on average to transverse the region near the saddle point where bonding changes occur. Even with symmetrical reactants, the trajectories invariably involve unequal bond formation in the transition state. Nevertheless, the time gap between formation of the two new bonds is shorter than a C─C vibrational period. At 298 K, most Diels–Alder reactions are concerted and stereospecific, but at high temperatures (approximately 1,000 K) a small fraction of trajectories lead to diradicals. The simulations illustrate and affirm the bottleneck property of the transition state and the close connection between dynamics and the conventional analysis based on saddle point structure.     

Determining complete electron flow in the cofactor photoreduction of oxidized photolyase

The flavin cofactor in photoenzyme photolyase and photoreceptor cryptochrome may exist in an oxidized state and should be converted into reduced state(s) for biological functions. Such redox changes can be efficiently achieved by photoinduced electron transfer (ET) through a series of aromatic residues in the enzyme. Here, we report our complete characterization of photoreduction dynamics of photolyase with femtosecond resolution. With various site-directed mutations, we identified all possible electron donors in the enzyme and determined their ET timescales. The excited cofactor behaves as an electron sink to draw electron flow from a series of encircling aromatic molecules in three distinct layers from the active site in the center to the protein surface. The dominant electron flow follows the conserved tryptophan triad in a hopping pathway across the layers with multiple tunneling steps. These ET dynamics occur ultrafast in less than 150 ps and are strongly coupled with local protein and solvent relaxations. The reverse electron flow from the flavin is slow and in the nanosecond range to ensure high reduction efficiency. With 12 experimentally determined elementary ET steps and 6 ET reaction pairs, the enzyme exhibits a distinct reduction–potential gradient along the same aromatic residues with favorable reorganization energies to drive a highly unidirectional electron flow toward the active-site center from the protein surface.     

Molecular dynamics simulations of cooling in laser-excited heme proteins.

In transient optical experiments the absorbed photon raises the vibrational temperature of the chromophore. In heme proteins at room temperature conversion of a 530-nm photon into vibrational energy is estimated to raise the temperature of the heme by 500-700 K. Cooling of the heme is expected to occur mainly by interacting with the surrounding protein. We report molecular dynamics simulations for myoglobin and cytochrome c in vacuo that predict that this cooling occurs on the ps time scale. The decay of the vibrational temperature is nonexponential with about 50% loss occurring in 1-4 ps and with the remainder in 20-40 ps. These results predict the presence of nonequilibrium vibrational populations that would introduce ambiguity into the interpretation of transient ps absorption and Raman spectra and influence the kinetics of sub-ns geminate recombination.