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Rapid and directed electron transfer (ET) is essential for biological processes. While the rates of ET over 1-2 nm in proteins can largely be described by simplified nonadiabatic theory, it is not known how these processes scale to microscopic distances. We generated crystalline lattices of Small Tetraheme Cytochromes (STC) forming well-defined, three-dimensional networks of closely spaced redox centers that appear to be nearly ideal for multistep ET. Electrons were injected into specific locations in the STC crystals by direct photoreduction, and their redistribution was monitored by imaging. The results demonstrate ET over mesoscopic to microscopic (∼100 μm) distances through sequential hopping in a biologically based heme network. We estimate that a hypothetical "nanowire" composed of crystalline STC with a cross-section of about 100 cytochromes could support the anaerobic respiration of a

Reorganization energies for an intramolecular self-exchange electron-transfer reaction are calculated by quantum-classical molecular dynamics simulations in four solvents with varying polarity and at temperatures ranging from 250 to 350 K. The reorganization free energies for polar solvents decrease systematically with increasing temperature, indicating that they include substantial contributions from entropy changes. The variances of the energy gap between the reactant and product states have a major component that is relatively insensitive to temperature. Explanations are suggested for these observations, which appear to necessitate rethinking the free energy functions of a distributed coordinate that frequently are used in discussions of reaction dynamics.

The Marcus equation for the rate of an electron-transfer reaction can be generalized to cover larger electronic-interaction matrix elements, irregular free-energy surfaces, and coupling to multiple vibrational modes and to recognize the different effects of vibrational relaxations and pure dephasing. Almost all the information needed to calculate the rate constant can be obtained from a quantum-classical molecular dynamics simulation of the system in the reactant state. Because the final expression for the rate constant does not depend on the reorganization energy, it is insensitive to slow relaxations that follow the reaction.

Rate constants for photochemical charge separation and recombination in a zinc-porphyrin-benzoquinone cyclophane are calculated by an approach that was developed recently to include effects of vibrational dephasing and relaxation and to reduce the dependence on freely adjustable parameters. The theory is extended to treat the rate of vibrational relaxation individually for each vibrational sublevel of the initial charge-transfer product. Quantum-mechanical/molecular-mechanical simulations of the reactions in iso-octane, toluene, dichloromethane, and acetonitrile suggest that charge separation occurs at conical intersections in the two more polar solvents, but at avoided crossings in the nonpolar solvents. In agreement with experimental measurements, however, the calculated rate constants for charge separation are similar in polar and nonpolar solvents. Charge recombination to the ground state is found to have electronic coupling factors smaller than that of charge separation and to be affected more strongly by interactions with the solvent.

Rates of intramolecular electron transfer from a 1,1 -biphenylyl radical anion to six different acceptors on an androstane scaffold are examined with the aid of a theory that was developed recently to include effects of vibrational relaxations and dephasing. The electronic- interaction matrix element and other parameters needed for the theory are obtained by quantum- mechanical/molecular-mechanical simulations of the reactions in five solvents ranging from iso-octane to methyltetrahydrofuran. Intramolecular vibrational modes that are coupled to electron transfer are resolved in simulations in iso-octane and cyclohexane. The energies and coupling factors for these modes allow the theory to be extended to incorporate transitions to and from excited vibrational levels. The calculated rates of electron transfer agree well with experimental measurements from the literature, except for reactions in which excited electronic states of the products become important.

In the initial charge-separation reaction of photosynthetic bacterial reaction centers, a dimer of strongly interacting bacteriochlorophylls (P) transfers an electron to a third bacteriochlorophyll...

The rates of nonadiabatic electron-transfer reactions depend on four main factors: the probability of finding the system in a conformation in which the reactant and product states have the same energy, the electronic coupling that drives oscillations between the two diabatic states, the dephasing that damps these oscillations, and the vibrational or electronic relaxations that trap the product state by transferring energy to the surroundings. This paper develops a simple expression that combines these factors in a relatively realistic manner. Values for all the parameters in the expression can be obtained from microscopic quantum-mechanical/molecular-mechanical simulations. The theory is tested by calculations of the rates of electron transfer from excited indole rings to a variety of acceptors in peptides and indole-acrylamide compounds. For the systems that are studied, the theory gives considerably better agreement with experiment than expressions that do not consider the rates of vibrational relaxations and dephasing.

Quantum mechanical/molecular mechanical simulations are used to explore the temperature dependence of intramolecular electron-transfer rates in systems that represent both the “normal” and the “inverted” regions of the Marcus curve. The treatment uses an approach that includes effects of vibrational relaxations and dephasing and is largely free of adjustable parameters. Effects of temperature on the distribution of the energy gap between the reactant and product (P(xo)), the electronic-interaction matrix element, and the rates of dephasing and vibrational relaxations are considered. The simulations reproduce the measured rate constant and temperature dependence well for photochemical charge separation in a porphyrin–benzoquinone cyclophane and for a ground-state charge-shift reaction in a biphenylyl-androstane–naphthylyl radical. They overestimate the rate of the charge-shift reaction in a biphenylyl-androstane–benzoquinone adduct but are in accordance with the observation that this reaction is almost ind...

The 35-residue, C-terminal headpiece subdomain of the protein villin folds to a stable structure on a microsecond time scale and has served as a model system in numerous studies of protein folding. To obtain a convenient spectroscopic probe of the folding dynamics, Kubelka et al. introduced an ionized histidine residue at position 27, with the expectation that it would quench the fluorescence of tryptophan 23 in the folded protein by extracting an electron from the excited indole ring [Kubelka, J., et al. (2003) J. Mol. Biol. 329, 625-630]. Although the fluorescence yield decreased as anticipated when the protein folded, it was not clear that the side chains of the two residues were sufficiently close together for electron transfer to compete effectively with fluorescence. Here, hybrid classical-quantum mechanical molecular dynamics simulations are used to examine the rates of transfer of an electron from the excited tryptophan to various possible acceptors in the modified headpiece and a smaller fragment comprised of residues 21-27 (HP7). The dominant reaction is found to be transfer to the amide group on the carboxyl side of W23 (amide a24). This process is energetically favorable and has a large coupling factor in the folded protein at 280 K but becomes unfavorable as HP7 unfolds at higher temperatures. Changes in electrostatic interactions of the solvent and other parts of the protein with the indole ring and a24 contribute importantly to this change in energy.

An X-linked myopathy was recently associated with mutations in the four-and-a-half-LIM domains 1 (FHL1) gene. We identified a family with late onset, slowly progressive weakness of scapuloperoneal muscles in three brothers and their mother. A novel missense mutation in the LIM2 domain of FHL1 (W122C) co-segregated with disease in the family. The phenotype was less severe than that in other reported families. Muscle biopsy revealed myopathic changes with FHL1 inclusions that were ubiquitin- and desmin-positive. This mutation provides additional evidence for X-linked myopathy caused by a narrow spectrum of mutations in FHL1, mostly in the LIM2 domain. Molecular dynamics (MD) simulations of the newly identified mutation and five previously published missense mutations in the LIM2 domain revealed no major distortions of the protein structure or disruption of zinc binding. There were, however, increases in the nonpolar, solvent-accessible surface area in one or both of two clusters of residues, suggesting that the mutant proteins have a variably increased propensity to aggregate. Review of the literature shows a wide range of phenotypes associated with mutations in FHL1. However, recognizing the typical scapuloperoneal phenotype and X-linked inheritance pattern will help clinicians arrive at the correct diagnosis.

A widely held hypothesis regarding the thermostability ofthermophilic proteins states asserts that, at any giventemperature, thermophilic proteins are more rigid thantheir mesophilic counterparts. Many experimental andcomputational studies have addressed this question withconflicting results. Here, we compare two homologousenzymes, one mesophilic (Escherichia coli FMN-dependentnitroreductase; NTR) and one thermophilic (Thermusthermophilus NADH oxidase; NOX), by multiple molecu-lar dynamics simulations at temperatures from 5 to1008C. We find that the global rigidity/flexibility of thetwo proteins, assessed by a variety of metrics, is similaron the time scale of our simulations. However, the ther-mophilic enzyme retains its native conformation to amuch greater degree at high temperature than does themesophilic enzyme, both globally and within the activesite. The simulations identify the helix F–helix G ‘arm’as the region with the greatest difference in loss of nativecontacts between the two proteins with increasing temp-erature. In particular, a network of electrostatic inter-actions holds helix F to the body of the protein in thethermophilic protein, and this network is absent in themesophilic counterpart.Keywords: corresponding states/flavoproteins/moleculardynamics simulations/nitroreductase/thermophilic proteinsIntroductionProteins derived from thermophilic organisms are moreresistant to thermal denaturation than homologous proteinsfrom organisms adapted to moderate temperatures (meso-philes). The differences in stability, structure and amino acidcomposition between thermophilic and mesophilic proteinshave been the subject of intense research (reviewed in Vieilleand Zeikus, 2001). In general, thermophilic enzymes areoptimally active at high temperatures at which their hostorganisms thrive, and they are relatively inactive at tempera-tures where mesophilic enzyme activity is optimal. It hasbeen proposed that the low activity of thermophilic proteinsat ‘mesophilic’ temperatures is due to their greater confor-mational rigidity at low temperatures relative to mesophilicproteins (Vihinen, 1987;Zavodsky et al., 1998).An early articulation of this idea, known as the ‘corre-sponding states hypothesis’, comes from Vihinen (1987):‘Flexibilities of proteins performing the same catalyticactivity seem to be about the same at their temperatureoptima, but the more rigid thermostable proteins reach theflexibility of the thermolabile proteins at higher tempera-tures’. Vihinen reached this conclusion based on the com-parison of normalized B-factors from a small number ofcrystal structures of proteins for which thermostability datawere also available. Although the validity of his analysismay be called into question, given the sensitivity ofB-factors to the details of the refinement process and tocrystal contacts, the underlying hypothesis has spawnednumerous studies of homologous mesophilic and thermophi-lic proteins.The results of both experimental and computationalstudies of matched mesophilic and thermophilic protein pairshave been mixed. For instance, Fourier-transform infraredspectroscopic (FTIR) hydrogen–deuterium exchange exper-iments on thermophilic and mesophilic isopropylmalatedehydrogenases (Zavodsky et al., 1998) and glyceraldehyde-3-phosphate dehydrogenases (Wrba et al., 1990) showed thatamide hydrogen exchange was less extensive in the thermo-philic protein than in the mesophilic protein at 258C, but thisdifference was greatly reduced when the measurements weremade at the respective optimal activity temperatures of thetwo enzymes. In contrast, a hyperthermophilic zinc-containing rubredoxin (from Pyrococcus furiosus) was foundto have hydrogen exchange rates similar to those of manymesophilic proteins (Hernandez et al., 2000). Neutron scat-tering experiments with live whole cells between 5 and 378C(Tehei et al., 2004) suggest that the overall population ofmacromolecules (predominantly proteins) from hyperthermo-philes and thermophiles have slightly lower mean-squarefluctuations on the 0.1 ns time scale than those from meso-philes. However, neutron scattering studies on dihydrofolatereductase found that the thermophilic protein had higheratomic mean-square fluctuations than the mesophilic homol-ogue (Meinhold et al., 2008). Nuclear magnetic resonance(NMR) spectroscopy studies on the ribonuclease H fromEscherichia coli and Thermus thermophilus indicated localdifferences in dynamics that may be related to thermal stab-ility and/or catalysis, but no global differences. In contrast,Kern and coworkers (Wolf-Watz et al., 2004) used NMR tocharacterize a lid closing/opening conformational change inadenylate kinase from E.coli and the hyperthermophileAquifex aeolicus. This hyperthermophilic enzyme is 9-foldless active than the mesophilic form at 208C. Each protein’slid-opening rate was found to be equal to its k

We use a multidimensional density-matrix model to explore the temperature dependence of electron transfer from the excited singlet state of the primary electron donor (P*) to the neighboring bacteriochlorophyll (B A ) in photosynthetic bacterial reaction centers. This reaction, which has the unusual property of increasing in rate with decreasing temperature, occurs too rapidly to be treated reliably by approaches that assume thermal equilibration of the vibrational levels of the reactant electronic state. In the density-matrix treatment, the frequencies and displacements of the vibrational modes that are coupled to electron transfer, and the microscopic time constants for transitions between different vibrational states, are obtained from molecular-dynamics simulations by the dispersed-polaron (spin-boson) approach. The electron-transfer dynamics are simulated by integrating the stochastic Liouville equation following excitation of the system with a short pulse of light. In this model, the increase in the rate with decreasing temperature depends strongly on the fact that electron transfer occurs more rapidly than vibrational thermalization. The high rate of electron transfer also affects the dependence of the kinetics on the energy difference between the reactant and product electronic states (ΔE°), making the optimal value of -AE° smaller than the reorganization energy. This interesting effect can be rationalized qualitatively in simple semiclassical and quantum mechanical models.

The dispersed-polaron (spin-boson) model is reviewed briefly and then used to develop a density-matrix model for studies of electron transfer in condensed phases. The frequencies and Franck–Condon factors for solvent vibrational modes that are coupled to electron transfer are obtained from molecular dynamics (MD) simulations by the dispersed-polaron treatment. Microscopic rate constants for vibrational relaxations, dephasing and coherence transfer between the solvent modes are obtained by fitting the time dependence of the solvent coordinates in the density-matrix treatment to the corresponding time dependence obtained from molecular-dynamics simulations with a classical linear-response approximation. This is done by adjusting a single parameter, the time constant for thermal equilibration of the two lowest levels of a solvent mode (T10). The model thus focuses on the coupling between solvent modes, rather than on the more widely studied coupling of solute modes by the thermal bath. The resulting density-matrix model is used to examine vibronic coupling in the initial electron-transfer step in photosynthetic bacterial reaction centers. Values of T10 in the range of 1–2 ps are consistent with molecular-dynamics simulations of the time-dependent energy gap between the reactant and product states (P* and P+B−), and also with the damping of coherent vibrational motions that are seen experimentally after excitation of reaction centers with a short pulse of light. In both the density-matrix model and the MD simulations, the autocorrelation function of the energy gap also has a decay component with a time constant of about 50 fs, which we ascribe to the group dephasing of oscillatory motions at many different frequencies. This component is insensitive to vibrational relaxations and is largely irrelevant to the electron-transfer dynamics. Using values of T10 in the range of 1–2 ps, a model with five vibrational modes reproduces the main features of electron transfer from P* to B, including stepwise formation of the product during the period when the system retains vibrational coherences. Although the rate does not depend strongly on whether P* is prepared coherently or incoherently, speeding up vibrational relaxations decreases the rate. At least part of the adverse effect of rapid relaxations can be viewed as a manifestation of the quantum Zeno paradox, which arises when off-diagonal elements of the density matrix decay very rapidly.

Effects of ionizable amino acids on spectroscopic properties and electron-transfer kinetics in the photosynthetic reaction center (RC) of Rhodobacter sphaeroides are investigated by site-directed mutations designed to alter the electrostatic environment of the bacteriochlorophyll dimer that serves as the photochemical electron donor (P). Arginine residues at homologous positions in the L and M subunits (L135 and M164) are changed independently: Arg L135 is replaced by Lys, Leu, Glu, and Gln and Arg M164 by Leu and Glu. Asp L155 also is mutated to Asn, Tyr L164 to Phe, and Cys L247 to Lys and Asp. The mutations at L155, L164, and M164 have little effect on the absorption spectrum, whereas those at L135 and L247 shift the long-wavelength absorption band of P to higher energies. Fits to the ground-state absorption and hole-burned spectra indicate that the blue shift and increased width of the absorption band in the L135 mutants are due partly to changes in the distribution of energies for the zero-phonon absorption line and partly to stronger electron-phonon coupling. The initial electron-transfer kinetics are not changed significantly in most of the mutants, but the time constant increases from 3.0 +/- 0.2 in wild-type RCs to 4.7 +/- 0.2 in C(L247)D and 7.0 +/- 0.3 ps in C(L247)K. The effects of the mutations on the solvation free energies of the product of the initial electron-transfer reaction (P(+)) and the charge-transfer states that contribute to the absorption spectrum ( and ) were calculated by using a distance-dependent electrostatic screening factor. The results are qualitatively in accord with the view that electrostatic interactions of the bacteriochlorophylls with ionized residues of the protein are strongly screened and make only minor contributions to the energetics and dynamics of charge separation. However, the slowing of electron transfer in the Cys L247 mutants and the blue shift of the spectrum in some of the Arg L135 and Cys L247 mutants cannot be explained consistently by electrostatic interactions of the mutated residues with P and B(L); we ascribe these effects tentatively to structural changes caused by the mutations.

The discovery by Louis N. M. Duysens in the 1950s that illumination of photosynthetic purple bacteria can cause oxidation of either a bacteriochlorophyll complex (P) or a cytochrome was followed by an extended period of uncertainty as to which of these processes was the `primary' photochemical reaction. Similar questions arose later about the roles of bacteriopheophytin (BPh) and quinones as the initial electron acceptor. This is a personal account of kinetic measurements that showed that electron transfer from P to BPh occurs in the initial step, and that the oxidized bacteriochlorophyll complex (P+) then oxidizes the cytochrome while the reduced BPh transfers an electron to a quinone.

This chapter considers various types of light scattering, including Rayleigh scattering, Stokes and anti-Stokes Raman scattering, resonance Raman scattering, surface-enhanced Raman scattering, coherent (stimulated) Raman scattering, and dynamic light scattering (photon correlation spectroscopy). We also consider the closely related phenomenon of multi-photon absorption. We derive and discuss the Kramers-Heisenberg-Dirac expression, and relate light scattering to the quantum theory of electronic polarizability. We also show how Raman scattering by complex systems can be described using the wavepacket picture developed in Chap. 11.

In this chapter we discuss the basic principles of quantum mechanics that underlie optical spectroscopy. We consider wavefunctions, operators and expectation values, atomic and molecular orbitals, harmonic and Morse oscillators, spin wavefunctions for singlet and triplet states, time-dependent perturbation theory, and the dynamics of transitions between states.

This chapter launches a more advanced discussion of the dynamics of systems comprised of many molecules with multiple quantum states and complex intermolecular interactions. We introduce the density matrix of an ensemble and show how the stochastic Liouville equation and the Redfield relaxation matrix describe its time dependence, and we examine mechanisms and effects of dephasing by static inhomogeneity and dynamic interactions with the surroundings. We relate these notions to the rates of absorption and stimulated emission during continuous illumination, and show how they can account for the remarkable “quantum Zeno” effect. We consider several different spectral-density functions and increasingly general relaxation functions, and discuss how these affect absorption and emission lineshapes. As a final illustration of effects of electronic coherence, we consider the anomalous fluorescence anisotropy of systems with several excited states.

In this chapter, we address transfer of energy between chromophores. We develop expressions for dipole-dipole interactions, beginning with the Forster theory and the point-dipole approximation and progressing to transition-monopole treatments. We also treat exchange coupling. We discuss the use of energy transfer to study conformational changes and fast processes in single protein molecules, and we describe energy transfer to and from carotenoids in photosynthesis.

A compact apparatus for femtosecond pump–probe experiments is described. The apparatus is based on a cavity-dumped titanium:sapphire laser. Probe pulses are generated by focusing weak (∼1 nJ) pulses into a microstructure fiber that produces broadband continuum pulses with high efficiency. With the pump pulses compressed and probe pulses uncompressed, the rise time of the pump–probe signals is

The photosynthetic reaction center (RC) is an integral membrane protein that carries out the initial charge-separation reactions of photosynthesis. Upon light excitation, a pair (P) of bacteriochlorophylls (Bchls) donates an electron to a bacteriopheophytin (HL), generating an ion-pair state (P+HL-). Previous ENDOR studies of RCs from the purple bacterium Rhodobacter sphaeroides have shown that the unpaired electron of P+ is distributed unequally between the two Bchls of P, with about 2/3 of the unpaired spin and positive charge residing on the Bchl bound to subunit L (PL) and 1/3 on the Bchl bound to M (PM). To investigate the protein's role in establishing the energies of the cations PL+ and PM+ through long-range electrostatic interactions, we mutated Arg L135 and Arg M164 individually to Leu or Glu and measured the effects on the Special TRIPLE and FTIR spectra of P+. These highly conserved residues occupy homologous positions on either side of P but have no hydrogen bonds or steric interactions with ...

1. Introduction 5632. Obtaining rate constants from molecular-dynamics simulations 5642.1 General relationships between quantum electronic structures and reaction rates 5642.2 The transition-state theory (TST) 5692.3 The transmission coefficient 5723. Simulating biological electron-transfer reactions 5753.1 Semi-classical surface-hopping and the Marcus equation 5753.2 Treating quantum mechanical nuclear tunneling by the dispersed-polaron/spin-boson method 5803.3 Density-matrix treatments 5833.4 Charge separation in photosynthetic bacterial reaction centers 5844. Light-induced photoisomerizations in rhodopsin and bacteriorhodopsin 5965. Energetics and dynamics of enzyme reactions 6145.1 The empirical-valence-bond treatment and free-energy perturbation methods 6145.2 Activation energies are decreased in enzymes relative to solution, often by electrostatic effects that stabilize the transition state 6205.3 Entropic effects in enzyme catalysis 6275.4 What is meant by dynamical contributions to catalysis? 6345.5 Transmission coefficients are similar for corresponding reactions in enzymes and water 6365.6 Non-equilibrium solvation effects contribute to catalysis mainly through Δg[Dagger], not the transmission coefficient 6415.7 Vibrationally assisted nuclear tunneling in enzyme catalysis 6485.8 Diffusive processes in enzyme reactions and transmembrane channels 6516. Concluding remarks 6587. Acknowledgements 6588. References 658Obtaining a detailed understanding of the dynamics of a biochemical reaction is a formidable challenge. Indeed, it might appear at first sight that reactions in proteins are too complex to analyze microscopically. At room temperature, even a relatively small protein can have as many as 1034 accessible conformational states (Dill, 1985). In many cases, however, we have detailed structural information about the active site of an enzyme, whereas such information is missing for corresponding chemical systems in solution. The atomic coordinates of the chromophore in bacteriorhodopsin, for example, are known to a resolution of 1–2 Å. In addition, experimental studies of biological processes such as photoisomerization and electron transfer have provided a wealth of detailed information that eventually may make some of these processes classical problems in chemical physics as well as biology.

Infrared absorption (IR), Raman, and resonance Raman spectra have been obtained from 500 to 1700 cm −1 for 4-hydroxybenzylidene-2,3-dimethyl-imidazolinone (HBDI), an analog of the green-fluorescent protein (GFP) chromophore. Numerous transitions are evident in both the IR and Raman spectra, with the resonance Raman spectrum of HBDI dominated by a subset of transitions in the 1430–1700 cm −1 region. Assignment of the transitions in this frequency region to the corresponding normal coordinates is accomplished through computational studies employing density functional and Hartree–Fock theory. The computational results indicate that the vibrational transitions in this frequency range are dominated by in-plane stretching modes that are localized to the imidazolinone or tyrosine portions of the chromophore, rather than being delocalized over the entire chromophore. No evidence is obtained for significant excited-state structural evolution along the O–H stretching coordinate. The implications of these findings with respect to the excited-state proton transfer dynamics of GFP are discussed.