Reorganization Energy of Electron Transfer in Viscous Solvents above the Glass Transition

Ghorai, Pradip Kr.; Matyushov, Dmitry V.

doi:10.1021/jp055235h

Cited by 17 publications

(26 citation statements)

References 64 publications

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“…The downward turnover of λ(T ) for the 1 ns observation window (upper curve in Figure 6b) marks the return of the system to equilibrium statistics with the negative slope of λ(T ) also seen in our previous simulations of a small solute in SPC/E water. 93 The opposite temperature dependence of the protein and water reorganization energies at long observation windows points to a distinctly different character of the corresponding nuclear modes. While water molecules alter the donor-acceptor energy gap mostly by librational/rotational motions typical of polar liquids, the protein nuclear modes are predominantly vibrational.…”

Section: Resultsmentioning

confidence: 99%

Energetics and Kinetics of Primary Charge Separation in Bacterial Photosynthesis

2008

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We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

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Section: Resultsmentioning

confidence: 99%

Energetics and Kinetics of Primary Charge Separation in Bacterial Photosynthesis

2008

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“…3). If this condition is violated, the low-frequency motions do not participate in fluctuations of the donoracceptor energy gap and the above equation for the thermodynamic reorganization energy needs to be replaced with a nonergodic (non-canonical) reorganization energy 51,54,84 depending on the rate constant k,…”

Section: 82mentioning

confidence: 99%

“…51,52 The resulting dynamical arrest of corresponding nuclear modes, an almost trivial and common phenomenon in glass science, 53 does not allow full statistical averages to develop on the limited time-scale of the reaction. 54 In terms of protein electron transfer occurring on the nanosecond time-scale, this picture implies that the distance, along the reaction coordinate, between the minima of the free energy surfaces cannot be characterized by the same nuclear reorganization parameter as the curvature at the free energy's bottom. 52 If λ St is used for the former (Fig.…”

Section: Introductionmentioning

confidence: 99%

Protein electron transfer: Dynamics and statistics

Matyushov

2013

The Journal of Chemical Physics

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A statistical-mechanical analysis on the hypermobile water around a large solute with high surface charge density J. Chem. Phys. 130, 014707 (2009) Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.

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“…15 The partial charges for this molecule, used in the calculations were tabulated in Ref. 99. The comparison with the NRFT method is somewhat complicated in this case by nonlinear solvation effects seen in the deviation of the half of the Stokes shift from the reorganization energy.…”

Section: Solvent Gibbs and Reorganization Free Energiesmentioning

confidence: 99%

Redox entropy of plastocyanin: Developing a microscopic view of mesoscopic polar solvation

LeBard

Matyushov

2008

The Journal of Chemical Physics

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A statistical-mechanical analysis on the hypermobile water around a large solute with high surface charge density A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tun-neling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of timescales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein. © 2013 AIP Publishing LLC. [http://dx.

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Reorganization Energy of Electron Transfer in Viscous Solvents above the Glass Transition

Cited by 17 publications

References 64 publications

Energetics and Kinetics of Primary Charge Separation in Bacterial Photosynthesis

Energetics and Kinetics of Primary Charge Separation in Bacterial Photosynthesis

Protein electron transfer: Dynamics and statistics

Redox entropy of plastocyanin: Developing a microscopic view of mesoscopic polar solvation

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