Modulation of electron transfer kinetics by protein conformational fluctuations during early-stage photosynthesis

Explicit analytical form for memory kernel in the generalized Langevin equation for end-to-end vector of Rouse chains

The generalized Langevin equation (GLE) provides an attractive theoretical framework for investigating the dynamics of conformational fluctuations of polymeric systems. While the memory kernel is a central function in the GLE, explicit analytical forms for this function have been challenging to obtain, even for the simple models of polymer dynamics. Here, we achieve an explicit analytical expression for the memory kernel in the GLE for the end-to-end vector of Rouse chains in the overdamped limit. Our derivation takes advantage of the finding that the dynamics of the end-to-end vector of Rouse chains with both free ends are equivalent to those of Rouse chains with one free end and the other fixed. For the latter model, we first show that the equations of motion of the Rouse modes as well as their statistical properties can be obtained under the boundary conditions where the free end is held fixed temporarily. We then analytically solve the terms associated with intrachain interactions in the GLE. By formally comparing these terms with the GLE based on the Rouse modes, we obtain an explicit expression for the memory kernel, along with analytical forms for the potential field and the random colored noise force. Our analytical memory kernel is confirmed by numerical calculations in the Laplace space and is shown to yield asymptotic behaviors that are consistent with previous studies. Finally, we utilize our analytical result to simulate the cyclization dynamics of Rouse chains and discuss the scaling of the cyclization time with chain length.

Kinetics of Initial Charge Separation in the Photosynthetic Reaction Centers of Rhodobacter sphaeroides

A stochastic kinetic study of the initial electron transfer reaction in the reaction centers of wild-type and different mutants of photosynthetic bacterium Rhodobacter sphaeroides is suggested. The present approach to the disorder-driven complex kinetics skilfully offers an alternative to the earlier dynamic analyses. Exploiting a rational description of the reaction coordinate, effected by the relaxation of the surrounding protein environment, the measured kinetics were reproduced quantitatively. Notably, comparisons of the extracted relative free energies of electron transfer for the selected mutants and the available independent electrochemical estimates show exact agreement in some cases.

Fluctuating bottleneck model studies on kinetics of DNA escape from α-hemolysin nanopores

We have proposed a fluctuation bottleneck (FB) model to investigate the non-exponential kinetics of DNA escape from nanometer-scale pores. The basic idea is that the escape rate is proportional to the fluctuating cross-sectional area of DNA escape channel, the radius r of which undergoes a subdiffusion dynamics subjected to fractional Gaussian noise with power-law memory kernel. Such a FB model facilitates us to obtain the analytical result of the averaged survival probability as a function of time, which can be directly compared to experimental results. Particularly, we have applied our theory to address the escape kinetics of DNA through α-hemolysin nanopores. We find that our theoretical framework can reproduce the experimental results very well in the whole time range with quite reasonable estimation for the intrinsic parameters of the kinetics processes. We believe that FB model has caught some key features regarding the long time kinetics of DNA escape through a nanopore and it might provide a sound starting point to study much wider problems involving anomalous dynamics in confined fluctuating channels.

Subdiffusion in hair bundle dynamics: the role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. [Proc. Natl. Acad. Sci. U.S.A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link.

Fokker-Planck equation in a wedge domain: anomalous diffusion and survival probability

We obtain exact solutions and the survival probability for a Fokker-Planck equation subjected to the two-dimensional wedge domain. We consider a spatial dependence in the diffusion coefficient and the presence of external forces. The results show an anomalous spreading of the solution and, consequently, a nonusual behavior of the survival probability which can be connected to anomalous diffusion.

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.

Energetics and kinetics of primary charge separation in bacterial photosynthesis

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.