Ergodicity breaking of iron displacement in heme proteins

Conformational dynamics modulating electron transfer

Diffusional dynamics of the donor-acceptor distance are responsible for the appearance of a new time scale of diffusion over the distance of electronic tunneling in electron-transfer reactions. The distance dynamics compete with the medium polarization dynamics in the dynamics-controlled electron-transfer kinetics. The pre-exponential factor of the electron-transfer rate constant switches, at the crossover distance, between a distance-independent, dynamics-controlled plateau and exponential distance decay. The crossover between two regimes is controlled by an effective relaxation time slowed down by a factor exponentially depending on the variance of the donor-acceptor displacement. Flexible donor-acceptor complexes must show a greater tendency for dynamics-controlled electron transfer. Energy chains based on electron transport are best designed by placing the redox cofactors near the crossover distance.

Why are Vibrational Lines Narrow in Proteins?

The vibrational Stark effect in proteins yields line shifts indicative of strong internal electric fields up to a few volts per angstrom. These values are supported by numerical simulations of proteins. The simulations also show a significant breadth of field fluctuations translating to inhomogeneous broadening of vibrational lines. According to fluctuation-dissipation arguments, strong internal fields should lead to broad lines. Experimentally reported vibrational lines in proteins are, however, very narrow. This disconnect is explained here in terms of the insufficient (nonergodic) sampling of the protein's configurations on the lifetime of the vibrational probe. The slow component of the electric field fluctuations in proteins relaxes on the time scale of tens of nanoseconds and is dynamically frozen on the vibrational lifetime.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

Termination of Biological Function at Low Temperatures: Glass or Structural Transition?

Energy of life is produced by electron transfer in energy chains of respiration or photosynthesis. A small input of free energy available to biology puts significant restrictions on how much free energy can be lost in each electron-transfer reaction. We advocate the view that breaking ergodicity, leading to violation of the fluctuation-dissipation theorem (FDT), is how proteins achieve high reaction rates without sacrificing the reaction free energy. Here we show that a significant level of nonergodicity, represented by a large extent of the configurational temperature over the kinetic temperature, is maintained in the entire physiological range for the cytochrome c electron transfer protein. The protein returns to the state consistent with the FDT below the crossover temperature close to the temperature of the protein glass transition. This crossover leads to a sharp increase in the activation barrier of electron transfer and is displayed by a kink in the Arrhenius plot for the reaction rate constant.