Nanosecond-Regime Correlation Time Scales for Equilibrium Protein Structural Fluctuations of Metal-Free Cytochrome c from Picosecond Time-Resolved Fluorescence Spectroscopy and the Dynamic Stokes Shift

Protein electron transfer: Dynamics and statistics

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.

Dynamic solvation and coupling of the hydration shell of Zn(II)-substituted cytochrome c in the presence of guanidinium ions

The fluorescence Stokes shift (FSS) response of Zn(II)-substituted cytochrome c (ZnCytc) is transformed from a monotonic red-shifting response in water to a bidirectional response with much slower time constants in the presence of low concentrations of guanidinium (Gdm(+)) ions. The FSS response in water observed over the 100 ps to 10 ns range has two exponential components with time constants of 135 ps and 1.6 ns that account for a total shift of 30 cm(-1), about one-half of the solvation reorganization energy. In contrast, in the presence of only 0.25 M Gdm(+), the FSS response initially shifts 21 cm(-1) to the blue with a 820 ps time constant and then shifts 60 cm(-1) back to the red with a 3.5 ns time constant. The effect of Gdm(+) on the FSS response effectively saturates at 1.0 M, well below the 1.75 M midpoint of the two-state unfolding transition. These results establish that the FSS response in ZnCytc includes a significant contribution from the surrounding hydration shell, which assumes a perturbed hydrogen-bonding network owing to the binding of Gdm(+) ions to the protein surface. The blue-shifting part of the FSS response arises from a light-induced conformational change that expands the protein- and solvent-derived cavity around the excited-state Zn(II) porphyrin. This non-polar part of the solvation response is enhanced in the presence of Gdm(+) because the protein/solvent surroundings of the Zn(II) porphyrin are effectively more flexible than in water. The enhanced flexibility in the presence of Gdm(+) increases the amplitudes and accordingly lengthens the correlation time scales for the protein and hydration-shell fluctuations that contribute to the FSS response.

Non-Gaussian statistics and nanosecond dynamics of electrostatic fluctuations affecting optical transitions in proteins

We show that electrostatic fluctuations of the protein-water interface are globally non-Gaussian. The electrostatic component of the optical transition energy (energy gap) in a hydrated green fluorescent protein is studied here by classical molecular dynamics simulations. The distribution of the energy gap displays a high excess in the breadth of electrostatic fluctuations over the prediction of the Gaussian statistics. The energy gap dynamics include a nanosecond component. When simulations are repeated with frozen protein motions, the statistics shifts to the expectations of linear response and the slow dynamics disappear. We therefore suggest that both the non-Gaussian statistics and the nanosecond dynamics originate largely from global, low-frequency motions of the protein coupled to the interfacial water. The non-Gaussian statistics can be experimentally verified from the temperature dependence of the first two spectral moments measured at constant-volume conditions. Simulations at different temperatures are consistent with other indicators of the non-Gaussian statistics. In particular, the high-temperature part of the energy gap variance (second spectral moment) scales linearly with temperature and extrapolates to zero at a temperature characteristic of the protein glass transition. This result, violating the classical limit of the fluctuation-dissipation theorem, leads to a non-Boltzmann statistics of the energy gap and corresponding non-Arrhenius kinetics of radiationless electronic transitions, empirically described by the Vogel-Fulcher-Tammann law.

Dissipative electro-elastic network model of protein electrostatics

We propose a dissipative electro-elastic network model to describe the dynamics and statistics of electrostatic fluctuations at active sites of proteins. The model combines the harmonic network of residue beads with overdamped dynamics of the normal modes of the network characterized by two friction coefficients. The electrostatic component is introduced to the model through atomic charges of the protein force field. The overall effect of the electrostatic fluctuations of the network is recorded through the frequency-dependent response functions of the electrostatic potential and electric field at the protein active site. We also consider the dynamics of displacements of individual residues in the network and the dynamics of distances between pairs of residues. The model is tested against loss spectra of residue displacements and the electrostatic potential and electric field at the heme's iron from all-atom molecular dynamics simulations of three hydrated globular proteins.