Protein electron transfer: Dynamics and statistics

Abstract

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.

Communication: Microsecond dynamics of the protein and water affect electron transfer in a bacterial bc1 complex

“…A significant mechanistic question relevant to protein electron transfer is what are the interaction mechanisms influencing the breadth of the fluctuations (statistics) and what are the relevant time-scales (dynamics). [4][5][6] Both questions are essential for the modeling of the electron-transfer rates. Clearly, the amplitude of the fluctuations affects the reaction activation barrier.…”

“…The connection between the first and second moments is lost and two reorganization energies, λ St and λ, are required. 6 One still has the condition of crossing of two parabolas in Eq. (1) at X = 0, which results in the relation ⟨X⟩ i = κ G ∆F 0 ± λ, where the same convention as above applies to the ± sign and κ G = λ/λ St .…”

High-resolution electrochemical STM of redox metalloproteins

“…The local structure of water molecules at interfaces is, for example, well known to be partly ordered. Recently, Matyushov et al [47][48][49][50] have explored how experimentally rather smaller reorganisation energies than expected from atomistic simulations might be explained, examining the case [47] of cytochrome c. They extend the Marcus/Gerischer model to distinguish between two types of reorganisation energy representing medium polarisation and (a typically large) thermal fluctuation contribution, the latter being linked to a heterogeneous region surrounding the protein cofactor. The arguments are interesting and would perhaps apply a fortiori to the local geometry of the EC-STM set up.…”

Progress and challenges in simulating and understanding electron transfer in proteins

“…The superscript St refers to the fact that this reorganization energy equals half the Stokes shift DX [46,47]. Finally one can define the reorganization energy k r as the work to bring the system to the equilibrium geometry of the final state.…”

“…In charge migration over multiple fragments such freezing of nuclear modes can lead to non-equilibrium effects as seen for example in the case of DNA photolyase by direct FB-DFTB/MD simulations [41]. Matyushov and co-workers developed a consistent set of tools and concepts to comprehend ET in non-ergodic biological systems [47,115,119]. Looking again at their study of the photoreactive center (see previous sub-section), they showed that the reorganization energy calculated from the width of the energy gap fluctuations largely exceeded that calculated by the Stoke shift (k var ) k St ), enabling the ET process to take place in a near activation-less manner.…”