Protein–water electrostatics and principles of bioenergetics

Abstract

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.

Protein electron transfer: Dynamics and statistics

“…52 The consequences of this perspective for the performance of biology's energy chains are quite dramatic, as we discuss below, since the energy released in the form of heat in activationless electron transfer can be reduced by a factor of χ G . The ability of proteins to increase χ G is therefore directly related to their performance as energetically efficient enzymatic machines.…”

“…These mechanistic and energetic constraints, mostly dictated by the structural arrangement of the cofactors in the membrane and the amount of the redox energy provided by food, pose the question of how biology achieves its energy production goals and, in case of bacterial photosynthesis, does it with a high quantum yield of generating an across-membrane electron-hole pair per absorbed photon. 119 The new mechanistic properties of protein electron transfer, first revealed by simulations 43,52 and more recently supported by electro-elastic models of proteins, 28 provide the resolution of the paradox of energetic efficiency of biology. As discussed above, two components are important here, the breadth of electrostatic fluctuations produced by the proteinwater interface and the ability to dynamically freeze some of the nuclear degrees of freedom on the time-scale of the reaction.…”

“…This condition is typically satisfied for not too fast reactions in polar molecular solvents, but often becomes compromised for the protein-water solvent. 52 The protein-water thermal bath becomes nonergodic when the reaction rate exceeds one of the characteristic relaxation frequencies (peaks) in χ (ω). There is of course nothing specific to protein in this phenomenon, which is also realized for redox couples in solution.…”

“…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. 2) and λ var is used for the latter, the distinction between the two reorganization energies can be characterized by the parameter…”

“…40,[46][47][48][49][50] These, and possibly even longer, 28 electrostatic relaxation times create the possibility for breaking the ergodicity of the system and making some parts of the proteinwater phase space inaccessible on the time-scale of the reaction or on the time-scale of electron residence on a cofactor in a redox chain. 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.…”