Monte Carlo simulation and thermodynamic integration applied to protein charge transfer.

We introduce a combination of Monte Carlo simulation and thermodynamic integration methods to address a model problem in free energy computations, electron transfer in proteins. The feasibility of this approach is tested using the ferredoxin protein from Clostridium acidurici. The results are compared to numerical solutions of the Poisson-Boltzmann equation and data from recent molecular dynamics simulations on charge transfer in a protein complex, the NrfHA nitrite reductase of Desulfovibrio vulgaris. Despite the conceptual and computational simplicity of the Monte Carlo approach, the data agree well with those obtained by other methods. A link to experiments is established via the cytochrome subunit of the bacterial photosynthetic reaction center of Rhodopseudomonas viridis.

Long-range electron-electron interaction and charge transfer in protein complexes: a numerical approach.

With application to the nitrite reductase hexameric protein complex of Desulfovibrio vulgaris, NrfH2A4, we suggest a strategy to compute the energy landscape of electron transfer in large systems of biochemical interest. For small complexes, the energy of all electronic configurations can be scanned completely on the level of a numerical solution of the Poisson-Boltzmann equation. In contrast, larger systems have to be treated using a pair approximation, which is verified here. Effective Coulomb interactions between neighbouring sites of excess electron localization may become as large as 200 meV, and they depend in a nontrivial manner on the intersite distance. We discuss the implications of strong Coulomb interactions on the thermodynamics and kinetics of charging and decharging a protein complex. Finally, we turn to the effect of embedding the system into a biomembrane.

Simulating biological charge transfer: Continuum dielectric theory or molecular dynamics?

We study the thermodynamic parameters of Marcus's theory of charge transfer, the driving forces and the reorganization energies, using two widely applied approaches to bioenergetic problems that seem to be radically different: continuum dielectric theory via a numerical solution of Poisson's equation, and the thermodynamic integration approach based upon classical Newtonian molecular dynamics, as perfomed by Na et al., PCCP 19, 18,938 (2017). With application to a nitrite reductase NrfHA protein heterodimer, we obtain an excellent agreement between the respective driving forces with an r.m.s. deviation of 1.7 kcal/mol, and a lower limit to the reorganization energies. The computational methods turn out to be mutually supportive: molecular dynamics can be used to determine the parameters of a dielectric theory computation, which on the other hand can be used to properly rescale the reorganization energies and partition them into aqueous and protein contributions. In addition, we use the electrostatic approach to study the influence of Ca2+ ions on the free energy landscape of charge transfer.

Charge transfer in strongly correlated systems: an exact diagonalization approach to model Hamiltonians.

We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

Artificial metalloenzymes for olefin metathesis based on the biotin-(strept)avidin technology.

Incorporation of a biotinylated Hoveyda-Grubbs catalyst within (strept)avidin affords artificial metalloenzymes for the ring-closing metathesis of N-tosyl diallylamine in aqueous solution. Optimization of the performance can be achieved either by chemical or genetic means.

Protein displacements under external forces: An atomistic Langevin dynamics approach.

We present a fully atomistic Langevin dynamics approach as a method to simulate biopolymers under external forces. In the harmonic regime, this approach permits the computation of the long-term dynamics using only the eigenvalues and eigenvectors of the Hessian matrix of second derivatives. We apply this scheme to identify polymorphs of model proteins by their mechanical response fingerprint, and we relate the averaged dynamics of proteins to their biological functionality, with the ion channel gramicidin A, a phosphorylase, and neuropeptide Y as examples. In an environment akin to dilute solutions, even small proteins show relaxation times up to 50 ns. Atomically resolved Langevin dynamics computations have been performed for the stretched gramicidin A ion channel.