Theory of Protein Charge Transfer: Electron Transfer between Tryptophan Residue and Active Site of Azurin

Abstract

One reaction step in the conductivity relay of azurin, electron transfer between the Cu-based active site and the tryptophan residue, is studied theoretically and by classical molecular dynamics simulations. Oxidation of tryptophan results in electrowetting of this residue. This structural change makes the free energy surfaces of electron transfer nonparabolic as described by the Qmodel of electron transfer. We analyze the medium dynamical effect on protein electron transfer produced by coupled Stokes-shift dynamics and the dynamics of the donor−acceptor distance modulating electron tunneling. The equilibrium donor−acceptor distance falls in the plateau region of the rate constant, where it is determined by the protein−water dynamics, and the probability of electron tunneling does not affect the rate. The crossover distance found here puts most intraprotein electron-transfer reactions under the umbrella of dynamical control. The crossover between the medium-controlled and tunneling-controlled kinetics is combined with the effect of the protein−water medium on the activation barrier to formulate principles of tunability of protein-based charge-transfer chains. The main principle in optimizing the activation barrier is the departure from the Gaussian-Gibbsian statistics of fluctuations promoting activated transitions. This is achieved either by incomplete (nonergodic) sampling, breaking the link between the Stokes-shift and variance reorganization energies, or through wetting-induced structural changes of the enzyme's active site.

Effect of Water Deuteration on Protein Electron Transfer

“…The activation barrier entering the Boltzmann factor in the rate constant in eq is the main focus of Marcus theory of electron transfer. , It is commonly determined through the crossing point of two Marcus parabolas F i ( X ), i = 1, 2, given as functions of the energy-gap reaction coordinate. , However, electron transfer between azurin’s active site and Trp creates different wetting patterns in two electron-transfer states, resulting in nonparabolic free-energy surfaces discussed next.…”

“…The lower portions of the curves are simulation points produced directly from MD. The upper parts of the free-energy surfaces are obtained by shifting the lower sets of points according to the linear relation between the free-energy surfaces ,, F 2 ( X ) = F 1 ( X ) + X required when Gibbsian ensemble statistics hold. , …”

“…Here and elsewhere 34 we use MD simulations to study the activation parameters of transferring a hole from Trp + cation radical to Cu I active site of azurin: 35…”

“…MD simulations were set up as described elsewhere 34 and in the Supporting Information (SI). Briefly, azurin protein in two electron-transfer states was solvated with 36469 TIP3P/ TIP3P-HW (Table 1) water molecules, and the production simulations of 300 ns were done in the NVT ensemble.…”

“…8,9 It is commonly determined through the crossing point of two Marcus parabolas F i (X), i = 1, 2, given as functions of the energy-gap reaction coordinate. 42,46 However, electron transfer between azurin's active site and Trp creates different wetting patterns 34 produce different results (Table 2). The reorganization energy of electron transfer is best defined through the variance of the reaction coordinate in the corresponding state:…”