Electron transfer (ET) in biological system such as redox proteins usually undergoes by incoherent electron-hopping mechanism described by Marcus theory. Within this theoretical framework the free energy surfaces of the initial and final states are parabolic and the free energy barrier for ET is fully determined by the driving force DG and the reorganization free energy l. The theory is valid as far as distribution of the vertical energy gap DE fluctuations is Gaussian and the phase space is sampled with Boltzmann distribution on the time scale of the ET process, meaning that the system must be ergodic.
However, it has been suggested in literature that heme-containing cytochrome c, due to its slow molecular motions and large anisotropy in polarizability of the its active site, operates in ergodicity-breaking regime violating the Marcus theory. This would lead to large imbalance between Stokes-shift reorganization free energy lst and variational reorganization free energy lvar related to thermal fluctuations of the vertical energy gap, and, as a result, to considerably lower free energy barrier for ET. Yet, by applying various sampling techniques involving high-level QM/MM calculations with the whole cytochrome active site treated by DFT with electrostatic embedding, we were not able to reproduce such behavior.
By detail analyses of extensive molecular dynamics (MD) trajectories and decomposition of reorganization free energy to its potential and electric-field contributions we show that due to the alignment of intrinsic electric-field vector to direction of the largest polarizability, the calculations are extremely sensitive to the field distribution. However, both lst and lvar converge to the same value in accord with the Marcus theory. Therefore, the free energy barrier lowering leading to fast ET kinetics observed experimentally is more-likely caused by electronic polarization of the environment, rather than ergodicity breaking.