The study on the electron transfer between cytochrome c and single-walled carbon nanotube – The calculations of the reorganization free energy, the coupling matrix element and the rate constant

We have studied the electron transfer (ET) reaction between the cytochrome c (Cyt c) and the single-walled carbon nanotube (SWCNT). The ET reorganization energy, the ET coupling matrix element and the ET rate constant for Cyt c-SWCNT system have been calculated using QM + MM and the pathway tunneling model based on semi-classical Marcus theory. The reorganization energy is 0.9 ± 0.1 eV for polarized systems and 1.4 eV for nonpolarized system. The number of atoms along the ET pathway and the number of through-space jumps are the two key conformational factors determining the coupling matrix element. Although the conformation of Cyt c and the relative orientation of Cyt c to SWCNT have little influence on the reorganization energy, they make a significant influence on the coupling matrix element, resulting in the tremendously different ET rate constants by different orders of magnitudes. The reorganization of solvent molecules, the conformation of Cyt c and the relative orientation of Cyt c to SWCNT are the three key factors determining the ET rate constant. The inclusion of the explicit electronic polarizability of Cyt c and solvent in polarized force field decreases the outer-sphere reorganization energy by 38 %, and it makes little influence on the coupling matrix element. This results in the difference in the ET rate constants between polarized system and nonpolarized system by two orders of magnitude. Comparing the ET rate constant between Cyt c and SWCNT with that between Cyt c and Cyt c1 (the reductase of Cyt c), it predicts that SWCNT is able to compete with Cyt c1 to reduce Cyt c, thus make an influence on the ET of Cyt c and Cyt c1 if it is accumulated in cell for a long time, resulting in the interference on the metabolism of living cell.