Theoretical determination of the standard reduction potentials of pheophytin-a in N,N-dimethyl formamide and membrane

Quantum mechanical/molecular mechanics (QM/MM) calculations were performed on the neutral, anionic, and dianionic forms of Pheophytin-a (Pheo-a) in N,N-dimethyl formamide (DMF) in order to calculate the absolute free energy of reduction of Pheo-a in solution. The geometry of the solvated species was optimized by restricted open-shell density functional treatment (ROB3LYP) using the 6-31G(d) basis set for the molecular species while the primary solvent shell consisting of 45 DMF molecules was treated by the MM method using the universal force field (UFF). Electronic energies of the neutral, anionic, and dianionic species were obtained by carrying out single point density functional theory (DFT) calculations using the 6-311+G(2d,2p) basis set on the respective ONIOM optimized geometries. The CHARMM27 force field was used to account for the dynamical nature of the primary solvation shell of 45 DMF molecules. In the calculations using solvent shells, the required atomic charges for each solvent molecule were obtained from ROB3LYP/6-31G(d) calculation on a single isolated DMF molecule. Randomly sampled configurations generated by the Monte Carlo (MC) technique were used to determine the contribution of the primary shell to the free energy of solvation of the three species. The dynamical nature of the primary shell significantly corrects the free energy of solvation. Frequency calculations at the ROB3LYP/6-31G(d) level were carried out on the optimized geometries of truncated 47-atom models of the neutral and ionic species in vacuum so as to determine the differences in thermal energy and molecular entropy. The Born energy of ion-dielectric interaction, the Onsager energy of dipole-dielectric interaction, and the Debye-Hückel energy of ion-ionic cloud interaction for the pheophytin-solvent aggregate were added as perturbative corrections. The Born interaction also makes a large contribution to the absolute free energy of reduction. An implicit solvation model (DPCM) was also employed for the calculation of standard reduction potentials in DMF. Both the models were successful in reproducing the standard reduction potentials. An explicit solvent treatment(QM/MM/MC + Born + Onsager + Debye corrections) yielded the one electron reduction potential of Pheo-a as -0.92 +/- 0.27 V and the two electron reduction potential as -1.34 +/- 0.25 V at 298.15 K, while the implicit solvent treatment yielded the corresponding values as -1.03 +/- 0.17 and -1.30 +/- 0.17 V, respectively. The calculated values more or less agree with the experimental midpoint potentials of -0.90 and -1.25 V, respectively. Moreover, a numerical finite difference Poisson-Boltzmann solver (FDPB) along with the DPCM methodology was employed to obtain the reduction potential of pheophytin in the thylakoid membrane. The calculated reduction potential value of -0.58 V is in excellent agreement with the reported value -0.61 V.