One possibility to describe reactions in large systems is based on force fields which are suitably constructed to allow for bond breaking and bond foming processes. The advantage of such a methodology is the rapid evaluation of the total interaction potential and the forces required to propagate the system. One possible implementation and application is the study of ligand binding in Myoglobin. This study investigates the energetic requirements for ligand rebinding in MbNO . The next figure shows an overview of the solvated (stochastic boundaries) system.
A more detailed view of the active site is shown below.
After the N-Fe bond is broken the system evolves on the unbound (mostly repulsive) potential energy surface. During this time the NO molecule interacts with residues that form the primary binding pocket. Occasionaly, however, recrossing to the bound state is possible on energetic grounds. For this, the Fe atom has to return approximately to the position shown in the picture above. In its unbo und state the Fe atom has moved below the heme plane (through interaction with the distal histidine HSD93). To understand the rebinding dynamics the trajectories are segmented in an early (0 to 25ps) and a late (25ps to 50ps) interval and the occurrence of such possible recrossings are statistically analzed. It is found that for the early interval the distribution of recrossings is such that shortly after an attempted recrossing another recrossing can occur.
However, for the later interval the distribution is shifted to significantly longer times between successive recrossings. This finding can be understood by the internal energy redistribution within the protein. During the early parts of the trajectories sizeable amounts of internal energy are still stored within the heme unit while this energy redistributes then within the heme during the later parts. It takes some time (on the order of 10ps) until this energy "returns" to the relevant degrees of freedom for rebinding. This leads to the change in the distribution of rebinding times. Barriers arising from protein relaxation are in addition to any other barriers originating from electronic degrees of freedom. M. Meuwly, R. Stote, O. Becker, and M. Karplus, Biophysical Chemistry 98, 183, (2002)
Much experimental effort has been devoted to measuring the infrared spectrum of photodissociated carbon monoxyde from myoglobin on different time scales. These studies found different substates within the heme pockets. The free energy differences between the substates were also measured and related to different conformational states. However, a theoretical understanding e.g. on the basis of molecular dynamics simulations, was still lacking. The recently developed fluctuating point charge model for CO, based on fits of the atomic charges to accurate ab initio calculations of the dipole and quadrupole moment as a function of the CO separation, for the first time yielded the correct splitting in the infrared spectrum of photodissociated CO. The theoretically calculated splitting of 8 cm-1 compares quantitatively with the experimentally measured value of 10 cm-1.Also, the measured barrier for internal rotation of the CO molecule is correctly estimated to be 0.3 kcal/mol, compared with 0.29 kcal/mol from the experiment. Another important finding concerns recently measured infrared absorptions of photodissociated CO from a particular myoglobin mutant, L29F. Here, the Leucine at position 29 is mutated into Phenylalanine whereby a CH3 group is replaced by a more bulky aromatic ring. It was found that the spectrum of photodissociated CO is unsplit and that the CO molecule moves away from the primary binding site on a time scale of a few ten picoseconds. These results were also quantitatively reproduced using the new 3-point fluctuating charge model and by running mixed QM/MM MD simulations which treated the dissociated CO at the MP2/6-31G* level. D. R. Nutt and M. Meuwly, Biophysical Journal 85, 3612 (2003).