A method is described for calculating the reaction rate in globular proteins ofactivated processes such as ligand binding or enzymatic catalysis. The method is based on the determination of the probability that the system is in the transition state and of the magnitude of the reactive flux for transition-state systems. An "umbrella sampling" simulation procedure is outlined for evaluating the transition-state probability. The reactive flux is obtained from an approach described previously for calculating the dynamics of transition-state trajectories. An application to the rotational isomerization of an aromatic ring in the bovine pancreatic trypsin inhibitor is presented. The results demonstrate the feasibility ofcalculating rate constants for reactions in proteins and point to the importance of solvent effects for reactions that occur near the protein surface.Many of the biological functions of globular proteins involve activated processes in which the motion from one stable or intermediate state to another is limited by the rate of activation to a transition state of relatively high energy. Processes of this kind include side-chain rotational isomerization (1-5), motion of small ligand molecules through steric bottlenecks within a protein (6, 7), and covalent bond rearrangements in enzymes (8,9). In these cases, the important energy changes during the transition are associated with displacements of atoms within a local region (4,5,7,10), while the remainder ofthe protein plays a role analogous to a solvent or a solid matrix in other condensedphase reactions (11)(12)(13)(14).An important goal in the theoretical study ofprotein dynamics is the characterization of such activated processes (15,16). This includes the calculation ofexperimentally accessible quantities, like rate constants and activation energies, and the determination of the space and time correlations of the atomic motions involved in the transitions. Some progress toward this goal has been achieved in studies of the rotation of the rings of aromatic side chains in globular proteins (4, 5, 10) for which NMR data are available (1-3).In the initial investigations, empirical energy functions ofthe molecular mechanics type were used to estimate the effective energy barriers for ring rotation in the pancreatic trypsin inhibitor (4,5,17). In these calculations, each ring was held fixed in several orientations while the remainder of the protein was allowed to relax somewhat by partial energy minimization. The residual barriers, which are much smaller than those calculated with a rigid protein matrix, are in general agreement with the experimental activation enthalpies. These studies showed that the observed barriers are primarily due to repulsive nonbonded interactions between the rings and neighboring atoms and that matrix relaxation plays an essential role in allowing the rotations to occur at observable rates. However, the static character of this approach does not allow study of the dynamical details of the transitions nor of the entropic con...

A Brownian dynamics model for the backbone chain of a macromolecule is developed as a system of linked rigid bodies so that constraints on valence angles and bond lengths are satisfied exactly. For comparison, a corresponding flexible model is developed in which bond lengths and valence angles are held nearly constant by strong harmonic potentials. Equilibrium properties and barrier crossing rates are examined theoretically and by computer simulation of both models, with differences arising due to the presence of constraints in the rigid case. A compensating potential based on the metric determinant of unconstrained coordinates in the rigid model is found to eliminate the effect of constraints. Barrier crossing rates in the transition state approximation are studied when a force fixed in space is applied to the end atoms of the three-bond chain. An exact transition state rate formula developed for this case predicts curved Arrhenius plots of barrier crossing rates; this result is confirmed by computer simulation.

No abstract

No abstract