Dynamical Theory of Activated Processes in Globular ProteinsScott H. Northrup, Michael R. Pear, Chyuan-Yih Lee, J. Andrew McCammon and Martin KarplusProceedings of the National Academy of Sciences of the USA, Vol. 79, No. 13, pp. 4035-4039 (1982) [PubMed 6955788]A method is described for calculating the reaction rate in globular proteins of activated 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 of calculating rate constants for reactions in proteins and point to the importance of solvent effects for reactions that occur near the protein surface.
Molecular Dynamics of Ferrocytochrome c: Anharmonicity of Atomic DisplacementsBoryeu Mao, Michael R. Pear, J.A. McCammon and S.H. NorthrupBiopolymers, Vol. 21, Issue 10, pp. 1979-1989 (1982) [PubMed 6293599]The atomic position distributions obtained from a 32-ps molecular-dynamics simulation of tuna ferrocytochrome c at 297 K are analyzed in terms of their second, third, and fourth moments. Non-Gaussian relations among these moments are found for the majority of atoms in the molecule, indicating anharmonicity in the effective potential functions for the atomic motions. Many atoms exhibit only slightly anharmonic mobility during the 32-ps period, but about half of the atoms exhibit sizeable anharmonicity. For a typical atom, the anharmonic effects are largest for motions in the direction along which the largest displacements occur. Two classes of significantly anharmonic atoms are apparent: those whose effective potentials are distorted toward a square-well shape and those whose effective potentials have secondary minima corresponding to conformational substates.
Hinge-bending in L-Arabinose-binding Protein: The "Venus's-Flytrap" ModelBoryeu Mao, Michael R. Pear, J. Andrew McCammon and Florante A. QuiochoJournal of Biological Chemistry, Vol. 257, Issue 3, pp. 1131-1133 (1982) [PubMed 7035444]Theoretical conformational energy calculations show that large changes in the width of the binding-site cleft in the L-arabinose-binding protein involve only modest changes in the protein internal energy. Solvation energy changes associated with such variations of the cleft width and with protein-ligand interactions are estimated to be significantly larger than the internal energy changes. These results indicate that the binding-site cleft is open in the unliganded protein and is induced to close upon ligation. This picture is consistent with experimental data on the structure and binding kinetics of the L- arabinose-binding protein and provides a physical framework for interpreting such data.
Surface Temperature Effects in Molecule-Surface CollisionsM. Berkowitz, D.J. Kouri and J.A. McCammonJournal of Physical Chemistry, Vol. 86, No. 14, pp. 2669-2671 (1982)
An approximate, analytic technique is outlined for estimating the effect of surface temperature on the probabilities of molecular quantum state transitions induced by molecule-surface collisions. Applications to vibrational and electronic transitions are made. The results for the vibrational case may be useful in the problem of isotope separation.
Rate Theory for Gated Diffusion-Influenced Ligand Binding to ProteinsScott H. Northrup, Fahimeh Zarrin and J. Andrew McCammonJournal of Physical Chemistry, Vol. 86, No. 13, pp. 2314-2321 (1982)
The rate of binding of ligands to proteins may be determined not only by the relative diffusion rate of species through the solvent medium but also by the accessibility of the binding site. Because of the inherent flexibility and internal motion of proteins, this accessibility may fluctuate on the time scale of reaction, thereby causing the intrinsic reactivity of the protein to be a time-dependent quantity. Here, we present a general formulation of the kinetics of such gated reactions. Approximate analytical expressions for the rate constant are obtained for important limiting cases. These compare favorably with exact numerically obtained values for the gated reaction rate constant over a wide range of system parameters.
Molecular Dynamics with Stochastic Boundary ConditionsMax Berkowitz and J. Andrew McCammonChemical Physics Letters, Vol. 90, Issue 3, pp. 215-217 (1982)
We present and illustrate a simple approach for carrying out molecular dynamics simulations subject to stochastic boundary conditions. Methods of this type are expected to be useful in the study of chemical reactions and other localized processes in dense media.
Macromolecular Conformational Energy Minimization: An Algorithm Varying Pseudodihedral AnglesStephen C. Harvey and J. Andrew McCammonComputers & Chemistry, Vol. 6, Issue 4, pp. 173-179 (1982)
The algorithms which have been traditionally used in the minimization of the conformational energies of macromolecules do not move groups of atoms collectively and thus ignore one of the obvious aspects of intramolecular motion. We present here an algorithm which is designed to do that and apply it to a test study on the hinge-bending motion in phenylalanine transfer RNA. Based on the observation that dihedral angles (torsions about bonds) are much more easily deformed than bond lengths or bond angles, it rotates groups of atoms in a manner that leaves bond lengths unchanged and makes minimal changes in bond angles. Each axis of rotation connects two atoms and is similar to a virtual bond, so we call the rotations pseudodihedrals. The algorithm is physically plausible, and it is efficient in the sense that when structures that have been refined by this method are subjected to more rigorous refinement by steepest descent minimization, lower final energies are obtained than when steepest descent is used alone and total computational time is reduced by about 40%.
Stochastically Gated Diffusion-Influenced ReactionsAttila Szabo, David Shoup, Scott H. Northrup and J. Andrew McCammonJournal of Chemical Physics, Vol. 77, Issue 9, pp. 4484-4493 (1982)
The theory of diffusion-influenced reactions is extended to cases where the reactivity of the species fluctuates in time (e.g., the accessibility of a binding site of a protein is modulated by a gate). The opening and closing of the gate is assumed to be a stationary Markov process i.e., it is described by the kinetic scheme (open) a ⇔ b (closed). When the reaction is described by suitable boundary conditions, by solving the appropriate reaction-diffusion equations, it is shown that the stochastically gated association rate constant (k_{SG}) is given by k_{SG}^{-1} = k_{∞}^{-1} + a^{-1}b(a+b)κ_{u}(a+b)^{-1}, where κ_{u} is the Laplace transform of the time-dependent rate constant of the ungated problem and k_{∞} is the corresponding steady-state rate constant. The limits when the relaxation time for gate fluctuations is larger or smaller than the characteristic time for diffusion are considered. The relation to previous work is discussed. The theory is applied to three models: (i) a gated sphere, (ii) a gated disk on an infinite plane (e.g., a channel in a membrane), and (iii) a gated localized axially symmetric reactive site on the surface of a spherical macromolecule.