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The Internal Dynamics of Globular Proteins.
Martin Karplus, J. Andrew McCammon and Warner L. Peticolas
Although many globular proteins have a well-defined equilibrium geometry in the native state, their flexibility and structural fluctuations play an important role in their activity. Examination of the X-ray structures reveals that transient packing defects must occur in myoglobin and hemoglobin to allow oxygen penetration to the heme binding sites. Functional interactions of flexible ligands with their binding sites often require conformational adjustments in both the ligands and the binding proteins; the ligands involved include drugs, hormones, and enzyme substrates. The conformational adjustments in the binding proteins are known to be important in regulating the activity of many of these molecules through induced fit and allosteric effects. The chemical transformations of substrates by enzymes typically involve significant atomic displacements in the enzyme-substrate complexes; the mechanisms and rates of such transformations are sensitive to the dynamical properties of these complexes since, for example, the differences in the vibrational properties of the initial and the transition states affect the activation free energies and catalytic rates. Electron transfer processes may depend strongly on vibronic coupling and on fluctuations which alter the distance between the donor and acceptor. The relative motion of distinct structural domains is important in the activities of myosin, other enzymes, and antibody molecules, as well as in the assembly of supramolecular structures such as viruses.
Molecular Dynamics of Ferrocytochrome c: Fluctuation Anisotropy.
S.H. Northrup, M.R. Pear, J.D. Morgan and J.A. McCammon
In "Protein Dynamics and Energy Transduction," S. Ishiwata, Ed., Taniguchi Foundation Press, Japan, pp. 134-162 (1981)
Correlated Helix-Coil Transitions in Polypeptides.
Michael R. Pear, Scott H. Northrup, J. Andrew McCammon, Martin Karplus and Ronald M. Levy
In past discussions of the growth or decay of a polypeptide α-helix in solution; it has usually been assumed that successive residue transitions occur independently at the helix-coil interface. Helix growth or decay has thus been viewed as a Markov process in that the probability that a transition will occur has been assumed not to depend on the elapsed time from the preceding transition. We have been studying helix-coil transitions by computer simulation of the diffusional motions of a model polypeptide and have found that many of the transitions that occur in the simulations are correlated; e.g., the unwinding of a residue is simultaneous with or closely followed by the unwinding of the next residue in the helix. In this note, we consider the nature of correlated helix-coil transitions that occur at the end of a polypeptide chain.
Increase of carbon-13 NMR Relaxation Times in Proteins due to Picosecond Motional Averaging.
Ronald M. Levy, Martin Karplus and J. Andrew McCammon
The nature of atomic motions in the interior of proteins is currently a topic of great interest.
Pressure Dependence of Aromatic Ring Rotations in Proteins: A Collisional Interpretation.
Martin Karplus and J. Andrew McCammon
Activated processes are of central importance to many biochemical phenomena, including ligand binding and enzyme catalysis. A simple model for such processes, provided by the rotation ('flipping') of aromatic amino acid sidechains in the interior of globular protein has been studied intensively by experimental and theoretical techniques. Energy minimization and activated trajectory calculations have demonstrated that the nature of the rotational transition and its effective barrier are determined by the positions and fluctuations of the protein matrix atoms surrounding the aromatic ring. The importance of frictional effects for the ring motion and for other processes involving fluctuations in the protein interior has been pointed out.
Repulsive Interactions Between Polar and Apolar Atoms in Globular Proteins.
Boryeu Mao, Michael R. Pear, J. Andrew McCammon and Scott H. Northrup
A significant number of tetrahedral carbon-backbone nitrogen pairs in ferrocytochrome c have interatomic distances that are more than 0.4 Â shorter than the sum of the atomic van der Waals' radii. The non-bonded repulsions of these pairs destabilize the native structure by as much as 50 to 60 kcal/mol. A detailed examination of the close contacts suggests that these result from packing forces associated with the formation of secondary and tertiary structure in the protein.
Hydrodynamic Interaction Effects on Local Motions of Chain Molecules.
M.R. Pear and J.A. McCammon
The librational motions of a butane molecule in water are simulated by Brownian dynamics with and without inclusion of hydrodynamic interactions. Inclusion of the hydrodynamic interactions is found to increase the torsional correlation times by 35% to 46%, depending on the isomeric state of the butane molecule, and to decrease the rate constants for gauche-trans isomerization by about 28%. A critical discussion of the approximations involved in such simulations is presented.
Molecular Dynamics of Ferrocytochrome c: Magnitude and Anisotropy of Atomic Displacements.
Scott H. Northrup, Michael R. Pear, John D. Morgan, J. Andrew McCammon and Martin Karplus
Two computer simulations of the atomic motion in tuna ferrocytochrome c have been carried out. The average structures and the structural correlations of the magnitudes of the atomic position fluctuations are in substantial agreement with recent X-ray diffraction results, particularly for the protein interior. The simulations show, however, that the atomic displacements are quite anisotropic. The degree of anisotropy and the preferred directions of atomic displacement exhibit correlations with structural features of the protein.
Brownian Motion of a System of Coupled Harmonic Oscillators.
M. Berkowitz and J.A. McCammon
The dynamics of a system of coupled Langevin oscillators is considered. Convenient algorithms are derived for computing the displacement and velocity time correlation functions of one of the oscillating particles, and generalized Langevin equations for these functions are developed. Illustrative results indicate that this model should be useful in the description of single-atom librations in globular proteins.
Memory Kernels from Molecular Dynamics.
Max Berkowitz, John D. Morgan, Donald J. Kouri and J. Andrew McCammon
A numerical procedure is presented for the direct computation of memory kernels in generalized Langevin representations of time correlation functions. The procedure will facilitate analysis of the microscopic dynamics of a wide variety of systems, ranging from simple solids to globular proteins.
Gated Binding of Ligands to Proteins.
J. Andrew McCammon and Scott H. Northrup
The binding of ligands to proteins often occurs at rates that approach the diffusion-controlled limit. For spherical molecules with negligible interactions apart from isotropic reactivity on contact, the diffusion-controlled rate constant is KD = 4πRD, where R is the distance between molecular centres at contact and D is the relative translational diffusion constant. Deviations from this limiting rate due to interaction potentials, hydrodynamic interactions and static geometric features of the binding sites have previously received much attention. Here, we point out another possible cause of such deviations, the dynamic modulation of binding site accessibility due to internal motions of the protein. Such motions may occur, for example, in proteins such as lysozyme, in which the active site cleft opens and closes in a stochastic manner.
Intramolecular Flexibility in Phenylalanine Transfer RNA.
Stephen C. Harvey and J. Andrew McCammon
Yeast tRNAPhe is an L-shaped molecule, where each arm is a short segment of double-helical RNA. Examination of the crystal structure has suggested that the molecule may be hinged, perhaps in the region where the anticodon stem meets the D stem, or where the two arms of the molecule meet. Because tRNA interacts with a variety of macromolecules during protein synthesis, and because it performs various functions in addition to its role in protein synthesis, the idea of a hinge is attractive: such conformational flexibility would facilitate functional flexibility. Here we present the results of a theoretical study of the bending of tRNAPhe about the proposed hinge at the junction of the two arms, applying the conformational energy calculation method used previously to examine flexibility in lysozyme and in DNA. The model is surprisingly flexible, swivelling with two degrees of freedom through angles as large as 30° at an energetic cost of only a few kcal per mol. These energies are comparable with that of a few hydrogen bonds, suggesting that solvent conditions and interactions with other molecules are important in modulating structure and flexibility.