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Diffusional Dynamics of Ligand-Receptor Association
J. Andrew McCammon, Scott H. Northrup and Stuart A. Allison
Biological molecules generally have complicated shapes and charge distributions. Their binding sites for ligands or substrates are often geometrically restrictive and may display fluctuating steric and electrostatic properties. Detailed studies of biomolecular associations that involve such complications can be carried out with the aid of new Brownian dynamics simulation methods. These methods should also prove useful in studies of diffusion-influenced processq in other areas of chemistry. This article provides a simple and pedagogic treatment of diffusional bimolecular association and describes some of the initial applications of Brownian dynamics to biochemical systems.
Dynamics of Macromolecular Interactions
S.A. Allison, J.A. McCammon and S.H. Northrup
In "Coulombic Interactions in Macromolecular Systems," A. Eisenberg and F.E. Bailey, Eds., American Chemical Society, Washington, D.C., pp. 216-231 (1986)
Simulation of Biomolecular Diffusion and Complex Formation
S.A. Allison, S.H. Northrup and J.A. McCammon
In "Macromolecular Assembly Analyzed by Converging Structural Techniques," V.A. Parsegian, Ed., Rockefeller University Press, New York, N.Y., pp. 167-175 (1986)
Ligand Binding: New Theoretical Approaches to Molecular Recognition
J.A. McCammon, T.P. Lybrand, S.A. Allison and S.H. Northrup
In "Biomolecular Stereodynamics III," R.H. Sarma, Ed., Adenine Press, N.Y., pp. 227-235 (1986)
Theoretical Calculation of Relative Binding Affinity in Host-Guest Systems
Terry P. Lybrand, J. Andrew McCammon and Georges Wipff
The relative free energy of binding the anions Cl- and Br- to the macrotricyclic receptor SC24 in water has been computed by a computer simulation technique. This result and an incidental result for the relative free energy of hydration of the anions are in excellent agreement with experimental data. The simulation approach to ligand-receptor interactions that is described here has significant potential as a predictive tool in chemistry, biochemistry, and pharmacology.
Solvation Structure of a Sodium Chloride Ion Pair in Water
Alan C. Belch, Max Berkowitz and J.A. McCammon
Changes in the equilibrium solvation structure associated with the separation of a Na+Cl- ion pair in water have been examined with use of computer simulation. At all separations, the Na+ attempts to maintain an octahedral shell of nearest neighbors. This shell is comprised of five waters and the chloride in the stable contact ion pair. When the ions are separated slightly, the five waters rotate, weakening their hydrogen bonding with the second shell waters and producing a distorted octahedron. Those waters which rotate toward the chloride assume "bridging" orientations characterized by favorable electrostatic interactions with both ions. Further separation leads to replacement of the chloride by a sixth water molecule and formation of a stable solvent-separated ion pair in which strong hydrogen bonds are again formed between the first and second shells near Na+. More subtle changes in structure and interactions occur farther from the Na+ and around the Cl-; these changes are noticeable up to about 7 Angstroms from each ion.
The Hinge-Bending Mode of a Lysozyme-Inhibitor Complex
Robert E. Bruccoleri, Martin Karplus and J. Andrew McCammon
The hinge-bending mode of hen egg white lysozyme is studied by a constrained minimization technique. Results with and without a bound inhibitor, tri-N-acetyl-glucosamine, are obtained. The frequency of the mode with the inhibitor is found to be 4.3 cm-1, in contrast to 3.0 cm-1 for the free enzyme. Also, the hinge-bending angle with the lowest energy is shifted 10° towards a more closed cleft in the bound species. The main contribution to these differences arise from interactions with the residues lining the cleft and those on the back side of it. Structural details that account for the energetics are presented. The method of calculation is somewhat different from a previous study [J.A. McCammon, B.R. Gelin, M. Karplus & P.G. Wolynes (1976) Nature 262, 325-326] to reduce the likelihood of artifacts in the results.
Dynamics of Proteins
Martin Karplus and J. Andrew McCammon
Transport Properties of Macromolecules by Brownian Dynamics Simulation: Vectorization of Brownian Dynamics on the Cyber-205
Girija Ganti and J. Andrew McCammon
Time consuming portions in the computation of transport properties of rigid and flexible molecules are the evaluation of subunit hydrodynamic interaction tensors Q and σ, and the procedure for satisfying subunit-subunit distance constraints. Vector algorithms to speed up these parts of the computation are given. Using these algorithms, a vector version of the Ermak-McCammon Brownian dynamics code has been developed on a Cyber-205. To demonstrate the order of speedups that can be achieved, the code was tested on a rigid "trimer" system comprising 24 spherical subunits with a fixed geometry. A speedup of about 14 times for the whole program, and of 45, 6, and 18 times for the computation of Q, σ, and for the procedure to enforce the constraints, respectively, were obtained.
Ionic Association in Water: From Atoms to Enzymes
J. Andrew McCammon, Omar A. Karim, Terry P. Lybrand and Chung F. Wong
Chemistry and biochemistry are largely concerned with the association and transformation of molecules in water. Theoretical studies of such processes have in the past been hindered by a number of difficulties. Within an aqueous system, there are strong, directional, attractive forces among the water molecules, and often also between solute and solvent molecules, in addition to the excluded volume forces that have made even simple liquids a challenging subject. For a model system comprising a few solute molecules and a few hundred water molecules, the competition among these interactions produces a complicated potential energy surface with many local minima. To calculate structural or thermodynamic properties, one must evaluate averages of certain quantities over a representative set of those configurations that have low enough energy to be thermally populated. To calculate kinetic properties, one must consider motions over energy barriers and, in the case of molecular association, motions corresponding to large displacements over the potential surface.
Dynamics of a Sodium Chloride Ion Pair in Water
Omar A. Karim and J. Andrew McCammon
A sodium chloride ion pair in water has quasi-stable states in which the ions are in contact or are separated by one or more bridging water molecules. The dynamics of the transitions between these two states have been explored by computer simulation. The transitions have a sluggish, diffusional character because the ion motions are concerted with the rearrangement of many water molecules in their hydration shells. Two types of separation mechanism are prominent. In one of these, a water molecule from the first hydration shell of chloride interacts with water in the first shell around sodium and is drawn into a bridging position between the ions. In the other mechanism, a water molecule in the first shell around sodium interacts directly with the chloride ion and is subsequently drawn into a bridging position.
Optimization of Brownian Dynamics Methods for Diffusion-Influenced Rate Constant Calculations
Scott H. Northrup, Marc S. Curvin, Stuart A. Allison and J. Andrew McCammon
One-dimensional Brownian dynamics algorithms for reaction and reflection recently developed by Lamm and Schulten are adapted into the special boundary topology necessary to compute diffusion-influenced rate constants of arbitrarily complicated bimolecular reactions in three dimensions. Performance of these relative to the primitive free diffusion algorithm commonly employed is discussed. Remaining sources of error arising from boundaries are (1) boundary curvature effects and (2) reactive discontinuity effects in cases where orientational criteria for reaction exist. The magnitudes of these errors are calculated as a function of simulation time step size. In addition, a special statistical sampling procedure is developed which allows the simultaneous treatment of a large class of reactive boundary problems in one simulation. This procedure is illustrated by the treatment of reactive patch size effects on the rate constant in the model of Solc and Stockmayer.
Salt Effects on Enzyme-Substrate Interactions by Monte Carlo Simulation
R.J. Bacquet and J.A. McCammon
It has been proposed that the long-range electrostatic field produced by an enzyme's charge distribution can be important in channeling diffusing substrate to an active site. In the case of superoxide dismutase (SOD) this steering effect competes with an overall repulsion which is due to the net negative charge on both substrate and enyzme. These opposing effects are both reduced by salt ions, which screen the electrostatic interaction of the reactants. The reaction rate of O2- SOD is found experimentally to decrease with increasing salt concentration, implying that impairment of the steering field is the dominant factor.
Theoretical calculation of the potential near an enzyme is complicated by the presence of small mobile salt ions which adopt an equilibrium distribution in response to the enzyme's innate field. The effect of this ionic atmosphere has been modeled only by application of Debye-Hückel screening to the enzyme-substrate interaction, which is of limited validity. More sophisticated approaches, such as nonlinear Poisson-Boltzmann theory, integral equation methods and computer simulation, generally founder on the topographic and electrostatic complexity of an enzyme such as SOD. However, the salt distribution responds to the macromolecular potential over a large region of space and is not expected to be very sensitive to fine details of the enzyme's shape and charge distribution. Thus a very simple SOD model can capture the essential features of the potential in the region exterior to the protein, and the techniques mentioned above become feasible.
The Interaction of O2- with Water
Jesus P. Lopez, Thomas A. Albright and J. Andrew McCammon
Ab initio calculations at the 4-31 + G level have been carried out for the interaction of F-, O2-, and Cl- with H2O. Computation of the binding energies gave reasonable agreement with hydration energies. The O2- (H2O) system was also investigated at the 6-31 + G** level including Møller-Plesset perturbation theory to second order. The strength of O2- binding to H2O is intermediate to that of F- and Cl- with H2O.
Dynamic Simulations of Oxygen Binding to Myoglobin
David A. Case and J. Andrew McCammon
We report dynamic simulations of the process by which a dioxygen molecule enters or leaves the heme pocket region of myoglobin along a path between the distal histidine (E7) and valine (E11). Our reaction coordinate measures the distance of the ligand from a "dividing plane" defined by three protein atoms. The equilibrium probability distribution as a function of this coordinate is determined by a series of molecular-dynamic simulations with overlapping "umbrella" constraining potentials; the resulting potential of mean force has a barrier of about 7 kcal/mol for exit from the heme pocket. A comparison of this free energy profile with the corresponding potential energy profile suggests that entropy effects dominate the kinetic barrier. Reactive trajectories are generated from dynamic simulations beginning at the top of the potential of mean force; only a small fraction of these recross the dividing surface, indicating that transition state theory may be a good approximation for this process.
Dynamics and Design of Enzymes and Inhibitors
Chung F. Wong and J. Andrew McCammon
The mutual recognition and binding of ligands and receptors represents the first step in many biochemical processes. The ability to predict changes in affinity that would result from modifications in a ligand or receptor would therefore be helpful in the design of molecules with specific activities. Here, we describe the first application to biological molecules of a new computer simulation approach to such problems. We compute the relative affinity of two benzamidine inhibitors for trypsin and of benzamidine for native and a mutant trypsin. The agreement with experimental data is encouraging.
Computer Simulation and the Design of New Biological Molecules
C.F. Wong and J.A. McCammon
Israel Journal of Chemistry, Vol. 27, pp. 211-215 (1986, Invited article)
Simulation of Biomolecular Diffusion and Complex Formation
Stuart A. Allison, Scott H. Northrup and J. Andrew McCammon
Diffusion is a phenomenon of very widespread importance in molecular biophysics. Diffusion can determine the rates and character of the assembly of multisubunit structures, the binding of ligands to receptors, and the internal motions of molecules and assemblies that involve solvent surface displacements. Current computer simulation techniques provide much more detailed descriptions of diffusional processes than have been available in the past. Models can be constructed to include such realistic features as structural subunits at the submolecular level (domains, monomers, or atoms); detailed electrostatic charge distributions and corresponding solvent-screened inter- and intramolecular interactions; and hydrodynamic interactions. The trajectories can be analyzed either to provide direct information on biomolecular function (e.g., the bimolecular rate constant for formation of an electron-transfer complex between two proteins), or to provide or test models for the interpretation of experimental data (e.g., the time dependence of fluorescence depolarization for segments of DNA). Here, we first review the theory of diffusional simulations, with special emphasis on new techniques such as those for obtaining transport properties of flexible assemblies and rate constants of diffusion-controlled reactions. Then we survey a variety of recent applications, including studies of large-scale motion in DNA segments and substrate "steering" in enzyme-substrate binding. We conclude with a discussion of current work (e.g., formation of protein complexes) and possible areas for future work.
Substrate Steering by Electrostatic Fields of Enzymes: Visualization by Computer Graphics
Girija Ganti and J. Andrew McCammon
The rates of reactions catalysed by certain enzymes are increased by electrostatic effects that steer substrate molecules toward the active sites of the enzyme. This phenomenon can be studied by using Brownian dynamics simulation to generate and analyse diffusional trajectories of substrate in the field of an enzyme. The paper demonstrates that computer graphics can be used to show how electrical fields influence the special dependence of substrate flux as calculated by Brownian dynamics. Because of the statistical noise associated with typical simulation runs, filtering techniques are helpful in determining systematic trends in the graphic displays.
Report of the Research Briefing Panel on Protein Structure and Biological Function
Frederic Richards, Robert Baldwin, Gerald R. Galluppi, Robert Griffin, Emil Thomas Kaiser, Brian Matthews, J. Andrew McCammon, Alfred Redfield, Brian Reid, Robert Sauer, Alan Schechter, Paul Sigler, Peter von Hippel and Don Wiley
Proteins are involved in every biological function. As enzymes, they catalyze the chemical reactions of cells. As hormones and growth factors, they regulate the development of cells and coordinate the functions of distant organs in the body. In various filamentous forms, they control the shape of cells and the dramatic alterations that occur during cell division. In muscle, proteins change chemical energy into mechanical energy and cause movement. As components of membranes, they control the traffic of molecules and information among the various cellular compartments. Hemoglobin, a protein in blood, is specifically designed to transport oxygen between organs; other blood proteins, such as clotting factors and circulating antibodies, act as defenses against trauma and infection. In plants, a highly organized collection of membrane proteins is involved in the complex process of photosynthesis, without which there would be no higher animal forms.
Rate Constants for Ion Pair Formation and Dissociation in Water
Omar A. Karim and J. Andrew McCammon
The reactive flux time correlation function for an associating ion pair in water is obtained by computer simulation. The transmission coefficient is found directly from the reactive flux and also through the method of absorbing barriers. Rate constants for the transitions between the contact and solvent-separated states of the ion pair are calculated.