Brock A. Luty

A molecular mechanics/grid method for evaluation of ligand–receptor interactions

We present a computational method for prediction of the conformation of a ligand when bound to a macromolecular receptor. The method is intended for use in systems in which the approximate location of the binding site is known and no large‐scale rearrangements of the receptor are expected upon formation of the complex. The ligand is initially placed in the vicinity of the binding site and the atomic motions of the ligand and binding site are explicitly simulated, with solvent represented by an implicit solvation model and using a grid representation for the bulk of the receptor protein. These two approximations make the method computationally efficient and yet maintain accuracy close to that of an all‐atom calculation. For the benzamidine/trypsin system, we ran 100 independent simulations, in many of which the ligand settled into the low‐energy conformation observed in the crystal structure of the complex. The energy of these conformations was lower than and well‐separated from that of others sampled. Extensions of this method are also discussed.

LATTICE-SUM METHODS FOR CALCULATING ELECTROSTATIC INTERACTIONS IN MOLECULAR SIMULATIONS

When simulating a periodic molecular system, lattice sum methods may be used to evaluate the electrostatic interactions without resorting to an unphysical truncation of the potential. In a previous publication, we compared the computational efficiency of the Ewald and Particle‐Particle Particle‐Mesh (PPPM) lattice‐sum methods. Because the PPPM method discretizes the field equations and utilizes the highly efficient fast Fourier transform algorithm, it requires significantly less computational effort than the Ewald method and scales almost linearly with system size. In this paper, we take a more detailed look into the theory behind the lattice‐sum methods to clarify the underlying similarities between the Ewald method and the PPPM method. We also investigate the errors introduced by different approximation used in the discretization of the field equations in the PPPM method.

A Comparison of Particle-Particle, Particle-Mesh and Ewald Methods for Calculating Electrostatic Interactions in Periodic Molecular Systems

Abstract We compare the Particle-Particle Particle-Mesh (PPPM) and Ewald methods for calculating electrostatic interactions in periodic molecular systems. A brief comparison of the theories shows that the methods are very similar differing mainly in the technique which is used to perform the “k-space” or mesh calculation. Because the PPPM utilizes the highly efficient numerical Fast Fourier Transform (FFT) method it requires significantly less computational effort than the Ewald method and scales almost linearly with system size.

Poisson-Boltzmann analysis of the lambda repressor-operator interaction.

A theoretical study of the ion atmosphere contribution to the binding free energy of the lambda repressor-operator complex is presented. The finite-difference form of the Poisson-Boltzmann equation was solved to calculate the electrostatic interaction energy of the amino-terminal domain of the lambda repressor with a 9 or 45 base pair oligonucleotide. Calculations were performed at various distances between repressor and operator as well as at different salt concentrations to determine ion atmosphere contributions to the total electrostatic interaction. Details in the distribution of charges on DNA and protein atoms had a strong influence on the calculated total interaction energies. In contrast, the calculated salt contributions are relatively insensitive to changes in the details of the charge distribution. The results indicate that the ion atmosphere contribution favors association at all protein-DNA distances studied. The theoretical number of ions released upon repressor-operator binding appears to be in reasonable agreement with experimental data.

Diffusive reaction rates from Brownian dynamics simulations: Replacing the outer cutoff surface by an analytical treatment

The algorithm of Northrup, Allison, and McCammon [J. Chem. Phys. 80, 1517 (1984)] for calculating diffusive reaction rates using Brownian dynamics simulations is reexamined. A new method is described in which a time‐consuming portion of the algorithm is replaced by an analytical solution. When applied to two illustrative model systems, the new method is found to reduce the computational work by a factor of 2 or more.

Diffusion-controlled enzymatic reactions

Publisher Summary The rate of diffusional encounter among reactant molecules in solution sets the ultimate limit on the speed of enzymatic and other reactions. If the reactant molecules are such that subsequent events develop very rapidly when the reactants come into contact, the net rate of the reaction will be equal to the rate of diffusional encounter. The reaction is then said to be diffusion-controlled. This chapter describes the way computer simulations may be used to highlight the nature of diffusion-controlled reactions. Such simulations can, in principle, aid in the detailed interpretation of experimental results or in the design of molecules with prescribed kinetic properties. The chapter also describes methods for calculating electrostatic interactions among solute molecules in solution. The long range of such interactions makes them particularly important in the consideration of diffusional encounters. Diffusional encounter involves the interaction of molecules at large separations. Electrostatic interactions are, therefore, particularly important because of the long-range nature of the Coulombic potential. At small separations, the effects of other interactions can often be represented by suitable boundary conditions. As a result, most attention has been paid to the calculation of electrostatic forces. The methods described in the chapter can also be used to study the role of electrostatics in determining equilibrium properties, such as the stability of molecular folding and association.

SPECIES DEPENDENCE OF ENZYME-SUBSTRATE ENCOUNTER RATES FOR TRIOSE PHOSPHATE ISOMERASES

Triose phosphate isomerase (TIM) is a diffusion‐controlled enzyme whose rate is limited by the diffusional encounter of the negatively charged substrate glyceraldehyde 3‐phosphate (GAP) with the homodimeric enzymes active sites. Translational and orientational steering of GAP toward the active sites by the electrostatic field of chicken muscle TIM has been observed in previous Brownian dynamics (BD) simulations. Here we report simulations of the association of GAP with TIMs from four species with net charges at pH 7 varying from ‐12e to +12e. Computed second‐order rate constants are in good agreement with experimental data. The BD simulations and computation of average Boltzmann factors of substrate–protein interaction energies show that the protein electrostatic potential enhances the rates for all the enzymes. There is much less variation in the computed rates than might be expected on the basis of the net charges. Comparison of the electrostatic potentials by means of similarity indices shows that this is due to conservation of the local electrostatic potentials around the active sites which are the primary determinants of electrostatic steering of the substrate. Proteins 31:406–416, 1998.

Space-time correlated reaction field: A stochastic dynamical approach to the dielectric continuum

In molecular dynamics (MD) simulations, the continuum description of electrostatic interactions has been based in most cases on the static response of the dielectric continuum. In this work, a time-dependent reaction field expression including stochastic and friction terms is derived in analogy to the generalized Langevin equation involving hydrodynamic interactions. Simulations of water using the extended simple-point charge model have been performed under different boundary conditions. The effects of a time-dependent treatment of the reaction field are demonstrated by comparing the results to those of MD simulations using a static, instantaneous reaction field and of MD simulations employing the Ewald sum. It is shown for the first time that the straight cutoff approach not only leads to a disruption of the time, but also of the spatial correlation of the dipole moment.

Hierarchy of simulation models in predicting molecular recognition mechanisms from the binding energy landscapes: Structural analysis of the peptide complexes with SH2 domains

Computer simulations using the simplified energy function and simulated tempering dynamics have accurately determined the native structure of the pYVPML, SVLpYTAVQPNE, and SPGEpYVNIEF peptides in the complexes with SH2 domains. Structural and equilibrium aspects of the peptide binding with SH2 domains have been studied by generating temperature‐dependent binding free energy landscapes. Once some native peptide–SH2 domain contacts are constrained, the underlying binding free energy profile has the funnel‐like shape that leads to a rapid and consistent acquisition of the native structure. The dominant native topology of the peptide–SH2 domain complexes represents an extended peptide conformation with strong specific interactions in the phosphotyrosine pocket and hydrophobic interactions of the peptide residues C‐terminal to the pTyr group. The topological features of the peptide–protein interface are primarily determined by the thermodynamically stable phosphotyrosyl group. A diversity of structurally different binding orientations has been observed for the amino‐terminal residues to the phosphotyrosine. The dominant native topology for the peptide residues carboxy‐terminal to the phosphotyrosine is tolerant to flexibility in this region of the peptide–SH2 domain interface observed in equilibrium simulations. The energy landscape analysis has revealed a broad, entropically favorable topology of the native binding mode for the bound peptides, which is robust to structural perturbations. This could provide an additional positive mechanism underlying tolerance of the SH2 domains to hydrophobic conservative substitutions in the peptide specificity region. Proteins 2001;45:456–470.

Simulation of bimolecular reactions: synthesis of the encounter and reaction steps

Abstract Computer simulations are playing an increasingly important role in the study of chemical and biochemical reactions in condensed phases [1, 2, 3]. For bimolecular reactions, the events leading to reaction can be separated into two steps: the initial encounter, followed by the actual reaction of the properly juxtaposed reactants. Current simulation methods allow the analysis of reactions whose rates are controlled by one or the other of these steps [1]. Here, we describe an approach that can be used for the general case. An advantage of this approach is that it allows the rigorous integration of a hierarchy of models. E.g., the encounter step can be treated by models with continuum and Brownian elements, and the reaction step by fully atomistic models.