Atomic-level molecular dynamics simulations of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) bilayers containing small, amphiphilic, drug-like molecules were carried out to examine the influence of polar functionality on membrane partitioning and transport. Three related molecules (tyramine, phenethylamine, and 4-ethylphenol) were chosen to allow a detailed study of the isolated effects of the amine and hydroxyl functionalities on the preferred solute location, free energies of transfer, and the effect of combining both functional groups in a same molecule. Transfer free energy profiles (from water) generated from molecular dynamics (MD) simulations as a function of bilayer depth compared favorably to comparable experimental results. The simulations allowed the determination of the location of the barrier domain for permeability where the transfer free energy is highest and the preferred binding region at which the free energy is a minimum for each of the three solutes. Comparisons of the free energy profiles reveal that the hydrocarbon chain interior is the region most selective to chemical structure of different solutes because the free energies of transfer in that region vary to a significantly greater extent than in other regions of the bilayer. The contributions of the hydroxyl and amino groups to the free energies of solute transfer from water to the interfacial region were close to zero in both the MD simulations and experimental measurements. This suggests that the free energy decrease observed for solute transfer into the head group region occurs with minimal loss in solvation by hydrogen bonding to polar functional groups on the solute and is largely driven by hydrophobicity. Overall, the joint experimental and simulation studies suggest that the assumption of additivity of free energy contributions from multiple polar functional groups on the same molecule may hold for predictions of passive bilayer permeability coefficients providing that the groups are well isolated. However, this assumption does not hold for predictions of relative liposome-binding affinities.

Molecular interactions and orientations responsible for differences in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) bilayer partitioning of three structurally related drug-like molecules (4-ethylphenol, phenethylamine, and tyramine) were investigated. This work is based on previously reported molecular dynamics (MD) simulations that determined their transverse free energy profiles across the bilayer. Previously, the location where the transfer free energy of the three solutes is highest, which defines the barrier domain for permeability, was found to be the bilayer center, while the interfacial region was found to be the preferred binding region. Contributions of the amino (NH2) and hydroxyl (OH) functional groups to the transfer free energies from water to the interfacial region were found to be very small both experimentally and by MD simulation, suggesting that the interfacial binding of these solutes is hydrophobically driven and occurs with minimal loss of hydrogen-bonding interactions of the polar functional groups which can occur with either water or phospholipid head groups. Therefore, interfacial binding is relatively insensitive to the number or type of polar functional groups on the solute. In contrast, the relative solute free energy in the barrier domain is highly sensitive to the number of polar functional groups on the molecule. The number and types of hydrogen bonds formed between the three solutes and polar phospholipid atoms or with water molecules were determined as a function of solute position in the bilayer. Minima were observed in the number of hydrogen bonds formed by each solute at the center of the bilayer, coinciding with a decrease in the number of water molecules in DOPC as a function of distance away from the interfacial region. In all regions, hydrogen bonds with water molecules account for the majority of hydrogen-bonding interactions observed for each solute. Significant orientational preferences for the solutes are evident in certain regions of the bilayer (e.g., within the ordered chain region and near the interfacial region 20-25 Å from the bilayer center). The preferred orientations are those that preserve favorable molecular interactions for each solute, which vary with the solute structure.

The method of conserved core substructure matching (CSM) for the overlay of protein ligand complexes is described. The method relies upon distance geometry to align structurally similar substructures without regard to sequence similarity onto substructures from a reference protein empirically selected to include key determinants of binding site location and geometry. The error in ligand position is reduced in reoriented ensembles generated with CSM when compared to other overlay methods. Since CSM can only succeed when the selected core substructure is geometrically conserved, misalignments only rarely occur. The method may be applied to reliably overlay large numbers of protein ligand complexes in a way that optimizes ligand position at a specific binding site or subsite or to align structures from large and diverse protein families where the conserved binding site is localized to only a small portion of either protein. Core substructures may be complex and must be chosen with care. We have created a database of empirically selected core substructures to demonstrate the utility of CSM alignment of ligand binding sites in important drug targets. A Web-based interface can be used to apply CSM to align large collections of protein ligand complexes for use in drug design using these substructures or to evaluate the use of alternative core substructures that may then be shared with the larger user community. Examples show the benefit of CSM in the practice of structure-based drug design.

A common problem in the calculation of electrostatic potentials with the Poisson-Boltzmann equation using finite difference methods is the effect of molecular position relative to the grid. Preciously a uniform charging method was shown to reduce the grid dependence substantially over the point charge model used in commercially available codes. In this article we demonstrate that smoothing the charge and dielectric values on the grid can improve the grid independence, as measured by the spread of calculated values, by another order of magnitude. Calculations of Born ion salvation energies, small molecule solvation energies, the electrostatic field of superoxide dismutase, and protein-protein binding energies are used to demonstrate that this method yields the same results as the paint charge model while reducing the positional errors by several orders of magnitude. (C) 1997 by John Wiley & Sons, Inc.

model-based method for estimating the shape d motion of 3D objects appearing in a video described. This technique is used for modelsed video coding (video compression). The thod is based on a new variant of optical ow d uses 3D computer graphics to represent and play an object. Though the algorithm is genl, this work concentrates on videos depicting e human head and face because of its relevance videotelephony and teleconferencing. Rigid dy motion of the head and facial expressions ening the mouth) are accommodated. Relts obtained from videos of a moving person e described.

Empirical Gibbs functions estimate free energies of non-covalent reactions (ΔG) from atomic coordinates of reaction products (e.g. antibody-antigen complexes). The function previously developed by us has four terms that quantify the effects of hydrophobic, electrostatic and entropy changes (conformational, association) upon complexation. The function was used to calculate ΔΔG of ten lysozyme mutants affecting the stability of the HyHEL-10 antibody-lysozyme complex. The mutants were computer-modeled from the X-ray structure of the wild-type, and free energy calculations produced a correlation coefficient of 0.5 with the experimental ΔΔG data (average absolute error ±3 kcal). The following changes were then introduced into the Gibbs function: (1) the hydrophobic force was made proportional to the molecular surface, as calculated by the GEPOL93 algorithm, with the scaling constant of 70 cal/mol/Å2; (2) calculation of the electrostatics of binding was carried out by the finite difference Poisson-Boltzmann algorithm, which employed uniform grid charging, dielectric boundary smoothing and charge anti-aliasing; and (3) side-chain conformational entropy was estimated from the CONGEN sampling of torsional degrees of freedom. In the new calculations, correlation with experimental data improved to 0.6 or 0.8 if a single outlying mutant, K96M, was neglected. Analysis of the errors remaining in our calculations indicated that molecular mechanics-based modeling of the mutants, rather than the form of our amended Gibbs function, was the main factor limiting the accuracy of the free energy estimates.

We describe a brownian dynamics simulation method that allows investigation of the effects of receptor flexibility on ligand binding rates. The method is applied to the encounter of substrate, glyceraldehyde 3-phosphate, with triose phosphate isomerase, a diffusion-controlled enzyme with flexible peptide loops at its active sites. The simulations show that while the electrostatic field surrounding the enzyme steers the substrate into its active sites, the flexible loops appear to have little influence on the substrate binding rate. The dynamics of the loops may therefore have been optimized during evolution to minimize their interference with the substrate's access to the active sites. The calculated and experimental rate constants are in good agreement.

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 scale's almost linearly with system size.

The N-terminal domain of the phage lambda repressor binds as a dimer to its palindromic DNA operator sequence. In addition to a helix-turn-helix DNA recognition motif, the first six amino acids of the phage lambda repressor form a flexible peptide segment which wraps around DNA. Site-directed mutagenesis studies have shown that amino acid replacements or partial removal of the arm structure, or changes in the DNA sequence contacting the N-terminal arm, can lower the repressor-operator binding affinity by several orders of magnitude. The finite-difference Poisson-Boltzmann approach in combination with a conformational search procedure was used to study energetic contributions of the lambda arm to repressor-operator recognition based on the high resolution X-ray structure. It allows for the local relaxation of the structure upon changing the DNA sequence in the lambda arm binding region. A simplified potential energy function including torsional, truncated Lennard-Jones and approximate electrostatic terms is used in the initial step to screen out energetically unfavorable structures. The electrostatic energy of selected conformations is subsequently calculated more accurately using the finite-difference Poisson-Boltzmann approach. The method was applied to study the effect of a C-->T mutation at position 6 of the consensus half-site of the operator. This base-pair contacts Lys4 which is part of the arm segment. Keeping only the Lys4 side-chain mobile and with the wild-type DNA operator sequence, several conformations close to the X-ray structure were identified as those with lowest energy. In the case of the DNA mutation, lowest energy conformations differed significantly from those selected for the wild-type sequence. These initial calculations indicate that the approach might be a useful tool to estimate conformational and energetic effects upon mutagenesis of protein-DNA complexes.

This chapter contains sections titled: Introduction Electrostatics Brownian Dynamics Simulations Conclusion Acknowledgments

Numerical solutions of the Poisson-Boltzmann equation (PBE) have found wide application in the computation of electrostatic energies of hydrated molecules, including biological macromolecules. However, solving the PBE for electrostatic forces has proved more difficult, largely because of the challenge of computing the pressures exerted by a high dielectric aqueous solvent on the solute surface. This paper describes an accurate method for computing these forces. We begin by presenting a novel derivation of the forces acting in a system governed by the PBE. The resulting expression contains three distinct terms: the effect of electric fields on 'fixed'' atomic charges; the dielectric boundary pressure, which accounts for the tendency of the high dielectric solvent to displace the low dielectric solute wherever an electric field exists; and the ionic boundary pressure, which accounts for the tendency of the dissolved electrolyte to move into regions of nonzero electrostatic potential. Techniques for extracting each of these three force contributions from finite difference solutions of the PBE for a solvated molecule are then described. Tests of the methods against both analytic and numeric results demonstrate their accuracy. Finally, the electrostatic forces acting on the two members of a salt bridge in the enzyme triosephosphate isomerase are analyzed. The dielectric boundary pressures are found to make substantial contributions to the atomic forces. In fact, their neglect leads to the unphysical situation of a significant net electrostatic force on the system. In contrast, the ionic boundary forces are usually extremely weak at physiologic ionic strength.

The Poisson–Boltzmann equation can be used to calculate the electrostatic potential field of a molecule surrounded by a solvent containing mobile ions. The Poisson–Boltzmann equation is a non‐linear partial differential equation. Finite‐difference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of non‐linear terms. Here we introduce a method based on a variational formulation of the electrostatic potential and standard multi‐dimensional maximization methods that can be used to solve the full non‐linear equation. © 1992 by John Wiley & Sons, Inc.

Finite‐difference Poisson–Boltzmann (FDPB) methods allow a fast and accurate calculations of the reaction field (charge–solvent) energies for molecular systems. Unfortunately, the energy in the FDPB calculations includes the self‐energies and the finite‐difference approximation to the Coulombic energies as well as the reaction field energy. A second finite‐difference calculation, in a uniform dielectric, is therefore necesssary to eliminate these contributions. In this article we describe a rapid and accurate method to calculate the self energy and finite‐difference Coulombic energies in a uniform dielectric thus eliminating the need for a second finite‐difference calculation. The computational savings for this method range from a factor of 4 for a typical protein to a factor of 10 3 for small molecules. © 1992 by John Wiley & Sons, Inc.