The potential of mean force between polyatomic molecules in polar molecular solvents

Designing molecular complexes using free-energy derivatives from liquid-state integral equation theory

Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute-solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute-solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems.

Interpreting the widespread nonlinear force spectra of intermolecular bonds

Single molecule force spectroscopy probes the strength, lifetime, and energetic details of intermolecular interactions in a simple experiment. A growing number of these studies have reported distinctly nonlinear trends in rupture force with loading rate that are typically explained in conventional models by invoking complex escape pathways. Recent analyses suggested that these trends should be expected even for simple barriers based on the basic assumptions of bond rupture dynamics and thus may represent the norm rather than the exception. Here we explore how these nonlinear trends reflect the two fundamental regimes of bond rupture: (i) a near-equilibrium regime, produced either by bond reforming in the case of a single bond or by asynchronized rupture of multiple individual bonds, and (ii) a kinetic regime produced by fast, non-equilibrium bond rupture. We analyze both single- and multi-bonded cases, describe the full evolution of the system as it transitions between near- and far-from-equilibrium loading regimes, and show that both interpretations produce essentially identical force spectra. Data from 10 different molecular systems show that this model provides a comprehensive description of force spectra for a diverse suite of bonds over experimentally relevant loading rates, removes the inconsistencies of previous interpretations of transition state distances, and gives ready access to both kinetic and thermodynamic information about the interaction. These results imply that single-molecule binding free energies for a vast number of bonds have already been measured.

Interaction between Colloids in Network Forming Solution

The effective interaction between colloids in a solvent of hard spheres, which can polymerize with the formation of cross-like molecular clusters, is studied on the basis of the solution of the associative Percus-Yevick/Ornstein-Zernike equation for spatial correlations in an infinitely dilute solution. It is found that at low solvent density and low temperature, the effective intermolecular potential between the colloidal particles is attractive, thus facilitating a phase separation or precipitation of the colloids. A depletion of the local solvent density around the colloidal particle is observed. If the solvent consists of extended associative complexes, compared with hard spheres, the correlation between the colloid particles are of longer range and barrier for flocculation shifts to the larger separations. The effect of size ratio of the colloid spheres and of solvent on the potential of mean force is also discussed. Copyright 1998 Academic Press.

On the attribution of binding energy in antigen-antibody complexes McPC 603, D1.3, and HyHEL-5

Using X-ray coordinates of antigen-antibody complexes McPC 603, D1.3, and HyHEL-5, we made semiquantitative estimates of Gibbs free energy changes (delta G) accompanying noncovalent complex formation of the McPC 603 Fv fragment with phosphocholine and the D1.3 or HyHEL-5 Fv fragments with hen egg white lysozyme. Our empirical delta G function, which implicitly incorporates solvent effects, has the following components: hydrophobic force, solvent-modified electrostatics, changes in side-chain conformational entropy, translational/overall rotational entropy changes, and the dilutional (cratic) entropy term. The calculated delta G ranges matched the experimentally determined delta G of McPC 603 and D1.3 complexes and overestimated it (i.e., gave a more negative value) in the case of HyHEL-5. Relative delta G contributions of selected antibody residues, calculated for HyHEL-5 complexes, agreed with those determined independently in site-directed mutagenesis experiments. Analysis of delta G attribution in all three complexes indicated that only a small number of amino acids probably contribute actively to binding energetics. These form a subset of the total antigen-antibody contact surface. In the antibodies, the bottom part of the antigen binding cavity dominated the energetics of binding whereas in lysozyme, the energetically most important residues defined small (2.5-3 nm2) "energetic" epitopes. Thus, a concept of protein antigenicity emerges that involves the active, attractive contributions mediated by the energetic antigenic epitopes and the passive surface complementarity contributed by the surrounding contact area. The D1.3 energetic epitope of lysozyme involved Gly 22, Gly 117, and Gln 121; the HyHEL-5 epitope consisted of Arg 45 and Arg 68. These are also the essential antigenic residues determined experimentally. The above positions belong to the most protruding parts of the lysozyme surface, and their backbones are not exceptionally flexible. Least-squares analysis of six different antibody binding regions indicated that the geometry of the VH-VL interface beta-barrel is well conserved, giving no indication of significant changes in domain-domain contacts upon complex formation.