Analysis of Energy Stabilization inside the Hydrophobic Core of Rubredoxin

Energy Matrix of Structurally Important Side-Chain/Side-Chain Interactions in Proteins

The interactions between amino acid side chains in proteins are generally considered to be the most important stabilizing factor controlling the precise arrangement of the polypeptide chain into a well-defined spatial structure. We used the RI-DFT-D method to calculate the full 20 × 20 matrix of interaction energies between all pairs of amino acid side chains. For each pair, we used a representative 3D conformation extracted from an analysis of known protein structures from Protein Data Bank (PDB). The representative comes from the largest cluster of relative orientations of the two side chains. We find that all of the calculated interaction energies between selected pairs of amino acids are attractive in the gas phase with the exception of side chain pairs having the same total charge. We compared these data with those calculated by the parm03 and OPLS-AA/L force fields to investigate the reliability of simple methods in modeling biomolecules and their behavior. The force fields yield good overall interaction energies for our set but have problems in evaluation of some particular interactions which could be of principal importance for protein stability. We then looked in detail at the 20 side chain interactions involving tryptophan. The histograms of interaction energies showed that the distributions of the interaction energies are neither normal nor Boltzmann-like and that our representative geometries correspond mostly to the minimum energy geometry which is rather poorly populated in the whole pairwise energy distribution. We concluded that cluster representatives obtained by the clusterization algorithm based on geometry criteria cannot be considered as a typical interaction for the whole side chain/side chain interaction distribution. They seem to epitomize the strongest interactions in a protein and are often functionally or structurally important.

Implicit treatment of solvent dispersion forces in protein simulations

A model is proposed for the evaluation of dispersive forces in a continuum solvent representation for use in large-scale computer simulations. The model captures the short- and long-range effects of water-exclusion in conditions of partial and anisotropic hydration. The model introduces three parameters, one of which represents the degree of hydration (water occupancy) at any point in the system, which depends on the solute conformation, and two that represent the strength of water-water and water-solute dispersive interactions. The model is optimized for proteins, using hydration data of a suboptimally hydrated binding site and results from dynamics simulations in explicit water. The model is applied to a series of aliphatic-alcohol/protein complexes and a set of binary and ternary complexes of various sizes. Implications for weak and ultra-weak protein-protein association and for simulation in crowded media are discussed.

On the origin of the substantial stabilisation of the electron-donor 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes

The stabilisation energies of the crystal structures of 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes determined by the CCSD(T)/CBS method are very large and exceed 8 and 15 kcal mol(-1), respectively. The DFT-D method (B97-D3/def2-QZVP) strongly overestimates these stabilisation energies, which support the well-known fact that the DFT-D method is not very applicable to the study of charge-transfer complexes. On the other hand, the M06-2X/def2-QZVP method provides surprisingly reliable energies. A DFT-SAPT analysis has shown that a substantial stabilisation of these complexes arises from the charge-transfer energy included in the induction energy and that the respective induction energy is much larger than that of other non-covalently bound complexes. The total stabilisation energies of the complexes mentioned as well as of those where iodine has been replaced by lighter halogens (Br2 and Cl2) or by hetero systems (IF, ICH3, N2) correlate well with the magnitude of the σ-hole (Vs,max value) as well as with the LUMO energy. The nature of the stabilisation of all complexes between both electron donors and X2 (X = I, Br, Cl, N) systems is explained by the magnitude of the σ-hole but surprisingly also by the values of the electric quadrupole moment of these systems. Evidently, the nature of the stabilisation of halogen-bonded complexes between electron donors and systems where the first non-zero electric multipole moment is the quadrupole moment can be explained not only by the recently introduced concept of the σ-hole but also by the classical concept of electric quadrupole moments.