Entropy in protein folding and in protein-protein interactions.

The reduction of conformational entropy is a major barrier that has to be overcome in protein folding and binding. Changes in solvent entropy are also a major factor. Recent advances include clarification of the fundamental issues concerning the separation of entropy into components, the treatment of association entropy in binding, and the role of size and shape effects in solvation entropy. Advances in the application of entropy calculations include an emerging consensus for estimates of backbone and sidechain entropy loss in protein folding via use of numerically intensive methods for sampling, and use of the expanding protein-structure database.

Decomposition of interaction free energies in proteins and other complex systems.

A recent analysis of Mark and van Gunsteren has questioned the validity of separating different free energy components in proteins, or indeed in any complex system. The separability of free energy terms is re-examined from both a theoretical and a numerical perspective. Using a power series expansion of the free energy, it is found that the leading terms are free energy components that arise from individual contributions to the Hamiltonian ("in situ" free energies). The energetic part of an in situ free energy component is given by the ensemble average of the corresponding Hamiltonian component, while the leading term in the entropic part, which was missing in the analysis of Mark and van Gunsteren, is given by the mean square fluctuation. In addition there are correlations between fluctuations in each Hamiltonian component, which give rise to a coupling, or correlation entropy. A simple system, whose configurational degrees of freedom can be completely sampled, was examined in order to determine the relative sizes of these different contributions to the free energy. Under certain conditions, the change in system free energy observed when a particular component of the Hamiltonian is removed or altered is well approximated by the change in the in situ free energy of that component. In practical terms, this allows one in these cases to separate out different free energy contributions.

On the decomposition of free energies.

The decomposition of free energies and entropies into components has recently been discussed within the framework of the free energy perturbation (FEP) and thermodynamic integration (TI) methods. In FEP, the cumulant expansion of the excess free energy contains coupling terms in second and higher orders. It is shown here that this expansion can be expressed in terms of temperature derivatives of the mean energy, suggesting a natural decomposition of the free energy into components corresponding to each term in the Hamiltonian. This result is derived in such a way that it establishes the equivalence to a particular form of component analysis based on TI in which all terms in the interaction energy are turned on simultaneously using 1/kT as the coupling parameter.

Energetics of cyclic dipeptide crystal packing and solvation.

Calculations of the thermodynamics of transfer of the cyclic alanine-alanine (cAA) and glycine-glycine (cGG) dipeptides between the gas, water, and crystal phases were carried out using a combination of molecular mechanics, normal mode analysis, and continuum electrostatics. The experimental gas-to-water solvation free energy and the enthalpy of gas-to-crystal transfer of cGG are accurately reproduced by the calculations. The enthalpies of cGG and cAA crystal-to-water transfer are close to the experimental values. A combination of experimental data and normal mode analysis of cGG provides an accurate estimate of the association entropy penalty (loss of rational and translational entropy and gain in vibrational entropy) for "binding" in the crystalline phase of -14.1 cal/mol/k. This is a smaller number than most previous theoretical estimates, but it is similar to previous experimental estimates. Calculated entropies of the crystal phase underestimate the experimental entropy by about 15 cal/mol/k because of neglect of long-range lattice motions. Comparison of the intermolecular interactions in the crystals of cGG and cAA provides a possible explanation of the puzzling decrease in enthalpy, with increasing hydrophobicity seen previously for both cyclic dipeptide dissolution and protein unfolding. This decrease arises from a favorable long-range electrostatic interaction between dipeptide molecules in the crystals, which is attenuated by the more hydrophobic side chains.

Fast prediction and visualization of protein binding pockets with PASS.

PASS (Putative Active Sites with Spheres) is a simple computational tool that uses geometry to characterize regions of buried volume in proteins and to identify positions likely to represent binding sites based upon the size, shape, and burial extent of these volumes. Its utility as a predictive tool for binding site identification is tested by predicting known binding sites of proteins in the PDB using both complexed macromolecules and their corresponding apoprotein structures. The results indicate that PASS can serve as a front-end to fast docking. The main utility of PASS lies in the fact that it can analyze a moderate-size protein (approximately 30 kDa) in under 20 s, which makes it suitable for interactive molecular modeling, protein database analysis, and aggressive virtual screening efforts. As a modeling tool, PASS (i) rapidly identifies favorable regions of the protein surface, (ii) simplifies visualization of residues modulating binding in these regions, and (iii) provides a means of directly visualizing buried volume, which is often inferred indirectly from curvature in a surface representation. PASS produces output in the form of standard PDB files, which are suitable for any modeling package, and provides script files to simplify visualization in Cerius2, InsightII, MOE, Quanta, RasMol, and Sybyl. PASS is freely available to all.