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.