Masahiro KINOSHITA (Kyoto Univ.), Yuko OKAMOTO and Fumio HIRATA
[J. Chem. Phys. 107, 1586 (1997)]
The full RISM equations have been solved for a dipeptide and Met-enkephalin in the SPC/E water using our robust, highly efficient algorithm. Some different conformations of these peptides have been considered. The site - site pair distribution functions and hydration free energies calculated as major output data have been analyzed in detail. It has been shown that solvent plays essential roles in determining the conformation of the peptide and that the RISM theory is a promising tool for taking account of the solvent effects.
The most stable conformation of the peptide in water is the one that has the lowest total energy. The total energy is determined not only from the conformational energy but from the interactions with water molecules which are greatly dependent on the peptide conformations. The conformations of Met-enkephalin determined in NMR experiments are quite different from the lowest-energy conformation in gas phase. We have tested four different conformations including the lowest-energy conformation (conformation 1) and a conformation which is similar to the experimentally determined conformations (conformation 4). It has been shown that conformation 4 is the most stable in water with the lowest total energy in both of the unionized and zwitterion cases. (Actually, we have tested more conformations that we described in the present article, and still conformation 4 is the most stable.) It is interesting that a conformation which is similar to that obtained from the NMR experiments in miceller solutions, is the least stable when it is put in water. Although the effects due to 0.05M CH3COONa in the solution used in the NMR experiments are unknown and need to be investigated in further studies, our results are quite encouraging. When the SPC/E water is replaced by a simple, repulsive potential system, the lowest-energy conformation in gas phase is still the most stable among the four conformations, because the solvation free energy is much less dependent on the conformations than in the water case. Water is clearly distinguished from the simple solvent even when all the site-charges of the peptide are set to zero.
The site-site pair distribution function gAB(r) for atom A (B is a water hydrogen or oxygen) and the conformation from this atom to the hydration free energy is greatly dependent on the neighboring atoms. An atom with a large (negative or positive) site - charge is covalently bonded with oppositely charged atoms with certain core diameters in most cases. Consequently, the first-peak values of gAB(r) for carbonyl carbons, oxygens, and nitrogens are much lower than those for the isolated atoms (imaginary spherical particles). Compared with the hydration free energies of the isolated atoms, the contributions from these atoms of the peptide to the hydration free energy are considerably shifted in more hydrophobic directions. The superposition approximation, in which the entire free energy of a peptide is expressed as the sum of the potential of mean forces between pairs of isolated atoms, is a poor approximation.
The carbonyl oxygen is covalently bonded only with one atom (carbonyl carbon), and it often forms very strong bonding with water-hydrogens. In general, oxygens and nitrogens often have relatively large, negative contributions to the hydration free energy due to the formation of hydrogen bonding. This is particularly true for the two oxygens at the C-terminus of zwitterions. When more than two carbonyl oxygens are close together, well exposed to water, and at least one of them is sufficiently far apart from a hydrophobic portion, strong hydrogen bonding is formed between the carbonyl oxygen and water-hydrogens.
The hydration free energy for a portion of the peptide is also greatly dependent on the neighboring portions. For example, the value for CONH of the unionized dipeptide is in the range from 1-3 kcal/mol, while that of Met-enkephalin (unionized) is more variable, ranging from 2-10 kcal/mol. The value for COOH of the dipeptide (1-5 kcal/mol) is smaller than that of Met-enkephalin (4-10 kcal/mol). (We repeat that we have tested more conformations than we describe in the present article.) This is because Met-enkephalin has larger hydrophobic portions (e.g. the phenyl group) and they are often close to CONH or COOH.
In the course of the present study, we have noticed the following. When a hydrophobic atom gets very close to a hydrophilic atom, the hydration free energy for the former decreases while that for the latter increases. However, the sum of the two hydration free energies tends to increase (i.e. shift in a more hydrophobic direction). Though this could be an artifact of the RISM theory and needs to be investigated further, we are inclined to think that for a larger peptide the contribution from the hydrophobic interaction with water becomes larger. In fact, the values of ((DELTA)(mu)SB-(DELTA)(mu)SA)/(DELTA)(mu)SB are around 0.9 for the dipeptide while they are -0.35 for Met-enkephalin.
We are now combining the solution of the full RISM equations with powerful conformational sampling methods to find the lowest-energy conformation of a peptide in water. This can be done with moderate computational effort on a workstation because the algorithm used for solving the RISM equations is robust and extremely fast.