Dynamics and thermodynamics of water in PAMAM dendrimers at subnanosecond time scales

Abstract

Atomistic molecular dynamics simulations are used to study generation 5 polyamidoamine (PAMAM) dendrimers immersed in a bath of water. We interpret the results in terms of three classes of water:  buried water well inside of the dendrimer surface, surface water associated with the dendrimer−water interface, and bulk water well outside of the dendrimer. We studied the dynamic and thermodynamic properties of the water at three pH values:  high pH with none of the primary or tertiary amines protonated, intermediate pH with only the primary amines protonated, and low pH with all amines protonated. For all pH values we find that both buried and surface water exhibit two relaxation times:  a fast relaxation (∼1 ps) corresponding to the libration motion of the water and a slow (∼20 ps) diffusional component related to the escaping of water from one domain to another. In contrast for bulk water the fast relaxation is ∼0.4 ps while the slow relaxation is ∼14 ps. These results are similar to those found in biological systems, where the fast relaxation is found to be ∼1 ps while the slow relaxation ranges from 20 to 1000 ps. We used the 2PT MD method to extract the vibrational (power) spectrum and found substantial differences for the three classes of water. The translational diffusion coefficient for buried water is 11−33% (depending on pH) of the bulk value while the surface water is about 80%. The change in rotational diffusion is quite similar:  21−45% of the bulk value for buried water and 80% for surface water. This shows that translational and rotational dynamics of water are affected by the PAMAM−water interactions as well as due to the confinement in the interior of the dendrimer. We find that the reduction of translational or rotational diffusion is accompanied by a blue shift of the corresponding libration motions (∼10 cm^-1 for translation, ∼35 cm^-1 for rotation), indicating higher local force constants for these motions. These effects are most pronounced for the lowest pH, probably because of the increased rigidity caused by the internal charges. From the vibrational density of states we also calculate the enthalpies and entropies of the various waters. We find that water molecules are enthalpically favored near the PAMAM dendrimer:  energy for surface water is ∼0.1 kcal/mol lower to that in the bulk, and ∼0.5−0.9 kcal/mol lower for buried water. In contrast, we find that both the buried and surface water are entropically unfavored:  buried water is 0.9−2.2 kcal/mol lower than the bulk while the surface water is 0.1−0.2 kcal/mol lower. The net result is a thermodynamically unfavored state of the water surrounding the PAMAM dendrimer:  0.4−1.3 kcal/mol higher for buried water and 0.1−0.2 kcal/mol for surface water. This excess free energy of the surface and buried waters is released when the PAMAM dendrimer binds to DNA or metal ions, providing an extra driving force.