Hydrophobic collapse and cold denaturation in the Jagla model of water

The Jagla model is a coarse-grained model of water which describes interactions between groups of water molecules by a spherically symmetric potential characterized by a hard core, a linear repulsive ramp and a long-range attractive ramp. The Jagla model qualitatively reproduces the thermodynamics and dynamics of liquid water including density and diffusion anomalies as well as certain chemical properties such the increase of solubility of small hydrophobic particles upon cooling. We examine, via molecular dynamics simulation, the behavior of the bead-on-a-string polymers of various lengths in the Jagla model. We find that such polymers exhibit swelling upon cooling similar to cold denaturation of proteins in water. We show that while for short polymers the swelling is gradual, longer polymers exhibit a first-order-like phase transition between a globular phase at high temperatures to a random coil state at cold temperatures. This transition is associated with the formation of a liquid-polymer phase boundary surrounding the globule and complete dewetting of the central parts of the globule at high temperatures. We study thermodynamics of this transition and find that the entropy, volume, and potential energy of the solvent-random coil system is lower than those of the globule-solvent system. Accordingly the slope of the coil-globule transition line on a PT plane has positive slope. We present simple thermodynamic considerations similar to classical nucleation theory, which relate the temperature of the cold swelling transition to polymer length and relate the dewetting of the globule to its diameter and to the Egelstaff-Widom length scale.