Statistical Physics of Water in Hydrophobic Nano-Confinement and at Proteins Interfaces

Water is commonly associated with life. This substance affects the living beings in countless aspects and length scales, ranging from molecular biology to climatology. Water exhibits a long series of anomalous behaviors. These anomalies can be rationalized as a consequence of a second critical point in the supercooled region of the liquid phase. Nevertheless, the large part of the phase diagram of supercooled water is to date experimentally inaccessible for the inevitable crystallization of the bulk liquid. Confinement of water in nano-structures is a possible way to prevent the crystallization of molecules. In this thesis we present a coarse-grain model to describe the physical behavior of water at hydrophobic interfaces. The essential feature of the model is the description of water-water interaction via directional and cooperative components of the hydrogen bond (HB). We explore the phase diagram of supercooled water nano-confined between hydrophobic walls. Our results, grounded in statistical physics methods and Monte Carlo simulations, show the presence of a line of first order phase transition in the temperature-pressure plane separating two liquid phases and ending in a liquid-liquid critical point (LLCP). The LLCP universality class approaches the one of the Ising model in two dimensions in the thermodynamic limit, while large deviations are observed for strong confinement. Below the LLCP we find the locus of maxima of correlation length (the Widom line) of the system. Near the LLCP we find a large increase of the thermodynamic response functions consistent with the anomalous behaviors of water. These predictions are confirmed by a percolation description of water molecules based on the definition of cluster of correlated degrees of freedom. Along the phase transition line and the Widom line we recover a power law cluster distribution. At the LLCP the scaling of the percolation quantities agree with the Ising critical exponents. The density, energy and entropy fluctuations that are at the base of the anomalies of water and the existence of its LLCP have also consequences in the context of protein stability. General thermodynamic prediction asserts the existence of a close stability region (SR) in temperature-pressure plane for the native folded state of a protein. Experimental evidences support this theory showing hot-, cold- and pressure-denaturation. Water behavior at the protein interface is expected to be the driving force for the folding-unfolding process. To shed light on this mechanism we study the SR of a folded hydrophobic polymer solvated in the coarse-grain water. Tuning the water-water interaction at the interface and the density of the hydration shell we find an elliptic protein SR in the temperature-pressure plane, qualitatively consistent with available experimental data. Our work contributes to the ongoing debate about the role of hydration water in stabilizing the native protein state. We show here that the physics of water, and in particular its energy, density and entropy fluctuations are sufficient to rationalize the existence of a protein SR with respect to temperature and pressure.