Water: The Essential Liquid in Biophysics : From the Scrutiny of the Complex Nature of its Molecular Interactions to the Hydration Properties of Nanomaterials, Proteins and Membranes, and the Fingerprints of Hydrophobicity.

The simplicity of its molecular formula does not prevent water from exhibiting a complex behavior that becomes exacerbated under the hydration and nanoconfinement conditions typical of biological interfaces. In this chapter, we explore the molecular underpinnings of membrane hydration by examining a fundamental molecular principle: the interplay between local structure and energy that governs water's two-state interaction nature. We introduce the V4S index, a parameter-free, energy-based structural indicator capable of discriminating between tetrahedral coordination and hydrogen-bond (HB) defects-the two inherently preferred local environments in water. Crucially, we employ this metric to provide the first non-arbitrary molecular definition of hydrophobicity: "hydrophobicity is the inability of a system to compensate for HB-defects in its hydration layer at the same energetic cost that bulk water pays for such defects (~ -6 kJ/mol, a value that amounts to only around 30% the energy of a typical HB)". This absolute scale removes the subjective status of hydrophobicity, accurately signaling the θ = 90° contact angle transition and predicting drying regimes in nanoconfined spaces. Applying these concepts to biophysics, we show that the hydration shells of proteins and lipid membranes are significantly enriched in coordination defects compared to bulk water. These "defect-type" molecules are not stochastically distributed but concentrate at functional areas, such as protein binding sites. Finally, we present preliminary results on how this defect-enrichment characterizes the hydration of lipid membranes, offering a high-resolution tool (down to the single-atom level) to map local hydrophobicity and improve our understanding of molecular recognition and membrane permeability.