The hydration of hydrophobic solutes is intimately related to the spontaneous formation of cavities in water through ambient density fluctuations. Information theory-based modeling and simulations have shown that water density fluctuations in small volumes are approximately Gaussian. For limiting cases of microscopic and macroscopic volumes, water density fluctuations are known exactly and are rigorously related to the density and isothermal compressibility of water. Here, we develop a theory—interpolated gaussian fluctuation theory (IGFT)—that builds an analytical bridge to describe water density fluctuations from microscopic to molecular scales. This theory requires no detailed information about the water structure beyond the effective size of a water molecule and quantities that are readily obtained from water’s equation-of-state—namely, the density and compressibility. Using simulations, we show that IGFT provides a good description of density fluctuations near the mean, that is, it characterizes the variance of occupancy fluctuations over all solute sizes. Moreover, when combined with the information theory, IGFT reproduces the well-known signatures of hydrophobic hydration, such as entropy convergence and solubility minima, for atomic-scale solutes smaller than the crossover length scale beyond which the Gaussian assumption breaks down. We further show that near hydrophobic and hydrophilic self-assembled monolayer surfaces in contact with water, the normalized solvent density fluctuations within observation volumes depend similarly on size as observed in the bulk, suggesting the feasibility of a modified version of IGFT for interfacial systems. Our work highlights the utility of a density fluctuation-based approach toward understanding and quantifying the solvation of non-polar solutes in water and the forces that drive them toward surfaces with different hydrophobicities.

In this study, NMR and molecular dynamics simulations were employed to study IgG1 F C binding to multimodal surfaces. Gold nanoparticles functionalized with two multimodal cation-exchange ligands (Capto and Nuvia) were synthesized and employed to carry out solutionphase NMR experiments with the F C . Experiments with perdeuterated 15 N-labeled F C and the multimodal surfaces revealed micromolar residuelevel binding affinities as compared to millimolar binding affinities with these ligands in free solution, likely due to cooperativity and avidity effects. The binding of F C with the Capto ligand nanoparticles was concentrated near an aliphatic cluster in the C H 2/C H 3 interface, which corresponded to a focused hydrophobic region. In contrast, binding with the Nuvia ligand nanoparticles was more diffuse and corresponded to a large contiguous positive electrostatic potential region on the side face of the F C . Results with lower-ligand-density nanoparticles indicated a decrease in binding affinity for both systems. For the Capto ligand system, several aliphatic residues on the F C that were important for binding to the higher-density surface did not interact with the lower-density nanoparticles. In contrast, no significant difference was observed in the interacting residues on the F C to the high-and low-ligand density Nuvia surfaces. The binding affinities of F C to both multimodal-functionalized nanoparticles decreased in the presence of salt due to the screening of multiple weak interactions of polar and positively charged residues. For the Capto ligand nanoparticle system, this resulted in an even more focused hydrophobic binding region in the interface of the C H 2 and C H 3 domains. Interestingly, for the Nuvia ligand nanoparticles, the presence of salt resulted in a large transition from a diffuse binding region to the same focused binding region determined for Capto nanoparticles at 150 mM salt. Molecular dynamics simulations corroborated the NMR results and provided important insights into the molecular basis of F C binding to these different multimodal systems containing clustered (observed at high-ligand densities) and nonclustered ligand surfaces. This combined biophysical and simulation approach provided significant insights into the interactions of F C with multimodal surfaces and sets the stage for future analyses with even more complex biotherapeutics.

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