Interactions between hydrophobic moieties steer ubiquitous processes in aqueous media, including the self-organization of biologic matter. Recent decades have seen tremendous progress in understanding these for macroscopic hydrophobic interfaces. Yet, it is still a challenge to experimentally measure hydrophobic interactions (HIs) at the single-molecule scale and thus to compare with theory. Here, we present a combined experimental-simulation approach to directly measure and quantify the sequence dependence and additivity of HIs in peptide systems at the single-molecule scale. We combine dynamic single-molecule force spectroscopy on model peptides with fully atomistic, both equilibrium and nonequilibrium, molecular dynamics (MD) simulations of the same systems. Specifically, we mutate a flexible (GS) peptide scaffold with increasing numbers of hydrophobic leucine monomers and measure the peptides' desorption from hydrophobic self-assembled monolayer surfaces. Based on the analysis of nonequilibrium work-trajectories, we measure an interaction free energy that scales linearly with 3.0-3.4 kT per leucine. In good agreement, simulations indicate a similar trend with 2.1 kT per leucine, while also providing a detailed molecular view into HIs. This approach potentially provides a roadmap for directly extracting qualitative and quantitative single-molecule interactions at solid/liquid interfaces in a wide range of fields, including interactions at biointerfaces and adhesive interactions in industrial applications.

Unravelling the complexity of the macroscopic world relies on understanding the scaling of single-molecule interactions towards integral macroscopic interactions. Here, we demonstrate the scaling of single acid-amine interactions through a synergistic experimental approach combining macroscopic surface forces apparatus experiments and single-molecule force spectroscopy. This experimental framework is ideal for testing the well-renowned Jarzynski's equality, which relates work performed under non-equilibrium conditions with equilibrium free energy. Macroscopic equilibrium measurements scale linearly with the number density of interfacial bonds, providing acid-amine interaction energies of 10.9±0.2 kT. Irrespective of how far from equilibrium single-molecule experiments are performed, the Jarzynski's free energy converges to 11±1 kT. Our results validate the applicability of Jarzynski's equality to unravel the scaling of non-equilibrium single-molecule experiments to scenarios where large numbers of molecules interacts simultaneously in equilibrium. The developed scaling strategy predicts large-scale properties such as adhesion or cell-cell interactions on the basis of single-molecule measurements.

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