Understanding Humidity-Enhanced Adhesion of Geckos: Deep Neural Network-Assisted Multi-Scale Molecular Modeling.

A higher relative humidity leads to an increased sticking power of gecko feet to surfaces. The molecular mechanism responsible for this increase, however, is not clear. Capillary forces, water mediating keratin-surface contacts and water-induced softening of the keratin are proposed as candidates. In previous work, strong evidence for water mediation is found but indirect effects via increased flexibility are not completely ruled out. This article studies the latter hypothesis by a bottom-up coarse-grained mesoscale model of an entire gecko spatula designed without explicit water particles, so that capillary action and water-mediation are excluded. The elasticity of this model is adjusted with a deep neural network to atomistic elastic constants, including water at different concentrations. Our results show clearly that on nanoscopic flat surfaces, the softening of keratin by water uptake cannot nearly account for the experimentally observed increase in gecko sticking power. Here, the dominant mechanism is the mediation of keratin-surface contacts by intervening water molecules. This mechanism remains important on nanostructured surfaces. Here, however, a water-induced increase of the keratin flexibility may enable the spatula to follow surface features smaller than itself and thereby increase the number of contacts with the surface. This leads to an appreciable but not dominant contribution to the humidity-increased adhesion. Recently, by atomistic grand-canonical molecular dynamics simulation, the room-temperature isotherm is obtained for the sorption of water into gecko keratin, to the authors' knowledge, the first such relation for any beta-keratin. In this work, it relates the equilibrium water content of the keratin to the ambient relative humidity.

Molecular Structure and Dynamics in Wet Gecko ß-Keratin.

Molecular dynamics simulations are performed to investigate the molecular picture of water sorption in gecko keratin and the influence of relative humidity (RH) on the local structure and dynamics in water-swollen keratin. At low RHs, water sorption occurs through hydrogen bonding of water with the hydrophilic groups of keratin. At high RHs (>80%), additional water molecules connect to the first "layer" of amide-connected water molecules (multimolecular sorption) through hydrogen bonds, giving rise to a sigmoidal shape of the sorption isotherm. This causes the formation of large chain-like clusters surrounding the hydrophilic groups of keratin, which upon a further increase of the RH form a percolating water network. An examination of the dynamics of water molecules sorbed in keratin demonstrates that there are two states, bound and free, for water. The dynamics of water in these states depends on the RH. At low RHs, large-scale translational motions of tightly bound water molecules to keratin are needed to remake the entire hydration shell of the keratin. At high RHs (>80%), the water molecules more quickly exchange between the two states. The center-of-mass mean-square displacement of water molecules indicates a hopping motion of water molecules in the keratin solvation shell. The hopping mechanism is more pronounced at RHs < 80%. At higher RHs, water translation through water clusters (water network) dominates. We have observed two regimes for the dependence of dynamical properties on the RH: a regime of gradual increase of the dynamics over 10% < RH < 80% and a regime of drastic dynamic acceleration at RH > 80%. The latter regime begins exactly where the water uptake and the volume swelling also increase much more and where a drastic change in the elastic properties of gecko keratin has been observed. A nearly linear relation between the relaxation times for all dynamical processes and the water content of gecko keratin is observed.

How Does Gecko Keratin Stick to Hydrophilic and Hydrophobic Surfaces in the Presence and Absence of Water? An Atomistic Molecular Dynamics Investigation.

We developed a united-atom model of gecko keratin to investigate the influence of electrostatic and van der Waals contributions to gecko adhesion in scenarios representing gecko's natural habitats. The keratin model assumes that only intrinsically disordered regions directly contact the surface. Contact angles of two generic substrate surfaces that we created match those previously used in AFM experiments on gecko adhesion. Force probe molecular dynamics simulations pulling the keratin from the surface show that the pull-off force increases with increased water content and is inversely related to the water contact angle of the surface. This matches experimental trends. We investigated the number and charge density of keratin and water at the surface, confirming a water-mediating effect and are able to show that keratin folds polar groups to the hydrophilic surface. We decomposed energetic contributions during pull-off, and our computational model shows that in contrast to popular hypotheses, long-range electrostatic interactions determine much of the pull-off process. The contribution of electrostatics to adhesion may be in the order of the van der Waals contributions.

Water uptake by gecko ß-keratin and the influence of relative humidity on its mechanical and volumetric properties.

Grand canonical ensemble molecular dynamics simulations are done to calculate the water content of gecko ß-keratin as a function of relative humidity (RH). For comparison, we experimentally measured the water uptake of scales of the skin of cobra Naja nigricollis. The calculated sigmoidal sorption isotherm is in good agreement with experiment. To examine the softening effect of water on gecko keratin, we have calculated the mechanical properties of dry and wet keratin samples, and we have established relations between the mechanical properties and the RH. We found that a higher RH causes a decrease in the Young's modulus, the yield stress, the yield strain, the stress at failure and an increase in the strain at failure of the gecko keratin. At low RHs (less than 80%), the change in the mechanical properties is small, with most of the changes occurring at higher RHs. The changes in the macroscopic properties of the keratin are explained by the action of sorbed water on the molecular scale. It causes keratin to swell, thereby increasing the distances between amino acids. This has a weakening effect on amino acid interactions and softens the keratin material. The effect is more pronounced at higher RHs.

Gecko Adhesion on Flat and Rough Surfaces: Simulations with a Multi-Scale Molecular Model.

A multiscale modeling approach is used to develop a particle-based mesoscale gecko spatula model that is able to link atomistic simulations and mesoscale (0.44 µm) simulations. It is used to study the detachment of spatulae from flat as well as nanostructured surfaces. The spatula model is based on microscopical information about spatulae structure and on atomistic molecular simulation results. Target properties for the coarse-graining result from a united-atom model of gecko keratin in periodic boundary conditions (PBC), previously developed by the authors. Pull-off forces necessary to detach gecko keratin under 2D PBC parallel to the surface are previously overestimated when only a small region of a spatula is examined. It is shown here that this is due to the restricted geometry (i.e., missing peel-off mode) and not model parameters. The spatula model peels off when pulled away from a surface, both in the molecular picture of the pull-off process and in the force-extension curve of non-equilibrium simulations mimicking single-spatula detachment studied with atomic force microscopy equipment. The force field and spatula model can reproduce experimental pull-off forces. Inspired by experimental results, the underlying mechanism that causes pull-off forces to be at a minimum on surfaces of varying roughnesses is also investigated. A clear sigmoidal increase in the pull-off force of spatulae with surface roughness shows that adhesion is determined by the ratio between spatula pad area and the area between surface peaks. Experiments showed a correlation with root-mean-square roughness of the surface, but the results of this work indicate that this is not a causality but depends on the area accessible.

Gecko adhesion: a molecular-simulation perspective on the effect of humidity.

Gecko adhesion is investigated by molecular dynamics simulations. It is known, that the gecko adhesion system shows increased pull-off forces in humid environments. A coarse-grained model of gecko beta keratin, previously developed in our group, is extended and used to elucidate the molecular mechanisms involved in this humidity effect on adhesion. We show that neither the change of the elastic properties of gecko keratin, nor capillary forces, can solely explain the increased pull-off forces of wet gecko keratin. Instead, we establish a molecular picture of gecko adhesion where the interplay between capillary bridges and a mediator effect of water, enhances pull-off forces, consistent with observations in AFM experiments at high humidities. We find that water density is raised locally, in molecular scale asperities of the gecko keratin and that this increase in local water density smoothes the surface-spatula interface. Water, which is absorbed into the keratin, acts as a mediator, and leads during pull-off to the dominant contribution in the van der Waals energy, because the dispersion interactions between water and surface are primarily opposing the pull-off.