C02 - Interface dynamics: Bridging stochastic and hydrodynamic descriptions
Head(s): Prof. Dr. Roland Netz (FU Berlin), Prof. Dr. Alexander Mielke (WIAS)
Project member(s): Laura Lavacchi, Sina Zendehroud
Participating institution(s): FU Berlin, WIAS
The properties of liquid water are relevant for a broad range of processes in biology, chemistry, and physics. The goal of this project is to relate macroscopic water properties in bulk and at interfaces to the microscopic structure and thus to the hydrogen bonding pattern between individual water molecules. We are striving at combining three different viewpoints on water dynamics, namely the large scale hydrodynamic description, the mid-scale diffusive description, and the microscopic viewpoint where the hydrogen bond network fluctuates on the pico-second scale. Interfaces play a dominant role in this project since they are abundant in nature and give rise to unique and intereresting phenomena.
Using Markov-state modeling as a diagnostic tool to understand the most elementary kinetic process of breaking a single H-bond between two water molecules that are embedded in the bulk liquid matrix, we could by transition path analysis show that there are different kinetic pathways that compete with each other. Only one of these pathways corresponds to Stillinger’s original switching-of-allegiance description of the local water dynamics, according to which after an H-bond breaking event a new H-bond forms right after. The other dominant pathways involve an intermediate state where no new H-bond is formed, which is a process that has been overlooked in previous MD simulation analysis due to the overwhelmingly large conformational space. These results and in particular the methodological advance will be helpful towards a full understanding of the kinetics of water molecules at interfaces and in particular in the hydration layer around proteins, membranes and other hydrated objects, which will be studied in the next funding period.
On an intermediate length scale and time scale we investigated how the diffusive description of molecular motion is modified in interfacial boundary layers. As an explicit system we analyzed experimental data of drug diffusion through human skin layers and developed a robust method to extract diffusivity and free-energy profiles from experimental concentration profiles recorded at subsequent different times. Multiscale behavior in the molecular penetration dynamics arises because human skin is a multilayered biological barrier and presents competing diffusional and free energetic barriers. Our modeling reveals that the first cell layers in the stratum corneum, which is the 10 micrometer thick top skin layer that consists of dead skin cells, are invaded on the second time scale, while the dermis, which is located underneath the roughly 100 micrometer thick epidermis, is reached only after weeks of diffusion. It would be interesting to add another length and time scale to the problem by including the sub-cellular skin structure by resolving water diffusion in and through cell membranes and organelles.
Lastly, we investigated how interfaces modify the hydrodynamic description, using two different geometries. First, we considered the case of a single interface and studied surface-localised wave phenomena in the presence of viscoelastic interfacial layers. The coupling between the viscous water bulk and the viscoelastic surface creates surface waves with fractional dispersion relations, which is a clear signature of dynamic multiscale behavior. Motivated by experimental results on waves traveling in lipid monolayers at the air-water interface, we derived a non-linear fractional wave equation for surface waves. We will further develop our model to include wave guiding phenomena in cylindrical membrane structures including the coupling to viscoelastic tissue embeddings, which has interesting applications to action potentials in nerve cells. Second, we studied how the hydrodynamic description has to be modified when the water slab between two surfaces reaches sub nanometer thicknesses. In particular we were interested in the transition from hydrodynamic friction between two surfaces that are far apart, to the dry friction limit when there is no water left between the surfaces. Here we could explain the simulation results by a three-scale model that includes the slip between water and the surfaces, the presence of nanometer thick interfacial hydration layers with modified viscous properties, and the bulk water layer. This research direction shall be enlarged to also include frequency-dependent viscosity effect, thereby combining the spatial multiscale model we have developed in the previous funding period with temporal multiscale effects.
Mielke, Alexander and Netz, Roland R. and Zendehroud, Sina (2020) A rigorous derivation and energetics of a wave equation with fractional damping. arXiv . pp. 1-20. (Submitted)
Schulz, R. and von Hansen, Y. and Daldrop, J.O. and Kappler, J. and Noé, F. and Netz, R.R. (2018) Collective hydrogen-bond rearrangement dynamics in liquid water. J. Chem. Phys., 149 (24). -244504. ISSN 0021-9606, ESSN: 1089-7690
Schulz, R. and Hansen, Y. von and Daldrop, J.O. and Kappler, J. and Noé, F. and Netz, R.R. (2018) Markov state modeling reveals competing collective hydrogen bond rearrangements in liquid water. SFB 1114 Preprint 02/2018 . (Unpublished)
Kappler, J. and Shrivastava, S. and Schneider, M.F. and Netz, R.R. (2017) Nonlinear fractional waves at elastic interfaces. Phys. Rev. Fluids, 2 (11). p. 114804.
Kappler, J. and Netz, R.R. (2017) Pulse propagation at interfaces and their possible relevance for biology. Journal Club for Condensed Matter Physics .
Schlaich, A. and Kappler, J. and Netz, R.R. (2017) Hydration Friction in Nanoconfinement: From Bulk via Interfacial to Dry Friction. Nano Lett., 17 (10). pp. 5969-5976.
Schulz, R. and Yamamoto, K. and Klossek, A. and Flesch, R. and Hönzke, S. and Rancan, F. and Vogt, A. and Blume-Peytavi, U. and Hedtrich, S. and Schäfer-Korting, M. and Rühl, E. and Netz, R.R. (2017) Data-based modeling of drug penetration relates human skin barrier function to the interplay of diffusivity and free-energy profiles. PNAS, 114 (14). pp. 3631-3636. ISSN 1091-6490 (online)
Kappler, J. and Netz, R.R. (2015) Multiple surface wave solutions on linear viscoelastic media. EPL, 112 (1). p. 19002.