C02 - Water diffusion at biological molecules and interfaces: Bridging stochastic and hydrodynamic descriptions
The unique properties of liquid water are relevant for a broad range of processes in biology, chemistry, and physics, as well as for technological applications [Bal08]. A prominent goal has been to relate macroscopic properties (among those the notable anomalies and singularities of equilibrium as well as transport properties of water) to the microscopic structure and thus to the hydrogen bonding pattern between individual water molecules . This goal has only partly been achieved. As a matter of fact, even the most elementary kinetic process of breaking a single H-bond between two water molecules that are embedded in the bulk liquid matrix is not fully understood: In an early application of transition path sampling, it was proposed that in roughly half of the H-bond breaking events a new bond forms right after [CC98], con.rming Stillinger’s switching-of-allegiance description of the local water dynamics [Sti80]. In later simulation works, the water reorientation during this H-bond switching was shown to occur quite abruptly, but further details could not be extracted due to the overwhelmingly large conformational space [LH08]. The current state of affairs for the kinetics of hydrogen bonds stands in considerable contrast to the relatively well-understood scenarios of hydrophobic solvation and hydrophobic forces, which constitute no substantial theoretical problems[HMB03, SD12]. Clearly, the H-bond and hydration water dynamics is intimately related to e.g. protein and membrane dynamics, thus, a full understanding of protein folding and membrane kinetics requires to include the coupled water dynamics and to clarify the kinetics of the binding and unbinding of water molecules in the hydration layer. In fact, it has been shown in recent experiments [FFCM04] and simulations [RSJ+06], that the interfacial water layer does not play the role of a passive bystander, as has been traditionally assumed, but rather takes an active role and critically determines macromolecular assembly and protein folding. Theoretical progress on the modeling of water dynamics in bulk and at surfaces has been made, but the coupling between solute dynamics and hydration water dynamics is only beginning to be unraveled. In particular, the trifold connection between the stochastic nature of these underlying microscopic processes, the mesoscopic diffusion of water within solvation layers around biomolecules and the macroscopic hydrodynamic description of water motion is not clear. Even in large-scale atomistic simulations, the microsopic dynamics of hydrogen bond breaking/forming between water molecules and polar surface groups poses substantial numerical problems because of the involved long time-scales. In this project we will analyze the hydrogen bond kinetics and the relative water diffusion as observed in atomistic MD simulations using minimum free energy path sampling as well as Markov state modeling and thereby bridge the stochastic description of water molecules at biologically relevant surfaces and the large-scale hydrodynamic description.
The main questions of this project are:
(1) What is the minimal microscopic framework for describing the stochastic process of breaking a single hydrogen bond between two water molecules or – more generally speaking – between a water molecule and a donor or acceptor group on another molecule or surface? This is related to the question of how many water molecules really participate in the breaking of a single hydrogen bond: Just the two water molecules that initially form the hydrogen bond, or also one or two additional water molecules that immediately form a new H-bond once the initial H-bond has been broken (related to Stillinger’s switching-of-allegiance hypothesis)? Are the neighbors of these additional water molecules also important? What are the relevant positional and angular degrees of freedom? In other words, what is the rational way of de.ning the space within which to describe the elementary process H-bond breaking, and how does one avoid an in.nite regression that would ultimately involve the whole ensemble of water molecules in order to describe the breaking of one individual hydrogen bond? Here, minimum free-energy paths in high-dimensional state space will be analyzed and appropriate Markov state models will be constructed that allow to test whether the elementary description chosen re.ects the long-time dynamics correctly; this part corresponds to research direction III de.ned within the SFB as the reduced Markov state model can be viewed as an ef.cient computational approximation of the underlying microscopic water dynamics.
(2) What is the relation of the microscopic kinetic processes involving H-bonds between individual water molecules to the mesoscopic scale description in terms of diffusing water molecules and to the macroscopic hydrodynamic description of water motion? In other words, how does the actual viscosity of bulk water, the slip lengths of surfaces of varying polarity, the friction coef.cients between different surfaces and the mobility of water itself and different solutes in the vicinity of surfaces depend on the elementary processes of hydrogen bond breaking and forming? We aim at a theoretical framework to bridge the local water dynamics with the mesocopic diffusional motion and the large-scale continuum representation, which will in turn be useful for understanding and predicting the dynamics of solvated biomolecules. In particular for systems with long time scales, that is systems showing high friction between polar surfaces because of essentially frozen water layers, the Markov state models will be useful for characterizing rare events and to reliably predict the dynamics of quasi-glassy water layers.
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.