Time-dependent trajectory of a one-dimensional Gaussian non-Markovian observable does not reveal its nonequilibrium character.

When analyzing experimental or simulation time-series data, the question arises whether it is possible to tell from the mere observation of the time-dependent trajectory of a one-dimensional observable whether the system is in equilibrium or not. We here consider the nonequilibrium version of the generalized Langevin equation for a Gaussian non-Markovian observable and show that (i) the multipoint joint distribution solely depends on the two-point correlation function and that (ii) for any nonequilibrium process an equilibrium process with uniquely determined parameters can be found that produces the same two-point correlation function. Since the multipoint joint distribution completely characterizes the dynamics of an observable, we conclude that the nonequilibrium character of a system, in contrast to its non-Markovianity, cannot be read off from the one-dimensional trajectory of a Gaussian observable.

Rapid state-recrossing kinetics and slow escape kinetics in non-Markovian systems.

Barrier-crossing processes are often described using Markovian models, where reaction rates are quantified by mean first-passage times (MFPTs), barrier-escape times, or state-correlation functions. However, for systems exhibiting non-Markovian dynamics, where memory effects play a significant role, these metrics can differ substantially, complicating the interpretation of reaction kinetics from experimental or simulated time-series data. Here, we investigate the numerical evaluation of MFPTs and escape times in non-Markovian systems.

Polysialosides Outperform Sulfated Analogs for Binding with SARS-CoV-2.

Both polysialosides and polysulfates are known to interact with the receptor binding domain (RBD) of the SARS-CoV-2 spike protein. However, a comprehensive site by site analysis of their binding affinities and potential synergistic antiviral effects have not been performed. Here, we report on the synthesis of polysialosides with nanomolar binding affinities to spike proteins of SARS-CoV-2 in solution using microscale thermophoresis.

Temporal coarse graining and elimination of slow and periodic dynamics with the generalized Langevin equation for convolution-time-filtered observables.

By exact projection in phase space, we derive the generalized Langevin equation (GLE) for convolution-time-filtered observables. We employ a general convolution filter that directly acts on arbitrary phase-space observables and can involve low-pass, high-pass, band-pass, and band-stop components. The derived filter GLE has the same form and properties as the ordinary GLE but exhibits modified potential, mass, and memory friction kernel.

Fluorinated Hexosome Carriers for Enhanced Solubility of Drugs.

Designing nanomaterials for drug encapsulation is a crucial, yet challenging, aspect for pharmaceutical development. An important step is synthesizing amphiphiles that form stable supramolecular systems for efficient drug loading. In the case of fluorinated drugs, these have superior properties and also a tendency toward reduced water solubility.

Non-Markovian equilibrium and non-equilibrium barrier-crossing kinetics in asymmetric double-well potentials.

Barrier-crossing processes in nature are often non-Markovian and typically occur over an asymmetric double-well free-energy landscape. However, most theories and numerical studies on barrier-crossing rates assume symmetric free-energy profiles. Here, we use a one-dimensional generalized Langevin equation (GLE) to investigate non-Markovian reaction kinetics in asymmetric double-well potentials.

Diffusion and friction from force correlations.

Friction from solute-solvent interactions governs processes from molecular diffusion to protein folding and is fundamental for understanding molecular dynamics in liquids. While the fluctuation-dissipation relation determines friction and diffusivity via the velocity autocorrelation function, this exact relation is inconvenient for interfacial systems involving extended surfaces. For interfacial systems, alternative approximate friction formulas based on the force autocorrelation function (FACF) have been introduced.

Dielectric Properties of Aqueous Electrolytes at the Nanoscale.

Despite the ubiquity of aqueous electrolytes, the effect of salt on water organization remains controversial. We introduce a nonlocal and nonlinear field theory for the nanoscale polarization of ions and water and derive the electrolyte dielectric response as a function of salt concentration to first order in a loop expansion. By comparison with molecular dynamics simulations, we show that rising salt concentration induces a dielectric permittivity decrement and Debye screening in the longitudinal susceptibility but leaves the water structure remarkably unchanged.

Three-Dimensional Polyglycerol-PEG-Based Hydrogels as a Universal High-Sensitivity Platform for SPR Analysis.

We developed a three-dimensional (3D) polyglycerol-poly(ethylene glycol)-based hydrogel as a new biosensing matrix for affinity analysis by surface plasmon resonance to enable a high loading of ligands for small molecule analysis while lacking a carbohydrate structure to reduce nonspecific binding. The hydrogel was synthesized by cross-linking a polyglycerol functionalized with carboxylate and maleimide groups with a dithiolated poly(ethylene glycol) by thiol-click chemistry. We demonstrated that the hydrogel coating enabled a high immobilization capacity of biomolecules and led to less nonspecific binding.

Effect of frequency-dependent shear and volume viscosities on molecular friction in liquids.

The relation between the frequency-dependent friction of a molecule in a liquid and the hydrodynamic properties of the liquid is fundamental for molecular dynamics. We investigate this connection for a water molecule moving in liquid water using all-atomistic molecular dynamics (MD) simulations and linear hydrodynamic theory. We analytically calculate the frequency-dependent friction of a sphere with finite surface slip moving in a viscoelastic compressible fluid by solving the linear transient Stokes equation, including frequency-dependent shear and volume viscosities, both determined from MD simulations of bulk liquid water.

Memory and Friction: From the Nanoscale to the Macroscale.

Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in the transition from a detailed molecular-level description to a simplified, coarse-grained model. It has long been understood that time-dependent (non-Markovian) friction effects are critical for describing the dynamics of many systems, but that they are notoriously difficult to evaluate for complex physical, chemical, and biological systems.

Molecular Stokes-Einstein and Stokes-Einstein-Debye relations for water including viscosity-dependent slip and hydrodynamic radius.

We perform molecular dynamics simulations of liquid water at different temperatures and calculate the water viscosity, the translational and rotational water diffusivities in the laboratory frame as well as in the comoving molecular frame. Instead of interpreting the results as deviations from the Stokes-Einstein and Stokes-Einstein-Debye relations, we describe the translational and rotational diffusivities of water molecules by three models of increasing complexity that take the structural anisotropy of water into account on different levels. We first compare simulation results to analytical predictions for a no-slip sphere and a no-slip ellipsoid.

Quantitative Prediction of Protein-Polyelectrolyte Binding Thermodynamics: Adsorption of Heparin-Analog Polysulfates to the SARS-CoV-2 Spike Protein RBD.

Interactions of polyelectrolytes (PEs) with proteins play a crucial role in numerous biological processes, such as the internalization of virus particles into host cells. Although docking, machine learning methods, and molecular dynamics (MD) simulations are utilized to estimate binding poses and binding free energies of small-molecule drugs to proteins, quantitative prediction of the binding thermodynamics of PE-based drugs presents a significant obstacle in computer-aided drug design. This is due to the sluggish dynamics of PEs caused by their size and strong charge-charge correlations.

Interfacial vs confinement effects in the anisotropic frequency-dependent dielectric, THz and IR response of nanoconfined water.

We investigate the anisotropic frequency-dependent dielectric, THz and IR response of liquid water confined between two planar graphene sheets with force-field- and density-functional-theory-based molecular dynamics simulations. Using spatially resolved anisotropic spectra, we demonstrate the critical role of the volume over which the spectral response is integrated when reporting spatially averaged electric susceptibilities. To analyze the spectra, we introduce a unique decomposition into bulk, interfacial, and confinement contributions, which reveals that confinement effects on the spectra occur only for systems with graphene separation below 1.

pH Modulates Friction Memory Effects in Protein Folding.

Protein folding is an intrinsically multitimescale problem. While it is accepted that non-Markovian effects are present on short timescales, it is unclear whether memory-dependent friction influences long-timescale protein folding reaction kinetics. We combine friction memory-kernel extraction techniques with recently published extensive all-atom simulations of the α3D protein under neutral and reduced pH conditions, and we show that the pH reduction modifies the friction acting on the folding protein by dramatically decreasing the friction memory decay time.

Propensity of hydroxide and hydronium ions for the air-water and graphene-water interfaces from ab initio and force field simulations.

Understanding acids and bases at interfaces is relevant for a range of applications from environmental chemistry to energy storage. We present combined ab initio and force-field molecular dynamics simulations of hydrochloric acid and sodium hydroxide highly concentrated electrolytes at the interface with air and graphene. In agreement with surface tension measurements at the air-water interface, we find that HCl presents an ionic surface excess, while NaOH displays an ionic surface depletion, for both interfaces.

How Thick is the Air-Water Interface?─A Direct Experimental Measurement of the Decay Length of the Interfacial Structural Anisotropy.

The air-water interface is a highly prevalent phase boundary impacting many natural and artificial processes. The significance of this interface arises from the unique properties of water molecules within the interfacial region, with a crucial parameter being the thickness of its structural anisotropy, or "healing depth". This quantity has been extensively assessed by various simulations which have converged to a prediction of a remarkably short length of ∼6 Å.

Derivation of the nonequilibrium generalized Langevin equation from a time-dependent many-body Hamiltonian.

It has become standard practice to describe systems that remain far from equilibrium even in their steady state by Langevin equations with colored noise which is chosen independently from the friction contribution. Since these Langevin equations are typically not derived from first-principle Hamiltonian dynamics, it is not clear whether they correspond to physically realizable scenarios. By exact Mori projection in phase space we derive the nonequilibrium generalized Langevin equation (GLE) for an arbitrary phase-space dependent observable A from a generic many-body Hamiltonian with a time-dependent external force h(t) acting on the same observable A.

Force field for halide and alkali ions in water based on single-ion and ion-pair thermodynamic properties for a wide range of concentrations.

A classical non-polarizable force field for the common halide (F-, Cl-, Br-, and I-) and alkali (Li+, Na+, K+, and Cs+) ions in SPC/E water is presented. This is an extension of the force field developed by Loche et al. for Na+, K+, Cl-, and Br- (JPCB 125, 8581-8587, 2021): in the present work, we additionally optimize Lennard-Jones parameters for Li+, I-, Cs+, and F- ions.

Modeling Water Interactions with Graphene and Graphite via Force Fields Consistent with Experimental Contact Angles.

Accurate simulation models for water interactions with graphene and graphite are important for nanofluidic applications, but existing force fields produce widely varying contact angles. Our extensive review of the experimental literature reveals extreme variation among reported values of graphene-water contact angles and a clustering of graphite-water contact angles into groups of freshly exfoliated (60° ± 13°) and not-freshly exfoliated graphite surfaces. The carbon-oxygen dispersion energy for a classical force field is optimized with respect to this 60° graphite-water contact angle in the infinite-force-cutoff limit, which in turn yields a contact angle for unsupported graphene of 80°, in agreement with the mean of the experimental results.

The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media.

Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral.

Accurate Memory Kernel Extraction from Discretized Time-Series Data.

Memory effects emerge as a fundamental consequence of dimensionality reduction when low-dimensional observables are used to describe the dynamics of complex many-body systems. In the context of molecular dynamics (MD) data analysis, accounting for memory effects using the framework of the generalized Langevin equation (GLE) has proven efficient, accurate, and insightful, particularly when working with high-resolution time series data. However, in experimental systems, high-resolution data are often unavailable, raising questions about the impact of the data resolution on the estimated GLE parameters.

Nanoscopic Interfacial Hydrogel Viscoelasticity Revealed from Comparison of Macroscopic and Microscopic Rheology.

Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects.

Water Structuring Induces Nonuniversal Hydration Repulsion between Polar Surfaces: Quantitative Comparison between Molecular Simulations, Theory, and Experiments.

Polar surfaces in water typically repel each other at close separations, even if they are charge-neutral. This so-called hydration repulsion balances the van der Waals attraction and gives rise to a stable nanometric water layer between the polar surfaces. The resulting hydration water layer is crucial for the properties of concentrated suspensions of lipid membranes and hydrophilic particles in biology and technology, but its origin is unclear.

Data-driven classification of individual cells by their non-Markovian motion.

We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e.