arXiv subjects

Roland R. Netz

Publications and source records attributed to Roland R. Netz.

At least 37 records · Page 2Linked to original sources

arXiv2025

Analysis and Simulation of Generalized Langevin Equations with Non-Gaussian Orthogonal Forces

The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection formalism. We compare parameters derived from different GLE formulations using molecular dynamics simulations of butane's dihedral angle dynamics. Our analysis reveals non-Gaussian contributions of the orthogonal force in different GLEs, being most enhanced for the Mori-GLE, where all non-linearities are relegated to the orthogonal force. We establish a simulation technique that correctly accounts for non-Gaussian orthogonal forces, which is critical for accurately predicting dihedral-angle mean first-passage times. We find that the accuracy of GLE simulations depends significantly on the chosen GLE formalism; the Mori-GLE offers the most numerically robust framework for capturing the statistical observables of the dihedral angle dynamics, provided the correct non-Gaussian orthogonal force distribution is used.

physics.comp-ph↗

arXiv2025

The Importance of Layer-Dependent Molecular Twisting for the Structural Anisotropy of Interfacial Water

The unique structural properties of interfacial water are at the heart of a vast range of important processes in electrochemistry, climate science, and biophysics. At interfaces, water molecules exhibit preferential orientations and an altered intermolecular H-bond connectivity. Characterising this layer-dependent anisotropic structure for such a thin molecular boundary, however, is a veritable challenge, with many important details remaining unknown. Here, we combine a novel depth-resolved second-order spectroscopy with molecular dynamics simulations to study the anisotropic structure at the air-water interface through the H-O-H bending vibration. We firstly show that the experimental nonlinear spectrum contains a large bulk like (quadrupolar) contribution that has hampered the assessment of the interfacial structure in previous investigations. By subtracting this contribution, we uncover the elusive anisotropic interfacial response that quantitatively matches the simulated prediction. Thereafter, by analysing both the vibrational line-shape of the interfacial spectrum and its depth-dependence, we demonstrate that both the molecular tilt and twist angles of water must be highly restricted at the interface, which is confirmed by the simulated orientational distribution. Finally, by analysing the depth and orientation dependence of the bending frequency, we show substantial deviations from the expected behaviour, revealing an anomalous character to the interfacial H-bond network.

physics.chem-ph↗

arXiv2025

Nonlocal dielectric properties of water: the role of electronic delocalisation

The nonlocal dielectric properties of liquid water are studied in the context of {\it ab initio} molecular dynamics simulations based on density functional theory. We calculate the dielectric response from the charge structure factor of the liquid using the fluctuation-dissipation theorem. We show that the dielectric response function of {\it ab initio} simulations differs significantly from that of classical force-fields, both qualitatively and quantitatively. In particular, it exhibits a larger amplitude and a wider range of responding wave numbers. We suggest that the difference is due to the localisation of the electronic charge density inherent in classical force files and Wannier post-treatment of DFT densities. The localised charge models do not reproduce the shape of the response function even for $q$ corresponding to intermolecular distances, and could lead to a significant underestimation of the dielectric response of the liquid by a factor of 10.

physics.chem-ph↗

arXiv2025

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.

cond-mat.soft↗

arXiv2025

Impact of Nanoscopic Impurity Aggregates on Cavitation in Water

The stability of water against cavitation under negative pressures is a phenomenon known for considerable discrepancies between theoretical predictions and experimental observations. Using a combination of molecular dynamics simulations and classical nucleation theory, we explore how nanoscopic hydrocarbon droplets influence cavitation in water. Our findings reveal that while a macroscopic volume of absolutely pure water withstands up to -120 MPa of tension, introducing a single nanoscopic oil droplet, merely a few nanometers in radius, brings this cavitation threshold to around -30 MPa, closely matching the values typically observed in highly controlled experiments. The unavoidable presence of nanoscopic hydrophobic impurities, even in highly purified water used in experiments, imposes a practical limit on achieving the theoretical tensile strength in realistic settings. More broadly, our study highlights the profound impact of nonpolar residues on nucleation phenomena and enhances our understanding of metastability in real-world systems.

cond-mat.soft↗

arXiv2025

Nanoscale defects and heterogeneous cavitation in water

Cavitation, the formation of vapor bubbles in metastable liquids, is highly sensitive to nanoscale surface defects. Using molecular dynamics simulations and classical nucleation theory, we show that pure water confined within defect-free walls can withstand extreme negative pressures, far beyond those observed experimentally. Hydrophobic surfaces trigger heterogeneous cavitation and lower the cavitation pressure magnitude, but not to experimental levels. Notably, a single nanoscopic surface defect capable of hosting a vapor bubble drastically reduces the tensile strength of water. We find that defects as small as 1-2 nm can act as effective cavitation nuclei, a scale smaller than predicted by simple mechanical stability arguments. This discrepancy arises from stochastic fluctuations of the vapor bubble, which can overcome the kinetic free-energy barrier for cavitation. Our findings show that cavitation is predominantly determined by the largest surface defect rather than the overall defect density, emphasizing the importance of eliminating the largest surface imperfections to enhance stability against cavitation.

cond-mat.soft↗

arXiv2025

Non-Markovianity increases transition path probability

Defining low-dimensional reaction coordinates is crucial for analyzing the dynamics of complex systems and for comparison with experiments. The maximal value of the transition-path probability along the reaction coordinate $x$, $p(\mathrm{TP}|x)$, is a common estimator for reaction-coordinate quality by comparing to the theoretical maximal value of 1/2 in the overdamped Markovian limit. We show by analytical arguments and simulations that for non-Markovian dynamics $p(\mathrm{TP}|x)$ is non-monotonic as a function of the memory time and exceeds 1/2 for long memory time. This disqualifies $p(\mathrm{TP}|x)$ as a criterion for reaction coordinate quality.

physics.chem-ph↗

arXiv2024

Water cavitation results from the kinetic competition of bulk, surface and surface-defect nucleation events

Water at negative pressures can remain in a metastable state for a surprisingly long time before it reaches equilibrium by cavitation, i.e. by the formation of vapor bubbles. The wide spread of experimentally measured cavitation pressures depending on water purity, surface contact angle and surface quality implicates the relevance of water cavitation in bulk, at surfaces and at surface defects for different systems. We formulate a kinetic model that includes all three different cavitation pathways and determine the needed nucleation attempt frequencies in bulk, at surfaces and at defects from atomistic molecular dynamics simulations. Our model reveals that cavitation occurs in pure bulk water only for defect-free hydrophilic surfaces with wetting contact angles below 50° to 60° and at pressures of the order of $-$100 MPa, depending only slightly on system size and observation time. Cavitation on defect-free surfaces occurs only for higher contact angles, with the typical cavitation pressure rising to about $-$30 MPa for very hydrophobic surfaces. Nanoscopic hydrophobic surface defects act as very efficient cavitation nuclei and can dominate the cavitation kinetics in a macroscopic system. In fact, a nanoscopic defect that hosts a pre-existing vapor bubble can raise the critical cavitation pressure much further. Our results explain the wide variation of experimentally observed cavitation pressures in synthetic and biological systems and highlight the importance of surface and defect mechanisms for the nucleation of metastable systems.

cond-mat.soft↗

arXiv2024

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. In recent years, the development of advanced numerical friction extraction techniques and methods to simulate the generalized Langevin equation have enabled exploration of the role of time-dependent friction across all scales. We discuss recent applications of these friction extraction techniques and the growing understanding of the role of friction in complex equilibrium and non-equilibrium dynamic many-body systems.

physics.chem-ph↗

arXiv2024

Intrinsic cell-to-cell variance from experimental single-cell motility data

When analyzing the individual positional dynamics of an ensemble of moving objects, the extracted parameters that characterize the motion of individual objects, such as the mean-squared instantaneous velocity or the diffusivity, exhibit a spread that is due to the convolution of three different effects: i) Motion stochasticity, caused by the fluctuating environment and enhanced by limited observation time, ii) measurement errors that depend on details of the detection technique, and iii) the intrinsic parameter variance that characterizes differences between individual objects, the quantity of ultimate interest. We develop the theoretical framework to separate these effects using the generalized Langevin equation (GLE), which constitutes the most general description of active and passive dynamics, as it derives from the general underlying many-body Hamiltonian for the studied system without approximations. We apply our methodology to determine intrinsic cell-to-cell differences of living human breast-cancer cells, algae cells and, as a benchmark, size differences of passively moving polystyrene beads in water. We find algae and human breast-cancer cells to exhibit significant individual differences, reflected by the spreading of the intrinsic mean-squared instantaneous velocity over two orders of magnitude, which is remarkable in light of the genetic homogeneity of the investigated breast-cancer cells and highlights their phenotypical diversity. Quantification of the intrinsic variance of single-cell properties is relevant for infection biology, ecology and medicine and opens up new possibilities to estimate population heterogeneity on the single-organism level in a non-destructive manner. Our framework is not limited to motility properties but can be readily applied to general experimental time-series data.

physics.bio-ph↗

arXiv2024

Predictability Analysis and Prediction of Discrete Weather and Financial Time-Series Data with a Hamiltonian-Based Filter-Projection Approach

The generalized Langevin equation (GLE), derived by projection from a general many-body Hamiltonian, exactly describes the dynamics of an arbitrary coarse-grained variable in a complex environment. However, analysis and prediction of real-world data with the GLE is hampered by slow transient or seasonal data components and time-discretization effects. Machine-learning (ML) techniques work but are computer-resource demanding and difficult to interpret. We show that by convolution filtering, time-series data decompose into fast, transient and seasonal components that each obey Hamiltonian dynamics and, thus, can be separately analyzed by projection techniques. We introduce methods to extract all GLE parameters from highly discretized time-series data and to forecast future data including the environmental stochasticity. For daily-resolved weather data, our analysis reveals non-Markovian memory that decays over a few days. Our prediction accuracy is comparable to commercial (weather.com) and ML long short-term memory (LSTM) methods at a reduced computational cost by a factor of $10^2-10^3$ compared to LSTM. For financial data, memory is very short-ranged and the dynamics effectively is Markovian, in agreement with the efficient-market hypothesis; consequently, models simpler than the GLE are sufficient. Our GLE framework is an efficient and interpretable method for the analysis and prediction of complex time-series data.

physics.data-an↗

arXiv2024

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

By exact projection in phase space we derive the generalized Langevin equation (GLE) for 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 or 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. Our filter-projection approach has diverse applications and can be used to i) systematically derive temporally coarse-grained models by low-pass filtering, ii) undo data smoothening inherent in any experimental measurement process, iii) decompose data exactly into slow and fast variables that can be analyzed separately and each obey Liouville dynamics. The latter application is suitable for removing slow transient or seasonal (i.e. periodic) components that do not equilibrate over simulation or experimental observation time scales and constitutes an alternative to non-equilibrium approaches. We derive integral formulas for the GLE parameters of filtered data for general systems. For the special case of a Markovian system we derive the filter GLE memory kernel in closed form and show that low-band pass smoothening of data induces exponentially decaying memory.

cond-mat.stat-mech↗

arXiv2024

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. In this paper, we introduce advanced sampling methods based on a force-spectroscopy setup and theoretical modeling to overcome this barrier. We exemplify our method with explicit solvent all-atom MD simulations of interactions of anionic PEs that show antiviral properties, namely heparin and linear polyglycerol sulfate (LPGS), with the SARS-CoV-2 spike protein receptor binding domain (RBD). Our prediction for the binding free energy of LPGS to the wild-type RBD matches experimentally measured dissociation constants within thermal energy, kT, and correctly reproduces the experimental PE-length dependence. We find that LPGS binds to the Delta-variant RBD with an additional free-energy gain of 2.4 kT, compared to the wild-type RBD, in accord with electrostatic arguments. We show that the LPGS-RBD binding is solvent-dominated and enthalpy-driven, though with a large entropy-enthalpy compensation. Our method is applicable to general polymer adsorption phenomena and predicts precise binding free energies and re-configurational friction as needed for drug and drug-delivery design.

q-bio.BM↗

arXiv2024

Effect of Frequency-Dependent Viscosity 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 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. We also determine the frequency-dependent friction of a single water molecule moving in liquid water, as defined by the generalized Langevin equation from MD simulation trajectories. By fitting the effective sphere radius and the slip length, the frequency-dependent friction and velocity autocorrelation function from the transient Stokes equation and simulations quantitatively agree. This shows that the transient Stokes equation accurately describes the important features of the frequency-dependent friction of a single water molecule in liquid water and thus applies down to molecular length and time scales, provided accurate frequency-dependent viscosities are used. The frequency dependence of the shear viscosity of liquid water requires careful consideration of hydrodynamic finite-size effects to observe the asymptotic hydrodynamic power-law tail. In contrast, for a methane molecule moving in water, the frequency-dependent friction cannot be predicted based on a homogeneous model, which suggests, supported by the extraction of a frequency-dependent surface-slip profile, that a methane molecule is surrounded by a finite-thickness hydration layer with viscoelastic properties that are significantly different from bulk water.

cond-mat.soft↗

arXiv2024

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 with a far-reaching impact on natural and industrial processes. Water molecules behave differently at the interface compared to the bulk, exhibiting anisotropic orientational distributions, reduced intermolecular connectivity in the hydrogen bond network, and significantly slower dynamics. Despite many decades of research, the thickness of the structural anisotropy in the interfacial layer remains controversial, with a direct experimental measurement being absent. In this study, we utilise an advancement in non-linear vibrational spectroscopy to gain access to this important parameter. Combining phase-resolved sum- and difference-frequency generation (SFG and DFG) responses, we directly measure the decay in structural anisotropy of the air-water interface. We find a decay length of ~6-8Å, in excellent agreement with depth-resolved SFG spectra calculated from ab initio parameterised molecular dynamics (MD) simulations. The result reveals surprisingly short anisotropic orientational correlations from the interfacial layer that are even shorter than in the bulk. Furthermore, the recorded SFG and DFG responses are decomposed into a vibrationally resonant and non-resonant contribution through isotopic exchange measurements. Through their separate analysis, we show that the resonant response is a sensitive probe of the structural anisotropy at the interface whereas the non-resonant contribution contains a significant isotropic contribution from the bulk and therefore only partially reports on the interfacial structure. This finding places stringent restrictions on the insight available through both purely non-resonant and second-order intensity studies.

physics.chem-ph↗

arXiv2024

Quantifying the efficiency of principal signal transmission modes in proteins

On the microscopic level, biological signal transmission relies on coordinated structural changes in allosteric proteins that involve sensor and effector modules. The timescales and microscopic details of signal transmission in proteins are often unclear, despite a plethora of structural information on signaling proteins. Based on linear-response theory, we develop a theoretical framework to define frequency-dependent force and displacement transmit functions through proteins and, more generally, viscoelastic media. Transmit functions quantify the fraction of a local time-dependent perturbation at one site, be it a deformation, a force, or a combination thereof, that survives at a second site. They are defined in terms of equilibrium fluctuations from simulations or experimental observations. We apply the framework to our all-atom molecular dynamics simulation data of a parallel, homodimeric coiled-coil (CC) motif that connects sensor and effector modules of a blue-light-regulated histidine kinase from bacterial signaling systems extensively studied in experiments. Our analysis reveals that signal transmission through the CC is possible via shift, splay, and twist deformation modes. Based on the results of mutation experiments, we infer that the most relevant mode for the biological function of the histidine kinase protein is the splay deformation.

cond-mat.soft↗

arXiv2024

Rapid state-recrossing kinetics in non-Markovian systems

The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that satisfy Markovian dynamics, it is not clear how to interpret MFPTs for experimental and simulation time-series data generated by non-Markovian systems. Here, we simulate a one-dimensional generalized Langevin equation (GLE) in a bistable potential and compare two related numerical methods for evaluating MFPTs: one that only incorporates information about first arrivals between subsequent states and is equivalent to calculating the waiting time, or dwell time, and one that incorporates information about all first-passages associated with a given barrier-crossing event and is therefore typically employed to enhance numerical sampling. In the Markovian limit, the two methods are equivalent. However, for significant memory times, the two methods suggest dramatically different reaction kinetics. By focusing on first-passage distributions, we systematically reveal the influence of memory-induced rapid state-recrossing on the MFPTs, which we compare to various other numerical or theoretical descriptions of reaction times. Overall, we demonstrate that it is necessary to consider full first-passage distributions, rather than just the mean barrier-crossing kinetics when analyzing non-Markovian time series data.

cond-mat.stat-mech↗

arXiv2024

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

Deviations between macrorheological and particle-based microrheological measurements are often considered 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 in fact 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. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for a nanoscopic interfacial shell around tracers with viscoelastic properties that significantly deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable with the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is generally applicable to different kinds of viscoelastic fluids and particles.

cond-mat.soft↗