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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., Comment: 26 pages, 6 figures

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{\deg} to 60{\deg} 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.

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., Comment: 10 pages main text including 6 figures , 3pages methods, 15 pages supplementary information including 8 more figures

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., Comment: 16 pages, 5 figures, 25 pages of Supplementary Information attached at the end

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.

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.

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., Comment: 25 pages, 13 figures

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 ~6-8\r{A}, 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., Comment: 18 pages, 4 figures, 1 table, supplementary information

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.

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., Comment: 7 pages, 5 figures

We study the non-Markovian folding dynamics of the $\alpha$3D protein under low- and neutral-pH conditions. Recently published all-atom simulations of $\alpha$3D by the Shaw group reveal that lowering the pH significantly reduces both native and non-native salt-bridge interactions, which dominate the folding dynamics. Here, we demonstrate that this physiochemical modulation directly perturbs the folding friction, which we evaluate using non-Markovian memory-kernel-extraction techniques. In doing so, we find that the reduction in pH not only decreases the magnitude of the time-dependent friction acting on the protein but also more dramatically shortens the time scale of the friction memory effects. As a result, the folding dynamics in the low pH system are well described by a purely Markovian model. In the neutral pH system, however, the memory time scale is of the same order as the folding time and is accelerated by a factor of 6 compared to a Markovian model prediction. We demonstrate that this memory-induced barrier-crossing speed-up is predicted by non-Markovian reaction-kinetic theories, confirming that non-Markovian models are, in general, necessary for a quantitative description of protein folding dynamics., Comment: 4 pages, 4 figures

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 is often unavailable, raising questions about the impact of the data resolution on the estimated GLE parameters. This study demonstrates that direct memory extraction remains accurate when the discretization time is below the memory time. To obtain memory functions reliably even when the discretization time exceeds the memory time, we introduce a Gaussian Process Optimization (GPO) scheme. This scheme minimizes the deviation of discretized two-point correlation functions between MD and GLE simulations and is able to estimate accurate memory kernels as long as the discretization time stays below the longest time scale in the data, typically the barrier crossing time.

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., Comment: 25 pages, 4 figures, 52 pages of Supporting Information

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 (CR). The GLE is the most general model for active or passive motion of organisms and particles and in particular includes non-Markovian effects, i.e., the trajectory memory of its past. We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas, our method that is based on motion trajectories offers wide-ranging applications in biology and medicine., Comment: 15 Pages main text including 5 figures, then 22 Pages Supplementary Information (SI) including 8 figures and 2 video files

When analyzing experimental or simulation time-series data, the question arises whether it is possible to tell from a one-dimensional time-dependent trajectory whether the system is in equilibrium or not. We here consider the non-equilibrium version of the generalized Langevin equation for a Gaussian observable and show that i) the multi-point joint distribution solely depends on the two-point correlation function and that ii) the two-point correlation function for a non-equilibrium process is identical to an equilibrium process with uniquely determined parameters. Since the multi-point joint distribution completely characterizes the dynamics of an observable, this means that the non-equilibrium character of a system, in contrast to its non-Markovianity, cannot be read off from a one-dimensional trajectory., Comment: arXiv admin note: text overlap with arXiv:2310.00748

It has been become standard practice to describe steady-state non-equilibrium phenomena by Langevin equations with colored noise and time-dependent friction kernels that do not obey the fluctuation-dissipation theorem, but 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 non-equilibrium generalized Langevin equation (GLE) from a generic many-body Hamiltonian with a time-dependent force h(t) acting on an arbitrary phase-space dependent observable $A$. The GLE is obtained in explicit form to all orders in $h(t)$. For non-equilibrium observables that correspond to a Gaussian process, the resultant GLE has the same form as the equilibrium Mori GLE, in particular the memory kernel is proportional to the total force autocorrelation function. This means that the extraction and simulation methods developed for equilibrium GLEs can be used also for non-equilibrium Gaussian variables. This is a non-trivial and very useful result, as many observables that characterize non-equilibrium systems display Gaussian statistics. For non-Gaussian non-equilibrium variables correction terms appear in the GLE and in the relation between the complementary force autocorrelations and the memory kernels, which are explicitly given in term of cubic correlation functions of $A$. Interpreting the time-dependent force h(t) as a stochastic process, we derive non-equilibrium corrections to the fluctuation-dissipation theorem and methods to extract all GLE parameters from experimental or simulation data, thus making our non-equilibrium GLE a practical tool to study and model general non-equilibrium systems.

Molecular isomerization kinetics in liquid solvents are determined by a complex interplay between the friction acting on a rotating dihedral due to interactions with the solvent, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the free energy profile over which a dihedral rotates. Currently, it is not understood how these quantities are related at the molecular scale. Here, we combine molecular dynamics simulations of isomerizing n-alkane chains and dipeptide molecules in mixed water-glycerol solvents with memory-kernel extraction techniques to directly evaluate the frequency-dependent friction acting on a rotating dihedral. We extract the friction and isomerization times over a range of glycerol concentrations and accurately evaluate the relationships between solvent viscosity, isomerization kinetics, and dihedral friction. We show that the total friction acting on a rotating dihedral does not scale linearly with solvent viscosity, thus violating the Stokes-Einstein relation. Additionally, we demonstrate that the kinetics of isomerization are significantly faster compared to the Kramers prediction in the overdamped limit. We suggest that isomerization kinetics are determined by the multi-time-scale friction coupling between a rotating dihedral and its solvent environment, which results in non-Markovian kinetic speed-up effects., Comment: 9 pages, 4 figures

Nanoscale fluid transport is typically pictured in terms of atomic-scale dynamics, as is natural in the real-space framework of molecular simulations. An alternative Fourier-space picture, that involves the collective charge fluctuation modes of both the liquid and the confining wall, has recently been successful at predicting new nanofluidic phenomena such as quantum friction and near-field heat transfer, that rely on the coupling of those fluctuations. Here, we study the charge fluctuation modes of a two-dimensional (planar) nanofluidic channel. Introducing confined response functions that generalize the notion of surface response function, we show that the channel walls exhibit coupled plasmon modes as soon as the confinement is comparable to the plasmon wavelength. Conversely, the water fluctuations remain remarkably bulk-like, with significant confinement effects arising only when the wall spacing is reduced to 7 A. We apply the confined response formalism to predict the dependence of the solid-water quantum friction and thermal boundary conductance on channel width for model channel wall materials. Our results provide a general framework for Coulomb interactions of fluctuating matter in nanoscale confinement.

We investigate the effect of pectin on the structure and ion transport properties of the room-temperature ionic liquid electrolyte 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) using molecular dynamics simulations. We find that pectin induces intriguing structural changes in the electrolyte that disrupt large ionic aggregates and promote the formation of smaller ionic clusters, which is a promising finding for ionic conductivity. Due to pectin in [BMIM][PF6] electrolytes, the diffusion coefficient of cations and anions is observed to decrease by a factor of four for a loading of 25 wt. % of pectin in [BMIM][PF6] electrolyte. A strong correlation between the ionic diffusivities (D) and ion-pair relaxation timescales ($\tau_C$) is observed such that D~$\tau_C^{-0.75}$ for cations and D~$\tau_C^{-0.82}$ for anions. The relaxation timescale exponents indicate that the ion transport mechanisms in pectin-[BMIM][PF6] electrolytes are slightly distinct from those found in neat [BMIM][PF6] electrolytes (D~$\tau_C^{-1}$). Since pectin marginally affects ionic diffusivities at the gain of smaller ionic aggregates and viscosity, our results suggest that pectin-IL electrolytes offer improved properties for battery applications, including ionic conductivity, mechanical stability, and biodegradability., Comment: Accepted for publication in the Journal of Chemical Physics

Using all-atom molecular dynamics simulations, we report the structure and ion transport characteristics of a new class of solid polymer electrolytes that contain biodegradable and mechanically stable biopolymer pectin. We simulate a highly conducting ethylene carbonate (EC) as a solvent for lithium-trifluoromethanesulfonimide (LiTFSI) salt containing different weight percentages of pectin. Our simulations reveal that the pectin chains reduce the coordination numbers of lithium ions around the counterions (and vice-versa) because of stronger lithium-pectin interactions compared to lithium-TFSI interactions. Further, the pectin is found to promote smaller ionic aggregates over larger ones, contrary to results typically reported for liquid and polymer electrolytes. We observe that the loading of pectin in EC-LiTFSI electrolytes increases the viscosity ($\eta$) and relaxation timescales ($\tau_c$), indicating higher mechanical stability and, consequently, the mean squared displacements, diffusion coefficients (D), and the Nernst-Einstein conductivity ($\sigma_{NE}$) decrease. Interestingly, while the lithium diffusivities are related to the ion-pair relaxation timescales as $D_+\sim \tau_c^{-3.1}$, the TFSI$^-$ diffusivities exhibit excellent correlations with ion-pair relaxation timescales as $D_-\sim \tau_c^{-0.95}$. On the other hand, the NE conductivities are dictated by distinct transport mechanisms and scales with ion-pair relaxation timescale as $\sigma_{NE}\sim \tau_c^{-1.85}$.

Despite the ubiquity of nanoconfined aqueous electrolytes, a theoretical framework that accounts for the nonlinear coupling of water and ion polarization is still missing. We introduce a nonlocal and nonlinear field theory for the nanoscale polarization of ions and water and derive the electrolyte dielectric properties as a function of salt concentration to first order in a loop expansion. Classical molecular dynamics simulations are favorably compared with the calculated dielectric response functions. The theory correctly predicts the dielectric permittivity decrement with rising salt concentration and furthermore shows that salt induces a Debye screening in the longitudinal susceptibility but leaves the short-range water organization remarkably unchanged., Comment: 6 pages, 3 figures

Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing to subtract the periodic boundary condition effects. By this we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from rather small simulation boxes., Comment: 6 pages, 4 figures, 9 pages of Appendices

When described by a low-dimensional reaction coordinate, the rates of protein folding are determined by a subtle interplay between free-energy barriers and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive, and one typically evaluates it indirectly via memoryless reaction rate theories. Here, using memory-kernel extraction methods founded on a generalised Langevin equation (GLE) formalism, we directly calculate the memory-dependent friction for eight fast-folding proteins, taken from a published set of large-scale molecular dynamics protein simulations. Our results reveal that, contrary to common expectation, friction is more important than free energy barriers in determining protein folding rates, particularly for larger proteins. We also show that proteins fold in a regime where the finite decay time of friction significantly reduces the folding times, in some instances by as much as a factor of 10, compared to predictions based on memoryless friction., Comment: 10 pages, 4 figures

Based on a Hamiltonian that incorporates the elastic coupling between a tracer and active particles, we derive a generalized Langevin model for the non-equilibrium mechanical response of active viscoelastic biomatter. Our model accounts for the power-law viscoelastic response of the embedding polymeric network as well as for the non-equilibrium energy transfer between active and tracer particles. Our analytical expressions for the frequency-dependent response function and the positional autocorrelation function agree nicely with experimental data for red blood cells and actomyosin networks with and without ATP. The fitted effective active-particle temperature, elastic constants and effective friction coefficients of our model allow straightforward physical interpretation., Comment: 6 pages, 2 figures; supplemental material (16 pages, 5 figures) is appended

We introduce a generalized Langevin model system for different non-Markovian effects in the well and barrier regions of a potential, and use it to numerically study the dependence of the barrier-crossing time. In the appropriate limits, our model interpolates between the theoretical barrier-crossing-time predictions by Grote and Hynes (GH), as well as by Pollak et al., which for a single barrier memory time can differ by several orders of magnitude. Our model furthermore allows to test an analytic rate theory for space-inhomogeneous memory, which disagrees with our numerical results in the long well-memory regime. In this regime, we find that short barrier memory decreases the barrier-crossing time as compared to long barrier memory. This is in contrast with the short well-memory regime, where both our numerical results and GH theory predict an acceleration of the barrier crossing time with increasing barrier memory time. Both effects, the `Markovian-barrier acceleration' and GH `non-Markovian-barrier acceleration' can be understood from a committor analysis. Our model combines finite relaxation times of orthogonal degrees of freedom with a space-inhomogeneous coupling to such degrees, and represents a step towards more realistic modeling of physical reaction coordinates.

Signatures of solvated excess protons in infrared difference absorption spectra, such as the continuum band between the water bend and stretch bands, have been experimentally known for a long time, but the theoretical basis for linking spectral signatures with the microscopic proton-transfer mechanism so far relied on normal-mode analysis. We analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric acid solutions by trajectory-decomposition techniques. The continuum band in the 2000 - 3000 cm$^{-1 }$ range is shown to be due to normal-mode oscillations of temporary H$_3$O$^+$ complexes. An additional prominent peak at 400 cm$^{-1}$ reports on the coupling of excess-proton motion to the relative vibrations of the two flanking water molecules. The actual proton transfer between two water molecules, which for large water separations involves crossing of a barrier and thus is not a normal mode, is characterized by two characteristic time scales: Firstly, the waiting time for transfer to occur in the range of 200 - 300 fs, which leads to a broad weak shoulder around ~100 cm$^{-1}$, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm$^{-1}$ and agrees in location and width with previous experimental mid-infrared spectra.

We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a Generalized Langevin Equation (GLE) for a general interacting many-body system. The resulting GLE includes i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, ii) a random force term that explicitly depends on the initial state of the system, and iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general non-linear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The non-linear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular, the non-linear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method to the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that non-linear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged non-linear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits adiabatic contributions at and below the vibrational time scales, but also much slower non-adiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Compared to the gas phase, hydration softens both stretch and bend potentials, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, non-adiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates and thus a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and non-adiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and non-adiabatic friction contributions for both, the stretch and bend modes in liquid water. Thus, the understanding of infrared vibrational frequencies and line shapes is considerably advanced by the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids.

Recent experiments have reported lower critical solution temperature (LCST) phase behavior of aqueous solutions of proteins induced by multivalent ions, where the solution phase separates upon heating. This phenomenon is linked to complex hydration effects that result in a net entropy gain upon phase separation. To decipher the underlying molecular mechanism, we use all-atom molecular dynamics simulations along with the two-phase thermodynamic method for entropy calculation. Based on simulations of a single BSA protein in various salt solutions (NaCl, CaCl_2, MgCl_2, and YCl_3) at temperatures (T) ranging 283-323 K, we find that the cation-protein binding affinity increases with T, reflecting its thermodynamic driving force to be entropic in origin. We show that in the cation binding process, many tightly bound water molecules from the solvation shells of a cation and the protein are released to the bulk, resulting in entropy gain. To rationalize the LCST behavior, we calculate the {\zeta}-potential that shows charge inversion of the protein for solutions containing multivalent ions. The {\zeta}-potential increases with T. Performing simulations of two BSA proteins, we demonstrate that the protein-protein binding is mediated by multiple cation bridges and involves similar dehydration effects that cause a large entropy gain which more than compensates for rotational and translational entropy losses of the proteins. Thus, the LCST behavior is entropy-driven, but the associated solvation effects are markedly different from hydrophobic hydration. Our findings have direct implications for tuning the phase behavior of biological and soft-matter systems, e.g., protein condensation and crystallization.

A stochastic theory is developed to predict the spectral signature of proton-transfer processes and applied to infrared spectra computed from ab initio molecular-dynamics simulations of a single H$_5$O$_2{}^{+}$ cation. By constraining the oxygen atoms to a fixed distance, this system serves as a tunable model for general proton-transfer processes with variable barrier height. Three spectral contributions at distinct frequencies are identified and analytically predicted: the quasi-harmonic motion around the most probable configuration, amenable to normal-mode analysis, the contribution due to transfer paths when the proton moves over the barrier and a shoulder for low frequencies stemming from the stochastic transfer-waiting-time distribution; the latter two contributions are not captured by normal-mode analysis but exclusively report on the proton-transfer kinetics. In accordance with reaction kinetic theory, the transfer-waiting-contribution frequency depends inverse exponentially on the barrier height, whereas the transfer-path-contribution frequency is rather insensitive to the barrier height.

Saliva is primarily composed of water, but additionally includes a variety of organic and inorganic substances such as salt, proteins, peptides, mucins, virions, etc. The presence of such solutes affects the evaporation time of respiratory droplets that are sedimenting in air, and thereby the airborne transmission of infections. From solutions of the coupled heat-conduction and water-diffusion equations within the droplet and in the ambient vapor phase, we find that the solute-induced water vapor-pressure reduction considerably slows down the evaporation process and dominates the solute-concentration dependence of the droplet evaporation time. The evaporation-induced solute-concentration gradient near the droplet surface, which is accounted for using a two-stage evaporation model, is found to further intensify the slowing down of the drying process. On the other hand, the presence of solutes is found to reduce evaporation cooling of the droplet, which causes a slight decrease in the evaporation time. Overall, the first two effects are dominant, meaning that the droplet evaporation time increases in the presence of solutes. The solute-concentration dependence of the water diffusivity inside the droplet does not significantly change the evaporation time. Finally, crust formation on the droplet surface is found to increase the final equilibrium size of the droplet., Comment: 40 pages, 8 figures

Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics and condensed matter physics. This review is intended as a toolbox for fluids at the nanometre scale. After presenting the basic equations that govern fluid behaviour in the continuum limit, we will show how these equations break down and new properties emerge in molecular scale confinement.

A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and non-equilibrium stationary states. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy, is constructed. For the stationary distribution the free entropy becomes maximal and its time derivative is minimal and vanishes. Thus, the free entropy characterizes equilibrium as well as non-equilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e. if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the non-equilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. Active particle models can be described in the same general framework, which thereby allows to characterize their entropy production not only in the stationary state but also in the approach to the stationary non-equilibrium state. Finally, the connection to non-equilibrium thermodynamics formulations that include the reservoir entropy production is discussed.

A combined experimental/theoretical method to simultaneously determine diffusivity and free-energy profiles of particles that penetrate into inhomogeneous hydrogel systems is presented. As the only input, arbitrarily normalized concentration profiles from fluorescence intensity data of labeled tracer particles for different penetration times are needed. The method is applied to dextran molecules of varying size which penetrate into hydrogels of polyethylene-glycol (PEG) chains with different lengths that are covalently cross-linked by hyperbranched polyglycerol (hPG) hubs. Extracted dextran bulk diffusivities agree well with fluorescence correlation spectroscopy data obtained separately. Scaling laws for dextran diffusivities and free energies inside the hydrogel are identified as a function of the dextran mass. An elastic free-volume model that includes dextran as well as PEG linker flexibility describes the repulsive dextran-hydrogel interaction free energy, which is of steric origin, quantitatively and furthermore suggests that the hydrogel mesh-size distribution is rather broad and particle penetration is dominated by large hydrogel pores. Particle penetration into hydrogels is for steric particle-hydrogel interactions thus suggested to be governed by an elastic size-filtering mechanism that involves the tail of the hydrogel pore-size distribution.

The effect of evaporation on droplet sedimentation times is crucial for estimating the risk of infection from virus-containing airborne droplets. For droplet radii in the range 100 nm < R < 60 {\mu}m, evaporation can be described in the stagnant-flow approximation and is diffusion limited. Analytical equations are presented for the droplet evaporation rate, the time-dependent droplet size and the sedimentation time, including the significant effect of evaporation cooling. Evaporation makes the time for large droplets to sediment much longer and thus significantly increases the viral air load. Using recent estimates for SARS-CoV-2 concentrations in sputum and droplet production rates while speaking, a single infected person that constantly speaks without a mouth cover produces a total air load of more than 10^4 virions. In a mid-size closed room, this leads to a viral inhalation frequency of at least 2.5 per minute. Low relative humidity, as encountered inside buildings in winter and in airliners, speeds evaporation and thus keeps initially larger droplets suspended in air., Comment: New version contains estimate of number of virions sedimenting in air in steady state and effect of air-exchange rate in closed room

We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air interface, which is an experimental setup that is relevant for understanding wave propagation in biological membranes. We study the scaling regime where the relevant horizontal length scale is much larger than the vertical length scale and provide a rigorous limit leading to a fractionally-damped wave equation for the membrane. We provide the associated existence results via linear semigroup theory and show convergence of the solutions in the scaling limit. Moreover, based on the energy-dissipation structure for the full model, we derive a natural energy and a natural dissipation function for the fractionally-damped wave equation with a time derivative of order 3/2

Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with rigorous theoretical arguments, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids; as a consequence, its origin is non-local in time. Concomitantly, the molecules experience Brownian forces that display persistent correlations and long-lasting memory. A critical test of the generalised Stokes-Einstein relation, mapping the friction of single molecules to the viscoelastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield novel insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.

Energy dissipation in water is very fast and more efficient than in many other liquids. This behavior is commonly attributed to the intermolecular interactions associated with hydrogen bonding. Here, we investigate the dynamic energy flow in the hydrogen-bond network of liquid water by a pump-probe experiment. We resonantly excite intermolecular degrees of freedom with ultrashort single-cycle terahertz pulses and monitor its Raman response. By using ultrathin sample-cell windows, a background-free bipolar signal whose tail relaxes mono-exponentially is obtained. The relaxation is attributed to the molecular translational motions, using complementary experiments, force-field and ab initio molecular dynamics simulations. They reveal an initial coupling of the terahertz electric field to the molecular rotational degrees of freedom whose energy is rapidly transferred, within the excitation pulse duration, to the restricted-translational motion of neighboring molecules. This rapid energy transfer may be rationalized by the strong anharmonicity of the intermolecular interactions.

Using classical as well as ab-initio molecular dynamics simulations, we calculate the frequency-dependent shear viscosity of pure water and water-glycerol mixtures. In agreement with recent experiments, we find deviations from Newtonian-fluid behavior in the THz regime. Based on an extension of the Maxwell model, we introduce a viscoelastic model to describe the observed viscosity spectrum of pure water. We find four relaxation modes in the spectrum which we attribute to i) hydrogen-bond network topology changes, ii) hydrogen-bond stretch vibrations of water pairs, iii) collective vibrations of water molecule triplets, and iv) librational excitations of individual water molecules. Our model quantitatively describes the viscoelastic response of liquid water on short timescales, where the hydrodynamic description via a Newtonian-fluid model breaks down., Comment: Supplemental material is provided as ancillary file

Absorption spectra of liquid water at 300 K are calculated from both classical and density functional theory molecular dynamics simulation data, which together span from 1 MHz to hundreds of THz, agreeing well with experimental data qualitativley and quantitavely over the entire range, including the IR modes, the microwave peak, and the intermediate THz bands. The spectra are decomposed into single-molecular and collective components as well as into components due to molecular reorientations and changes in induced intramolecular dipole moments. These decompositions shed new light on the motions underlying the librational and translational (hydrogen-bond stretch) bands at 20 and 5 THz respectively: interactions between donor protons and acceptor lone pair electrons are shown to be important for the line shape in both librational and translational regimes, and in- and out-of-phase librational dimer modes are observed and explored., Comment: Main text: 7 pages with 4 figures. Supplement: 8 pages with 5 figures. Submitted to Nature Communications on February 29, 2020

We investigate non-Markovian barrier-crossing kinetics of a massive particle in one dimension in the presence of a memory function that is the sum of two exponentials with different memory times $\tau_1$ and $\tau_2$. Our Langevin simulations for the special case where both exponentials contribute equally to the total friction show that the barrier crossing time becomes independent of the longer memory time if at least one of the two memory times is larger than the intrinsic diffusion time. When we associate memory effects with coupled degrees of freedom that are orthogonal to a one-dimensional reaction coordinate, this counterintuitive result shows that the faster orthogonal degrees of freedom dominate barrier-crossing kinetics in the non-Markovian limit and that the slower orthogonal degrees become negligible, quite contrary to the standard time-scale separation assumption and with important consequences for the proper setup of coarse-graining procedures in the non-Markovian case. By asymptotic matching and symmetry arguments, we construct a crossover formula for the barrier crossing time that is valid for general multi-exponential memory kernels. This formula can be used to estimate barrier-crossing times for general memory functions for high friction, i.e. in the overdamped regime, as well as for low friction, i.e. in the inertial regime. Typical examples where our results are important include protein folding in the high-friction limit and chemical reactions such as proton-transfer reactions in the low-friction limit.

We study the folding of RNA secondary structures with quenched sequence randomness by means of the constrained annealing method. A thermodynamic phase transition is induced by including the conformational weight of loop structures. In addition to the expected melting at high temperature, a cold melting transition appears. Our results suggest that the cold denaturation of RNA found experimentally is, in fact, a continuous phase transition triggered by quenched sequence disorder. We calculate both hot and cold melting critical temperatures for the competing energy scenario between favorable and unfavorable base pairs and present a phase diagram as a function of the loop exponent and temperature.