arXiv subjects

Roland R. Netz

Publications and source records attributed to Roland R. Netz.

At least 55 records · Page 3Linked to original sources

arXiv2024

pH modulates friction memory effects in protein folding

We study the non-Markovian folding dynamics of the $α$3D protein under low- and neutral-pH conditions. Recently published all-atom simulations of $α$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.

physics.bio-ph↗

arXiv2024

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 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.

physics.data-an↗

arXiv2023

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 (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.

physics.bio-ph↗

arXiv2023

Derivation of the non-equilibrium generalized Langevin equation from a generic time-dependent Hamiltonian

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.

cond-mat.stat-mech↗

arXiv2023

Insights into the Structure and Ion Transport of Pectin-[BMIM][PF$_6$] Electrolytes

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 ($τ_C$) is observed such that D~$τ_C^{-0.75}$ for cations and D~$τ_C^{-0.82}$ 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~$τ_C^{-1}$). 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.

cond-mat.soft↗

arXiv2023

Conformational isomerization dynamics in solvent violates both the Stokes-Einstein relation and Kramers' theory

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.

physics.chem-ph↗

arXiv2023

Collective modes and quantum effects in two-dimensional nanofluidic channels

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.

cond-mat.mes-hall↗

arXiv2023

Ion Transport Mechanisms in Pectin-containing EC-LiTFSI Electrolytes

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 ($η$) and relaxation timescales ($τ_c$), indicating higher mechanical stability and, consequently, the mean squared displacements, diffusion coefficients (D), and the Nernst-Einstein conductivity ($σ_{NE}$) decrease. Interestingly, while the lithium diffusivities are related to the ion-pair relaxation timescales as $D_+\sim τ_c^{-3.1}$, the TFSI$^-$ diffusivities exhibit excellent correlations with ion-pair relaxation timescales as $D_-\sim τ_c^{-0.95}$. On the other hand, the NE conductivities are dictated by distinct transport mechanisms and scales with ion-pair relaxation timescale as $σ_{NE}\sim τ_c^{-1.85}$.

cond-mat.soft↗

arXiv2023

Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail

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.

cond-mat.soft↗

arXiv2022

Fast protein folding is governed by memory-dependent friction

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.

cond-mat.soft↗

arXiv2022

Proton-transfer spectroscopy beyond the normal-mode scenario

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.

physics.chem-ph↗

arXiv2022

Non-Markovian modeling of non-equilibrium fluctuations and dissipation in active viscoelastic biomatter

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.

cond-mat.soft↗

arXiv2022

Barrier-crossing times for different non-Markovian friction in well and barrier $-$ A numerical study

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.

physics.chem-ph↗

arXiv2022

Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions

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.

physics.chem-ph↗

arXiv2022

Generalized Langevin Equation with a Non-Linear Potential of Mean Force and Non-Linear Memory Friction From a Hybrid Projection Scheme

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.

physics.chem-ph↗

arXiv2022

Time-dependent friction effects on vibrational infrared frequencies and line shapes of liquid water

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.

physics.chem-ph↗

arXiv2021

Role of Entropy in Determining the Phase Behavior of Protein Solutions Induced by Multivalent Ions

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 ζ-potential that shows charge inversion of the protein for solutions containing multivalent ions. The ζ-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.

cond-mat.soft↗

arXiv2021

Water evaporation from solute-containing aerosol droplets: effects of internal concentration and diffusivity profiles and onset of crust formation

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.

cond-mat.soft↗