Translational Diffusion Research Articles

Insight into the molecular basis of the soluble storage-state to fibrous-state structural transformation of spider pyriform silk

Pyriform (or piriform) silk is a fibrous spider silk used in a composite material to attach web silks to substrates and disparate silk types together. Argiope argentata pyriform silk is formed from a protein with a central repetitive region consisting of a 234-amino acid unit (the "Py unit") repeated 21 times. We have previously shown that the Py unit behaves modularly, with a structured core of 6 α-helices that retains its structuring upon truncation of N- and C-terminal intrinsically disordered segments. Here, we apply solution-state nuclear magnetic resonance (NMR) spectroscopy to investigate the structured core of the Py unit. Based on 15N spin relaxation measurements and reduced spectral density mapping at two field strengths, the α-helical core of the Py unit exhibits minimal backbone motion beyond the tumbling of the globular domain except for one interhelical linker that exhibits a notably higher degree of dynamics. Evaluation of rotational diffusion based on 15N spin relaxation and translational diffusion by pulsed field gradient diffusion NMR demonstrates that the core of the Py unit behaves as a compact structure, with hydrodynamic behaviour consistent with a well-packed protein. Pyriform silk protein undergoes a structural transformation upon conversion from the soluble-state to the fibrous-state, with a loss of αhelical content and gain of β-sheet content. The more dynamic segment we observe midway through the structured core of the Py core, especially in the context of the intrinsically disordered segments that flank the core, would provide an initiation point for decompaction, structural transformation, and/or intermolecular interactions.

Optical Kerr effect for underlying the orientational and translational fluctuations of molecular interactions in non-polar CS2 vapor and liquid states

A femtosecond optical Kerr gate is used for first time to experimentally study the temporal behavior of the molecular interactions of carbon disulfide (CS2) vapor in comparison to its liquid state. This Kerr effect is observed due to the optical birefringence induced in a CS2 sample. Results show that the Kerr relaxation time in the vapor state is faster than in the liquid state, with an overall exponential fit of 0.8 ps molecular relaxation time versus 1.7 ps, respectively. A faster relaxation decay time is observed for the first time in free CS2 molecules, this is attributed to fewer neighboring intermolecular interactions, which results in a lower local viscosity in the vapor compared to the liquid state. Fitting the temporal response of the Kerr vapor signal to individual components of n2 arising from the ultrafast and fast components yields two main decay times: τultrfast = 126 fs and τfast = 530 fs molecular relaxation times, one which agrees with the Debye equation for the air viscosity (associated to the free rotation in air) giving 126 fs and the other is approximately close to the translational diffusion equation producing 530 fs, respectively. In the liquid state, fitting yields three main components: τultrfast = 50 as, τfast = 500 fs, and τslow = 1.5 ps, overall, the tail fits the 1.7 ps molecular relaxation time.

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel–Fulcher–Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Hybrid Bonding Bottlebrush Polymers Grafted from a Supramolecular Polymer Backbone.

Bottlebrush polymers, macromolecules consisting of dense polymer side chains grafted from a central polymer backbone, have unique properties resulting from this well-defined molecular architecture. With the advent of controlled radical polymerization techniques, access to these architectures has become more readily available. However, synthetic challenges remain, including the need for intermediate purification, the use of toxic solvents, and challenges with achieving long bottlebrush architectures due to backbone entanglements. Herein, we report hybrid bonding bottlebrush polymers (systems integrating covalent and noncovalent bonding of structural units) consisting of poly(sodium 4-styrenesulfonate) (p(NaSS)) brushes grafted from a peptide amphiphile (PA) supramolecular polymer backbone. This was achieved using photoinitiated electron/energy transfer-reversible addition-fragmentation chain transfer (PET-RAFT) polymerization in water. The structure of the hybrid bonding bottlebrush architecture was characterized using cryogenic transmission electron microscopy, and its properties were probed using rheological measurements. We observed that hybrid bonding bottlebrush polymers were able to organize into block architectures containing domains with high brush grafting density and others with no observable brushes. This finding is possibly a result of dynamic behavior unique to supramolecular polymer backbones, enabling molecular exchange or translational diffusion of monomers along the length of the assemblies. The hybrid bottlebrush polymers exhibited higher solution viscosity at moderate shear, protected supramolecular polymer backbones from disassembly at high shear, and supported self-healing capabilities, depending on grafting densities. Our results demonstrate an opportunity for novel properties in easily synthesized bottlebrush polymer architectures built with supramolecular polymers that might be useful in biomedical applications or for aqueous lubrication.

Quasielastic neutron scattering study on low-hydrated myoglobin inside silica nanopores

In this study, nanosecond-scale dynamics of low-hydrated myoglobin (Mb) encapsulated in mesoporous silica (MPS) with 7.8 nm pores was investigated by using high resolution (energy resolution: 1 μeV) neutron backscattering spectroscopy. The apparent hydration level of the encapsulated myoglobin was 0.06, which was deduced by assuming a uniform distribution of water within myoglobin encapsulated mesoporous silica. The mean square displacement of myoglobin derived from an elastic fixed-window scan was essentially proportional to temperature in the range 120–300 K, indicating the absence of dynamical transition induced by the onset of translational diffusion in the hydration D2O. Since the width of quasielastic neutron scattering (QENS) peaks of the encapsulated Mb was Q-independent at 220, 240, and 265 K, the observed nanosecond-scale dynamics was attributed to internal motions of the encapsulated Mb, such as slow motions of amino acid groups or side chains. The fraction of immobile H-atoms in Mb was estimated to be above 0.8, which was larger than that for a free protein with a similar molecular weight to Mb. The large immobile fraction indicates that the nanosecond-scale motions of amino acid residues and side chains in the vicinity of the pore wall are restricted by the interfacial interactions with the rigid pore wall.

Evidence of a Rod-like Structure for Hydroxypropyl Cellulose Samples in Aqueous Solution.

Because hydroxypropyl cellulose (HpC) is a popular polymeric material that forms a liquid crystalline phase in solutions with various kinds of solvents, including water, it is commonly thought that HpC has a typical rod-like structure in solution. In this study, the structures of commercial HpC samples in aqueous solution with average molar substitution numbers (MS) ranging from 3.6 to 3.9 and weight-average molar masses (Mw) ranging from 36 to 740 kg mol-1 were investigated in detail. We first used multiple techniques, including standard static and dynamic light scattering (SLS and DLS), neutron and X-ray scattering experiments, and viscometric measurements, to obtain clear evidence of rod-like structures quantitatively. The dependence of excess scattering intensities for HpC samples under dilute conditions on the magnitude of the scattering vector over a wide range from 8.9 × 10-3 to 3.0 × 10 nm-1 was reasonably described by the form factor of rod particles with length (L) and diameter (d). Although the determined L value was close to the contour length (lc) calculated from the Mw values in the lower Mw range, L became obviously less than lc with increasing Mw. The radius of gyration (Rg) determined via SLS measurements was proportional to L by a factor of approximately 3.5 ∼ √12 over the Mw range examined. These observations revealed that the conformation of HpC molecules changes from an elongated single chain to a certain folded structure, maintaining the shape of the rod-shaped particles. Moreover, the Mw dependencies of the intrinsic viscosities and translational diffusion coefficients of the HpC samples resulting from DLS measurements were reasonably described with a theoretical rod-like particle model, assuming that L and d are identical to those resulting from the scattering behaviors.

Determination of Translational and Rotational Diffusivities of Anisotropic Nanoparticles by Heterodyne Polarized and Depolarized Dynamic Light Scattering

Determination of Translational and Rotational Diffusivities of Anisotropic Nanoparticles by Heterodyne Polarized and Depolarized Dynamic Light Scattering

Microscopic theory for nonequilibrium correlation functions in dense active fluids.

One of the key hallmarks of dense active matter in the liquid, supercooled, and solid phases is the so-called equal-time velocity correlations. Crucially, these correlations can emerge spontaneously, i.e., they require no explicit alignment interactions, and therefore represent a generic feature of dense active matter. This indicates that for a meaningful comparison or possible mapping between active and passive liquids one not only needs to understand their structural properties, but also the impact of these velocity correlations. This has already prompted several simulation and theoretical studies, though they are mostly focused on athermal systems and thus overlook the effect of translational diffusion. Here, we present a fully microscopic method to calculate nonequilibrium correlations in two-dimensional systems of thermal active Brownian particles (ABPs). We use the integration through transients formalism together with (active) mode-coupling theory and analytically calculate qualitatively consistent static structure factors and active velocity correlations. We complement our theoretical results with simulations of both thermal and athermal ABPs which exemplify the disruptive role that thermal noise has on velocity correlations.

Solution Dynamics of Covalent Open-[60]Fullerene Dimers.

The translational diffusivity of covalent open-[60]fullerene dimers in an organic solvent was found to be well describable by a prolate ellipsoid model while a monomeric open-[60]fullerene behaves like a sphere model. The water association dynamics were examined for two open-[60]fullerene dimers, showing a higher water affinity for the sp3-linked dimer relative to sp2-linked dimer owing to an effective orbital-orbital overlap identified by π(fullerene)→σ*(H2O) interactions as suggested by theoretical calculations.

In situ pulmonary mucus hydration assay using rotational and translational diffusion of gold nanorods with polarization-sensitive optical coherence tomography.

Assessing the nanostructure of polymer solutions and biofluids is broadly useful for understanding drug delivery and disease progression and for monitoring therapy. Our objective is to quantify bronchial mucus solids concentration (wt. %) during hypertonic saline (HTS) treatment in vitro via nanostructurally constrained diffusion of gold nanorods (GNRs) monitored by polarization-sensitive optical coherence tomography (PS-OCT). Using PS-OCT, we quantified GNR translational () and rotational () diffusion coefficients within polyethylene oxide solutions (0 to 3wt. %) and human bronchial epithelial cell (hBEC) mucus (0 to 6.4wt. %). Interpolation of and data is used to develop an assay to quantify mucus concentration. The assay is demonstrated on the mucus layer of an air-liquid interface hBEC culture during HTS treatment. In polymer solutions and mucus, and monotonically decrease with increasing concentration. is more sensitive than to changes above 1.5wt. % of mucus and exhibits less intrasample variability. Mucus on HTS-treated hBEC cultures exhibits dynamic mixing from cilia. A region of hard-packed mucus is revealed by measurements. The extended dynamic range afforded by simultaneous measurement of and of GNRs using PS-OCT enables resolving concentration of the bronchial mucus layer over a range from healthy to disease in depth and time during HTS treatment in vitro.

Dynamical properties of solid and hydrated collagen: Insight from nuclear magnetic resonance relaxometry.

1H spin-lattice Nuclear Magnetic Resonance relaxometry experiments have been performed for collagen and collagen-based artificial tissues in the frequency range of 10 kHz-20MHz. The studies were performed for non-hydrated and hydrated materials. The relaxation data have been interpreted as including relaxation contributions originating from 1H-1H and 1H-14N dipole-dipole interactions, the latter leading to Quadrupole Relaxation Enhancement effects. The 1H-1H relaxation contributions have been decomposed into terms associated with dynamical processes on different time scales. A comparison of the parameters for the non-hydrated and hydrated systems has shown that hydration leads to a decrease in the dipolar relaxation constants without significantly affecting the dynamical processes. In the next step, the relaxation data for the hydrated systems were interpreted in terms of a model assuming two-dimensional translational diffusion of water molecules in the vicinity of the macromolecular surfaces and a sub-diffusive motion leading to a power law of the frequency dependencies of the relaxation rates. It was found that the water diffusion process is slowed down by at least two orders of magnitude compared to bulk water diffusion. The frequency dependencies of the relaxation rates in hydrated tissues and hydrated collagen are characterized by different power laws (ωH-β, where ωH denotes the 1H resonance frequency): the first of about 0.4 and the second close to unity.

A Refined Thin-Film Model for Drug Dissolution Considering Radial Diffusion - Simulating Powder Dissolution.

We aim to present a refined thin-film model describing the drug particle dissolution considering radial diffusion in spherical boundary layer, and to demonstrate the ability of the model to describe the dissolution behavior of bulk drug powders. The dissolution model introduced in this study was refined from a radial diffusion-based model previously published by our laboratory (So et al. in Pharm Res. 39:907-17, 2022). The refined model was created to simulate the dissolution of bulk powders, and to account for the evolution of particle size and diffusion layer thickness during dissolution. In vitro dissolution testing, using fractionated hydrochlorothiazide powders, was employed to assess the performance of the model. Overall, there was a good agreement between the experimental dissolution data and the predicted dissolution profiles using the proposed model across all size fractions of hydrochlorothiazide. The model over-predicted the dissolution rate when the particles became smaller. Notably, the classic Nernst-Brunner formalism led to an under-estimation of the dissolution rate. Additionally, calculation based on the equivalent particle size derived from the specific surface area substantially over-predicted the dissolution rate. The study demonstrated the potential of the radial diffusion-based model to describe dissolution of drug powders. In contrast, the classic Nernst-Brunner equation could under-estimate drug dissolution rate, largely due to the underlying assumption of translational diffusion. Moreover, the study indicated that not all surfaces on a drug particle contribute to dissolution. Therefore, relying on the experimentally-determined specific surface area for predicting drug dissolution is not advisable.

Solidified water at room temperature hosting tailored fluidic channels by using highly anisotropic cellulose nanofibrils

Highly anisotropic cellulose nanofibrils can solidify liquid water, creating self-supporting structures by incorporating a tiny number of fibrils. These fibrillar hydrogels can contain as much as 99.99 wt% water. The structure and mechanical properties of fibrillar networks have so far not been completely understood, nor how they solidify the bulk water at such low particle concentrations. In this work, the mechanical properties of cellulose fibrillar hydrogels in the dilute regime from a wt% perspective have been studied, and an elastoplastic model describing the network structure and its mechanics is presented. A significant insight from this work is that the ability of the fibrils to solidify water is very dependent on particle stiffness and the number of contact points it can form in the network structure. The comparison between the experimental results and the theoretical model shows that the fibrillar networks in the dilute regime form via a non-stochastic process since the fibrils have the time and freedom to find contact points during network formation by translational and rotational diffusion. The formed, dilute fibrillar network deforms by sliding fibril contacts upon straining the network beyond its elastic limit. Our results also show that before macroscopic failure, the fibril contacts are restored once the load is released. The exceptional properties of this solidified water are exploited to host fluidic channels, allowing directed fluid transportation in water. Finally, the microfluidic channels formed in the hydrogels are tailored by the layer-by-layer technique to be interactive against external stimuli, a characteristic envisioned to be useful in biomedical applications.

Trapping of deformable active particles by a periodic background potential.

The dynamic behaviors, specifically trapping and sorting, of active particles interacting with periodic substrates have garnered significant attention. This study investigates numerically the trapping of soft, deformable particles on a periodic potential substrate, which can be experimentally verified through optical tweezers. The research demonstrates that multiple factors, including the relative size of traps, self-propelled velocity, shape parameters, ratio of particles to traps, and translational diffusion, can influence the trapping effect. Within certain parameter boundaries, it is shown that all particles can be consistently trapped. The research reveals that stable trapping typically occurs at median values of the relative trap size. An increase in the self-propelled velocity, the shape parameter, and the translational diffusion coefficient tends to facilitate the escapement of the particles from the traps. It is noteworthy that particles with larger shape parameters can escape even when the restoring force exceeds the self-propelled force. In addition, as the ratio of particles to traps grows, the fraction of trapped particles steadily reduces. Notably, rigid particles are consistently divided and trapped by traps closely approximating an integer multiple of the particles' area, up until the ratio reaches the aforesaid integer value. These findings can potentially enhance the understanding of the interactive effects between active deformable particles and periodic substrates. Moreover, this work suggests a different experimental approach to sort active particles based on rigidity disparities.

NMR investigation of multi-scale dynamics in ionic liquids containing Li+ and La3+: From vehicular to hopping transport mechanism

The dynamics in mixtures of ionic liquid and monoatomic cations has been studied at different time scales ranging from the nanosecond up to the second. The mixtures were composed of cholinium bis(trifluoromethanesulfonyl)imide ([Chol][TFSI]) and LiTFSI, with LiTFSI mole fraction, ▪, spanning from 0 to 0.5 (saturated solution), and [Chol][TFSI] and ▪ from 0 to 0.12. The translational self-diffusion coefficients of ▪, ▪ and ▪ have been measured, along with NMR their relaxation times at various magnetic fields, in order to decipher the intertwined dynamics between the ions, and to reveal how the local dynamics impact the long range translational diffusion. When the concentrations of lithium and lanthanum are increased in the liquid, the long range dynamics of all the ions drop. In the case of LiTFSI, the self-diffusion coefficient of lithium becomes higher than the one of TFSI at high concentration, revealing a change in lithium transport mechanisms. The NMR relaxation data confirm this change, showing a clearer transition at ▪. It is interpreted as a change from a vehicular transport mechanism of the lithium below ▪ to a hopping mechanism above. A similar crossover seems to occur in the lanthanum solutions. This phenomenon seems correlated to the departure of the hydroxyl group of the organic cation from the lithium solvation shell.

Measuring nanoparticles shape by structured illumination

Exploiting the size and shape of nanoparticles is critical for engineering the optical and mechanical properties of nanoparticle systems that are ubiquitous in everyday life. However, accurate determination of nanoparticle morphology usually requires elaborated methods such as XRD or TEM, which are not suitable for non-invasive and rapid control. Dynamic light scattering on the other hand, relies on the motion of nanoparticles and mixes different rotational and translational diffusion coefficients to infer synthetic information about the shape in terms of effective hydrodynamic characteristics. Here, we introduce a new scattering approach for measuring shape. We demonstrate analytically, numerically, and experimentally that the contrast of low-intensity fluctuations arising from the scattering of classically entangled optical fields allows determining the polarimetric anisotropy of nanoparticles. By leveraging the active variation of illumination structuring, we control the non-Gaussian statistics of the measured fluctuations, which, in turn, provides means to improve the measurement sensitivity. This technique offers practical opportunities for applications ranging from molecular chemistry to drug delivery to nanostructures synthesis where the real-time, quantitative assessment of nanoparticles shapes is indispensable.

Excited-State Symmetry Breaking in Solvent Mixtures.

A large number of multipolar dyes undergo excited-state symmetry breaking (ESSB) in polar media. During this process, electronic excitation, initially distributed evenly over the molecule, localizes, at least partially, on one donor-acceptor branch. To resolve its initial stage, ESSB is investigated with a donor-acceptor-donor dye in binary mixtures of nonpolar and polar solvents using time-resolved infrared absorption spectroscopy. The presence of a few polar molecules around the dye is sufficient to initiate ESSB. Although the extent of asymmetry in a mixture is close to that in a pure solvent of similar polarity, the dynamics are slower and involve translational diffusion. However, preferential solvation in the mixtures leads to a larger local polarity. Furthermore, inhomogeneous broadening of the S1 ← S0 absorption band of the dye is observed in the mixtures, allowing for a photoselection of solutes with different local environments and ESSB dynamics.

The effects of biological crowders on fibrillization, structure, diffusion, and conformational dynamics of α-synuclein.

α-synuclein is an intrinsically disordered protein (IDP) whose aggregation in presynaptic neuronal cells is a pathological hallmark of Lewy body formation and Parkinson's disease. This aggregation process is likely affected by the crowded macromolecular cellular environment. In this study, α-synuclein was studied in the presence of both a synthetic crowder, Ficoll70, and a biological crowder composed of lysed cells that better mimics the biocomplexity of the cellular environment. 15 N-1 H HSQC NMR results show similar α-synuclein chemical shifts in non-crowded and all crowded conditions implying that it remains similarly unstructured in all conditions. Nevertheless, both HSQC NMR and fluorescence measurements indicate that, only in the cell lysate, α-synuclein forms aggregates over a timescale of 48 h. 15 N-edited diffusion measurements indicate that all crowders slow down the α-synuclein's diffusivity. Interestingly, at high concentrations, α-synuclein diffuses faster in cell lysate than in Ficoll70, possibly due to additional soft (e.g., electrostatic or hydrophobic) interactions. 15 N-edited relaxation measurements show that some residues are more mobile in cell lysate than in Ficoll70; the rates that are most different are predominantly in hydrophobic residues. We thus examined cell lysates with reduced hydrophobicity and found slower dynamics (higher relaxation rates) in several α-synuclein residues. Taken together, these experiments suggest that while cell lysate does not substantially affect α-synuclein structure (HSQC spectra), it does affect chain dynamics and translational diffusion, and strongly affects aggregation over a timescale of days, in a manner that is different from either no crowder or an artificial crowder: soft hydrophobic interactions are implicated.

Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water.

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.