Time Scale Of Exchange Research Articles

Oxygen Isotope Exchange between Dust Aggregates and Ambient Nebular Gas

Meteorites and their components exhibit a diverse range of oxygen isotope compositions, and the isotopic exchange timescale between dust grains and ambient gas is a key parameter for understanding the spatiotemporal evolution of the solar nebula. As dust grains existed as macroscopic aggregates in the solar nebula, it is necessary to consider the isotopic exchange timescales for these aggregates. Here, we theoretically estimate the isotope exchange timescales between dust aggregates and ambient vapor. The isotope exchange process between aggregates and ambient vapor is divided into four processes: (i) supply of gas molecules to the aggregate surface, (ii) diffusion of molecules within the aggregate, (iii) isotope exchange on the surface of constituent particles, and (iv) isotope diffusion within the particles. We evaluate these timescales and assess which one becomes the rate-determining step. We reveal that the isotope exchange timescale is approximately the same as that of the constituent particles when the aggregate radius is smaller than the critical value, which is a few centimeters when considering the exchange reaction between amorphous forsterite aggregates and water vapor.

The General Relationship between Mean Dissolved Oxygen Concentrations and Timescales in Estuaries

The onset of hypoxia is a consequence of the competition between oxygen replenishment, production, and consumption. Dissolved oxygen (DO) levels inside an estuary depend on the balance between physical processes that transport oxygen-rich water into the estuary, including upstream freshwater advection, gravitational circulation, and vertical mixing, and biochemical processes that produce and consume oxygen, such as photosynthesis, respiration, and organic decomposition. We propose a general relationship between the physical and biochemical processes with a Lagrangian perspective to interpolate mean DO concentrations at local and system levels to assess the onset of hypoxia in an estuary. Simple parameters using timescales are proposed for cross-system comparison of hypoxia and anoxia conditions. Our study demonstrates that the hypoxia of an estuary system is determined by the timescales of vertical exchange, freshwater and saltwater transport, and DO consumption. When the vertical exchange timescale is shorter than the residence time in a system, vertical exchange dominates DO replenishment, while shorter residence time enhances advection, which quickly inputs DO-rich water to regulate hypoxia. The interplay between DO consumption and dynamic DO replenishment is the primary determinant of hypoxia in an estuary.

From Milliseconds to Minutes: Melittin Self-Assembly from Concerted Non-Equilibrium Pressure-Jump and Equilibrium Relaxation Nuclear Magnetic Resonance.

Non-equilibrium kinetics techniques like pressure-jump nuclear magnetic resonance (NMR) are powerful in tracking changes in oligomeric populations and are not limited by relaxation rates for the time scales of exchange that can be probed. However, these techniques are less sensitive to minor, transient populations than are Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments. We integrated non-equilibrium pressure-jump and equilibrium CPMG relaxation dispersion data to fully map the kinetic landscape of melittin tetramerization. While monomeric peptides weakly form dimers (Kd,D/M ≈ 26 mM) whose population never exceeds 1.6% at 288 K, dimers associate tightly to form stable tetrameric species (Kd,T/D ≈ 740 nM). Exchange between the monomer and dimer, along with exchange between the dimer and tetramer, occurs on the millisecond time scale. The NMR approach developed herein can be readily applied to studying the folding and misfolding of a wide range of oligomeric assemblies.

Water exchange and transport pathways in estuary-shelf region of Pearl River Estuary under multiple forcings

Using the Pearl River Estuary (PRE) as an example, the exposure time (θ‾) was calculated to investigate the dominant processes of three-dimensional water exchanges in the estuarine-shelf system and explore the underlying transport pathway. The θ‾, which quantifies the time of water stayed in a defined region, shows clear seasonality under the joint controls from river discharge, tides and wind forcing. It has the lowest domain-average value (∼6 days) in the early summer, then along with weakening of river discharge, it increases to the peak (∼13 days) at the beginning of the fall and remains relatively high during following fall and winter. In contrast, the vertical difference of θ‾ in the water column shows the opposite temporal variability. Spatially, θ‾ increased from the lower to the upper estuary, and in response to the gravitational circulation of surface seaward transport and the bottom intrusion, a larger θ‾ appeared in the bottom layer of water column. Numerical experiments show river discharge predominantly determined the θ‾ compared to the modulation from tides and wind. Based on the water exchange timescale in different subdomains, the transport pathway inside the estuary is controlled by river discharge and tides, which impose a net effect on weakening onshore transport. Outsides the estuary, the wind-driven shelf current modulates the remote influences from the regions far away from the PRE. The spatial structure and temporal variabilities of water exchange identified in this study help to utilize the water exchange capability and realize substance renewal in estuary-shelf regions.

Studying micro to millisecond protein dynamics using simple amide 15N CEST experiments supplemented with major-state R2 and visible peak-position constraints.

Over the last decade amide 15N CEST experiments have emerged as a popular tool to study protein dynamics that involves exchange between a 'visible' major state and sparsely populated 'invisible' minor states. Although initially introduced to study exchange between states that are in slow exchange with each other (typical exchange rates of, 10 to 400s-1), they are now used to study interconversion between states on the intermediate to fast exchange timescale while still using low to moderate (5 to 350Hz) 'saturating' B1 fields. The 15N CEST experiment is very sensitive to exchange as the exchange delay TEX can be quite long (~0.5s) allowing for a large number of exchange events to occur making it a very powerful tool to detect minor sates populated ([Formula: see text]) to as low as 1%. When systems are in fast exchange and the 15N CEST data has to be described using a model that contains exchange, the exchange parameters are often poorly defined because the [Formula: see text] versus [Formula: see text] and [Formula: see text] versus exchange rate ([Formula: see text]) plots can be quite flat with shallow or no minima and the analysis of such 15N CEST data can lead to wrong estimates of the exchange parameters due to the presence of 'spurious' minima. Here we show that the inclusion of experimentally derived constraints on the intrinsic transverse relaxation rates and the inclusion of visible state peak-positions during the analysis of amide 15N CEST data acquired with moderate B1 values (~50 to ~350Hz) results in convincing minima in the [Formula: see text] versus [Formula: see text] and the [Formula: see text] versus [Formula: see text] plots even when exchange occurs on the 100μs timescale. The utility of this strategy is demonstrated on the fast-folding Bacillus stearothermophilus peripheral subunit binding domain that folds with a rate constant ~104s-1. Here the analysis of 15N CEST data alone results in [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] plots that contain shallow minima, but the inclusion of visible-state peak positions and restraints on the intrinsic transverse relaxation rates of both states during the analysis of the 15N CEST data results in pronounced minima in the [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] plots and precise exchange parameters even in the fast exchange regime ([Formula: see text]~5). Using this strategy we find that the folding rate constant of PSBD is invariant (~10,500s-1) from 33.2 to 42.9°C while the unfolding rates (~70 to ~500s-1) and unfolded state populations (~0.7 to ~4.3%) increase with temperature. The results presented here show that protein dynamics occurring on the 10 to 104s-1 timescale can be studied using amide 15N CEST experiments.

Interface Adsorption versus Bulk Micellization of Surfactants: Insights from Molecular Simulations.

Surfactants play essential roles in many commonplace applications and industrial processes. Although significant progress has been made over the past decades with regard to model-based predictions of the behavior of surfactants, important challenges have remained. Notably, the characteristic time scales of surfactant exchange among micelles, interfaces, and the bulk solution typically exceed the time scales currently accessible with atomistic molecular dynamics (MD) simulations. Here, we circumvent this problem by introducing a framework that combines the general thermodynamic principles of self-assembly and interfacial adsorption with atomistic MD simulations. This approach provides a full thermodynamic description based on equal chemical potentials and connects the surfactant bulk concentration, the experimental control parameter, with the surfactant surface density, the suitable control parameter in MD simulations. Self-consistency is demonstrated for the nonionic surfactant C12EO6 (hexaethylene glycol monododecyl ether) at an alkane/water interface, for which the adsorption and pressure isotherms are computed. The agreement between the simulation results and experiments is semiquantitative. A detailed analysis reveals that the used atomistic model captures well the interactions between surfactants at the interface but less so their adsorption affinities to the interface and incorporation into micelles. Based on a comparison with other recent studies that pursued similar modeling challenges, we conclude that the current atomistic models systematically overestimate the surfactant affinities to aggregates, which calls for improved models in the future.

Transient dispersion regimes in heterogeneous porous media: On the impact of spatial heterogeneity in permeability and exchange kinetics in mobile–immobile transport

Transport processes in the subsurface are coupled with the heterogeneity of the porous structure. Obtaining an accurate description of mass transport in such media at all time scales remains a crucial task, as the subsurface is strongly impacted by human activity. Spreading of pollutants in the transient but also in the asymptotic regime, as well as the time to reach a critical location (e.g. aquifer, well) significantly depend on the underlying heterogeneity of the permeability field. Moreover, in the case of solute retention, transport is also characterized by local exchange kinetics that depend on the local aquifer properties. Consequently, exchange (retention) times are expected to be spatially heterogeneous. In this work we focus on the influence of spatially heterogeneous permeability and exchange times on the transient and asymptotic transport regimes and provide a parametric study. To this goal, we simulate in a first part the transport in a two-dimensional heterogeneous medium under spatially varying permeability and mobile–immobile mass transfer parameters. Equations are solved using a Lattice-Boltzmann two-relaxation-time (TRT) algorithm. We assume the following relation between the local permeability K and the local exchange time: τ∝Kγ. Taking into account this relation, we investigate the impact of the Damköhler number (Da, ratio of the advection and exchange time scales), the disorder of the permeability field and the value of the exponent of the coupling function (γ) on the spatial evolution of the concentration field and breakthrough curve. We show that, depending on the parameters (Da, γ, etc.), we can observe transient, non-Fickian dispersion, which is characterized by non-exponential tails of the solute breakthrough curves and a non-linear evolution of the spatial variance of the solute distribution.In a second part, we present a new continuous time random walk (CTRW) model to upscale these transport behaviors. The model is based on a spatial Markov model for particle velocities that couples advective–dispersive transport and heterogeneous mass transfer through a compound Poisson process. The upscaled model can be fully parameterized by the statistics of permeability and the hydraulic gradient (with no fitting parameter), that is, in terms of medium and flow characteristics. The results of the CTRW model fully capture the non-Fickian transient transport regimes both for the breakthrough curves and spatial concentration variance. In the longtime limit, as expected from the central limit theorem, the CTRW model predicts normal, Fickian behavior. Finally we show, that the time to reach the asymptotic regimes in heterogeneous media (e.g. heterogeneous exchange times) is parameter dependent and in average is two orders of magnitude larger than for the respective homogeneous case. To summarize, the coupling between the heterogeneous permeability field and the local mass transfer properties can strongly influence transient and asymptotic transport regimes and potentially explain experimentally observed non-Gaussian behaviors.

Flushing time variability in a short, low-inflow estuary

Flushing time, the time scale for exchange and mixing between embayed and oceanic waters in an estuary, plays an integral role in determining water quality and aquatic ecosystem health. Here, we investigated the spatiotemporal variability of flushing times throughout Morro Bay, a short, low-inflow estuary (LIE) on the California coast, using a calibrated and validated hydrodynamic model (Delft3D). Morro Bay has historically supported an extensive eelgrass (Zostera marina) habitat, which declined substantially from 139 to 5.4 ha during 2007–2017. Eelgrass decline motivated the current research into the role of changing bed roughness and oceanic drivers (i.e., tide and sea-level rise) on estuarine hydrodynamics and flushing times. We found that tidal variability exerts the strongest control on flushing times compared to other effects, i.e., bed roughness or sea-level rise. Additionally, we found that increasing sea level and decreasing bed roughness (associated with declining seagrass coverage) yielded higher rates of mixing (lower flushing times). We detected a strong correspondence between areas having shorter flushing times (e.g., near the estuary mouth) and areas occupied by resilient eelgrass populations in Morro Bay. Our findings further indicated that flushing times in short LIEs are particularly sensitive to several factors (e.g., bed roughness, sea level) that are susceptible to anthropogenic disturbance and future climate change.

Catalytic Control of Crystallization in Dynamic Networks.

The effect of catalysts with varying nucleophilic strength on thiol-thioester bond exchange dynamics and concomitant crystallization was studied in a model semicrystalline polymer network. It was found that the characteristic time scale of covalent bond exchange, τ, could be tuned over a ∼101-103 s range simply by changing the nucleophilicity of the catalyst. Using isothermal crystallization measurements via differential scanning calorimetry, thermodynamic and kinetic features of crystallization were considered. A depression in melting temperature was observed with increasing bond exchange rate, suggesting a dependence of crystalline organization on network dynamics. Furthermore, a systematic slowing of crystallization kinetics with faster covalent bond exchange rates was observed. Lauritzen-Hoffman analysis showed a near doubling in the barrier for secondary nucleation for dynamic networks, suggesting that that bond exchange slows crystallization by limiting secondary nucleation and further growth. Finally, longitudinal DSC studies reveal a long-term increase in melting temperature for samples held at ambient temperature with bond exchange activated at room temperature, indicating that while bond exchange slows crystallization on short time scales it facilitates isothermal long-term crystal rearrangement and growth on longer time scales.

Riverine groundwater discharge estimation in a dynamic river corridor using 222Rn

AbstractGroundwater discharge flux into rivers (riverine groundwater discharge or RGD) is essential information for the conservation and management of aquatic ecosystems and resources. One way to estimate area‐integrated groundwater discharge into surface water bodies is to measure the concentration of a groundwater tracer within the water body. We assessed groundwater discharge using 222Rn, a tracer common in many surface water studies, through field measurements, surface water 222Rn mass balance model, and groundwater flow simulation, for the seldom studied but ubiquitous setting of a flooding river corridor. The investigation was conducted at the dam‐regulated Lower Colorado River (LCR) in Austin, Texas, USA. We found that 222Rn in both the river water and groundwater in the river bank changed synchronously over a 12‐hour flood cycle. A 222Rn mass balance model allowed for estimation of groundwater discharge into a 500‐m long reach of the LCR over the flood. The groundwater discharge ranged between negative values (indicating recharge) to 1570 m3/h; groundwater discharge from groundwater flow simulations corroborated these estimates. However, for the dynamic groundwater discharge estimated by the 222Rn box model, assuming whether the groundwater 222Rn endmember was constant or dynamic led to notably different results. The resultant groundwater discharge estimates are also highly sensitive to river 222Rn values. We thus recommend that when using this approach to accurately characterize dynamic groundwater discharge, the 222Rn in near‐stream groundwater should be monitored at the same frequency as river 222Rn. If this is not possible, the 222Rn method can still provide reasonable but approximate groundwater discharge given background information on surface water‐groundwater exchange time scales.

SAM1 domain of SASH1 harbors distinctive structural heterogeneity

The sterile alpha motif (SAM) domains are among the most versatile protein domains in biology, and the variety of the oligomerization states contribute to their diverse roles in many diseases. A better understanding of the structure and dynamics of various SAM domains will provide a scientific basis for drug development targeting them. Here, we used SEC-MALS, HPLC, NMR, and other biophysical techniques to characterize the structural features and dynamics of the SAM1 domain in SASH1. SASH1 is a scaffold protein belonging to the same family as SASH3. Unlike the dimerization seen in SASH3′s SAM domain, our SEC-MALS and SE-HPLC showed that SAM1 exists primarily as a less compact monomer with a minor oligomer. NMR assignment, relaxation, and exchange experiments revealed the presence of both a disordered monomer and a more structured oligomer with multiple timescale exchange regimes in solution. Mutagenesis and SE-HPLC showed that D663A/T664K substitutions in SAM1 increased its oligomerization. In sum, this study is the first to characterize a disordered structure for a SAM domain, provides additional evidence and framework for the diversity of SAM domains, and identifies a region in SAM1 as a potential starting point to further characterize the structural mechanism of oligomerization of the domain.

Characterizing Fast Conformational Exchange of Aromatic Rings Using Residual Dipolar Couplings: Distinguishing Jumplike Flips from Other Exchange Mechanisms.

Aromatic ring flips are a hallmark of protein dynamics. They are experimentally studied by NMR spectroscopy, where recent advances have led to improved characterization across a wide range of time scales. Results on different proteins have been interpreted as continuous diffusive ring rotations or jumplike flips, leading to diverging views of the protein interior as being fluidlike or solidlike, respectively. It is challenging to distinguish between these mechanisms and other types of conformational exchange because chemical-shift-mediated line broadening provides only conclusive evidence for ring flips only if the system can be moved from the slow- to intermediate/fast-exchange regime. Moreover, whenever the chemical shift difference between the two symmetry-related sites is close to zero, it is not generally possible to determine the exchange time scale. Here we resolve these issues by measuring residual dipolar coupling (RDC)-mediated exchange contributions using NMR relaxation dispersion experiments on proteins dissolved in dilute liquid crystalline media. Excellent agreement is found between the experimental difference in RDC between the two symmetry-related sites and the value calculated from high-resolution X-ray structures, demonstrating that dynamics measured for F52 in the B1 domain of protein G reports on distinct, jumplike flips rather than other types of conformational exchange.

Oxygen isotope exchange kinetics between CAI melt and carbon monoxide gas: Implication for CAI formation in the earliest Solar System

Coarse-grained igneous calcium-aluminum-rich inclusions (CAIs) are suggested to have experienced gas–melt isotope exchange of oxygen during the melting events of their precursors. Therefore, their oxygen isotope variation would preserve information about the high-temperature processes in the earliest Solar System. We experimentally determined oxygen isotope exchange kinetics between CAI analog melt and carbon monoxide (CO) gas at 1420 °C and 1460 °C under CO gas partial pressures of 0.1, 0.5, and 1 Pa to understand the role of CO gas on the oxygen isotope exchange. We observed oxygen isotope zoning profiles inside the reacted samples that formed through the oxygen isotope exchange reaction at the melt surface and oxygen diffusion in the melt. The zoning profiles were fitted using a three-dimensional spherical diffusion model with time-dependent surface concentration. The oxygen isotope exchange efficiency for colliding CO molecules is estimated to be ∼3.3 × 10–4, which is much smaller than that for H2O (0.28). The oxygen diffusion coefficient obtained in this study is similar to that obtained in the oxygen isotope exchange experiments between the CAI melt and H2O, suggesting that the diffusion species in the melt is O2–, despite the surrounding atmospheres.A comparison of the isotope exchange reaction kinetics between (1) CAI melt and CO gas, (2) CAI melt and H2O gas, and (3) CO and H2O gases shows that the reaction rate decreases in the order of (3), (2), and (1). The rapid isotope exchange of the reaction (1) indicates that the oxygen isotopic compositions of H2O and CO should have been equilibrated during the melting and crystallization processes of igneous CAIs. Both H2O and CO change the oxygen isotope compositions of molten CAI in the same direction, although reaction (2) controls the isotope exchange timescale between the CAI melt and surrounding gas. Our dataset demonstrates that type B CAIs having melilite with homogeneous oxygen isotope composition should have been heated for 2–3 days at PH2 > 100 Pa above the melilite liquidus (∼1400 °C) in the solar protoplanetary disk.

Coupled Hydrodynamic Flow Focusing (cHFF) to Engineer Lipid-Polymer Nanoparticles (LiPoNs) for Multimodal Imaging and Theranostic Applications.

An optimal design of nanocarriers is required to overcome the gap between synthetic and biological identity, improving the clinical translation of nanomedicine. A new generation of hybrid vehicles based on lipid–polymer coupling, obtained by Microfluidics, is proposed and validated for theranostics and multimodal imaging applications. A coupled Hydrodynamic Flow Focusing (cHFF) is exploited to control the time scales of solvent exchange and the coupling of the polymer nanoprecipitation with the lipid self-assembly simultaneously, guiding the formation of Lipid–Polymer NPs (LiPoNs). This hybrid lipid–polymeric tool is made up of core–shell structure, where a polymeric chitosan core is enveloped in a lipid bilayer, capable of co-encapsulating simultaneously Gd-DTPA and Irinotecan/Atto 633 compounds. As a result, a monodisperse population of hybrid NPs with an average size of 77 nm, with preserved structural integrity in different environmental conditions and high biocompatibility, can be used for MRI and Optical applications. Furthermore, preliminary results show the enhanced delivery and therapeutic efficacy of Irinotecan-loaded hybrid formulation against U87 MG cancers cells.

Using Timescales of Deficit and Residence to Evaluate Near‐Bottom Dissolved Oxygen Variation in Coastal Seas

AbstractWe identify the local, vertical and lateral processes that cause bottom oxygen variation, and characterize timescales for each process using oxygen budget analysis based on a coupled physical‐biogeochemical model for the coastal seas in east China. Local oxygen deficit often occurs in the summer season due to the faster local consumption than the vertical replenishment in seasonal timescale. Lateral transport of oxygen‐rich ambient water replenishes local deficit of bottom dissolved oxygen. Competition between local deficit and lateral exchange determines seasonal hypoxia formation and sustainment. Short local consumption timescale is favorable for hypoxia formation, and transient hypoxia often forms when the local deficit and lateral exchange processes act on comparable timescales, such as the East China Sea in which the bottom hypoxia usually lasts for days. Extremely long lateral exchange timescale suggests that dissolved oxygen variation is predominantly controlled by local processes, and short local consumption timescale often causes increasingly severe seasonal hypoxia until the onset of the relaxation of local deficit, such as the bottom hypoxia in the Bohai Sea. Using these timescales to evaluate local deficit relative to vertical and lateral residence time and their variability is a convenient and potentially powerful general mechanistic framework to evaluate strategies to mitigate coastal hypoxia worldwide.

Association-Dissociation Dynamics of Ionic Electrolytes in Low Dielectric Medium.

Ionic electrolytes are known to form various complexes which exist in dynamic equilibrium in a low dielectric medium. However, structural characterization of these complexes has always posed a great challenge to the scientific community. An additional challenge is the estimation of the dynamic association-dissociation time scales (lifetime of the complexes), which are key to the fundamental understanding of ion transport. In this work, we have used a combination of infrared absorption spectroscopy, two-dimensional infrared spectroscopy, molecular dynamics simulations, and density functional theory calculations to characterize the various ion complexes formed by the thiocyanate-based ionic electrolytes as a function of different cations in a low dielectric medium. Our results demonstrate that thiocyanate is an excellent vibrational reporter of the heterogeneous ion complexes undergoing association-dissociation dynamics. We find that the ionic electrolytes exist as contact ion pairs, dimers, and clusters in a low dielectric medium. The relative ratios of the various ion complexes are sensitive to the cations. In addition to the interactions between the thiocyanate anion and the countercation, the solute-solvent interactions drive the dynamic equilibrium. We have estimated the association-dissociation dynamics time scales from two-dimensional infrared spectroscopy. The exchange time scale involving the cluster is faster than that between a dimer and an ion pair. Moreover, we find that the dynamic equilibrium between the cluster and another ion complex is correlated to the solvent fluctuations.

Structural and dynamical heterogeneity of water trapped inside Na+-pumping KR2 rhodopsin in the dark state.

Photoisomerization in the retinal leads to a channel opening in rhodopsins that triggers translocation or pumping of ions/protons. Crystal structures of rhodopsins contain several structurally conserved water molecules. It has been suggested that water plays an active role in facilitating the ion pumping/translocation process by acting as a lubricant in these systems. In this paper, we systematically investigate the localization, structure, dynamics, and energetics of the water molecules along the channel for the resting/dark state of KR2 rhodopsin. By employing several microseconds long atomistic molecular dynamics simulation of this trans-membrane protein system, we demonstrate the presence of five distinct water containing pockets/cavities separated by gateways controlled by protein side-chains. There exists a strong hydrogen bonded network involving these buried water molecules and functionally important key residues. We present evidence of significant structural and dynamical heterogeneity in the water molecules present in these cavities, with very rare exchange between them. The exchange time scale of such buried water with the bulk has an extremely wide range, from tens of nanoseconds to >1.5µs. The translational and rotational dynamics of buried water are found to be strongly dependent on the protein cavity size and local interactions with a classic signature of trapped diffusion and rotational anisotropy.

NMR Spin Relaxation Theory of Biomolecules Undergoing Highly Asymmetric Exchange with Large Interaction Partners

The transient interactions of proteins and other molecules with much larger structures, such as synthetic or biological nanoparticles, lead to certain types of enhanced nuclear magnetic resonance (NMR) spin relaxation effects, which can be accurately measured by multidimensional solution NMR techniques. These relaxation effects provide new information about the nanostructures and the protein, their interactions, internal dynamics, and associated kinetic and thermodynamic parameters, such as exchange rates and populations. Although theoretical treatments exist that cover either the fast or slow exchange limits, a theoretical treatment that applies to all practically relevant exchange processes is still missing. A unified theoretical framework is presented for this purpose based on a stochastic Liouville equation (SLE). It covers nuclear spin dynamics, overall rotational diffusion of both the protein and the nanostructure, the exchange process between a free state and a bound state, and internal protein dynamics. Although the numerical implementation of the SLE typically involves large matrices, it is shown here that it is computationally still tractable for situations relevant in practice. Application of the theory demonstrates how transverse relaxation is substantially impacted by the kinetics of binding on a wide range of exchange timescales. It is further shown that when exchange occurs on the appropriate timescale, transverse relaxation is able to report on internal dynamics far slower than observable by traditional transverse relaxation experiments. The SLE will allow the realistic and quantitative interpretation of experimental NMR data reporting about transient protein-nanoparticle interactions, thereby providing a powerful tool for the characterization of protein dynamics modes on a vast range of timescales including motions that may be functionally relevant.

Exact time scale of energy exchange in triad interactions of homogeneous isotropic turbulence

We solve analytically the period of a single triad interaction of homogeneous isotropic turbulence. Comparing with the traditional concept of the timescale of energy transfer, we found that this period is a timescale of energy exchange among the three wave vectors of a triad. Quantitatively, the timescale of energy exchange is usually longer if the equilibrium dissipation law is satisfied; however, when energy transfer is suppressed, the energy exchange becomes dominant. We extract the periods in typical numerical experiments of triad interactions and show that they are in good agreement with theoretical predictions. This picture implies that energy exchange corresponds to oscillation, while energy transfer corresponds to damping, and the damping rate is correlated with the oscillation. The present results of the timescale of energy transfer are expected to be applied in nonequilibrium turbulent flows.

Hydration structure and water exchange kinetics at xenotime-water interfaces: implications for rare earth minerals separation.

Hydration of surface ions gives rise to structural heterogeneity and variable exchange kinetics of water at complex mineral-water interfaces. Here, we employ ab initio molecular dynamics (AIMD) simulations and water adsorption calorimetry to examine the aqueous interfaces of xenotime, a phosphate mineral that contains predominantly Y3+ and heavy rare earth elements. Consistent with natural crystal morphology, xenotime is predicted to have a tetragonal prismatic shape, dominated by the {100} surface. Hydration of this surface induces multilayer interfacial water structures with distinct OH orientations, which agrees with recent crystal truncation rod measurements. The exchange kinetics between two adjacent water layers exhibits a wide range of underlying timescales (5-180 picoseconds), dictated by ion-water electrostatics. Adsorption of a bidentate hydroxamate ligand reveals that {100} xenotime surface can only accommodate monodentate coordination with water exchange kinetics strongly depending on specific ligand orientation, prompting us to reconsider traditional strategies for selective separation of rare-earth minerals.