Intermittent molecular hopping at the solid-liquid interface

Fractionation by Spatially Heterogeneous Diffusion: Experiments and the Two-Component Random Walk Model

The fundamental question regarding the fractionation phenomenon is whether diffusion alone is responsible for it or whether an additional advection dynamic is involved. We studied the fractionation by diffusion of particles in spatially heterogeneous environments. By experimentally observing the time-sequential fractionation patterns of dye particles diffusing across a solid-solid interface of varying polyacrylamide gel densities, we found that the two-component diffusion model accurately captures the observed fractionation dynamics. In contrast, single-component diffusion models by Fick, Wereide, and Chapman do not. Our results indicate that diffusion alone can explain the fractionation phenomenon and that additional advection dynamics are not involved. The underlying physics in the fractionation phenomenon is discussed by using a two-component random walk model.

Direct Visualization of Defect-Controlled Diffusion in van der Waals Gaps

Diffusion processes govern fundamental phenomena such as phase transformations, doping, and intercalation in van der Waals (vdW) bonded materials. Here, the diffusion dynamics of W atoms by visualizing the motion of individual atoms at three different vdW interfaces: hexagonal boron nitride (BN)/vacuum, BN/BN, and BN/WSe2, by recording scanning transmission electron microscopy movies is quantified. Supported by density functional theory (DFT) calculations, it is inferred that in all cases diffusion is governed by intermittent trapping at electron beam-generated defect sites. This leads to diffusion properties that depend strongly on the number of defects. These results suggest that diffusion and intercalation processes in vdW materials are highly tunable and sensitive to crystal quality. The demonstration of imaging, with high spatial and temporal resolution, of layers and individual atoms inside vdW heterostructures offers possibilities for direct visualization of diffusion and atomic interactions, as well as for experiments exploring atomic structures, their in situ modification, and electrical property measurements of active devices combined with atomic resolution imaging.

Anomalous Fluctuations in a Droplet of Chemically Active Colloids or Enzymes

Chemically active colloids or enzymes cluster into dense droplets driven by their phoretic response to collectively generated chemical gradients. Employing Brownian dynamics simulation techniques, our study of the dynamics of such a chemically active droplet uncovers a rich variety of structures and dynamical properties, including the full range of fluidlike to solidlike behavior, and non-Gaussian positional fluctuations. Our work sheds light on the complex dynamics of the active constituents of metabolic clusters, which are the main drivers of nonequilibrium activity in living systems.

Nanorod Diffusion near the Solid-Liquid Interface with Varied Wall Nonuniformity

The complex diffusion behaviors of rod-shaped nanoparticles near the solid-liquid interface are closely related to various biological processes and technological applications. Despite recent advancements in understanding the diffusion dynamics of nanoparticles near some specific solid-liquid interfaces, systematical studies to tune the interfacial interaction or fabricating nonuniform wall to see their effects on the nanorod (NR) diffusion are still lacking. This work utilized molecular dynamics simulations to investigate the rotational and translational diffusion dynamics of a single NR near the solid-liquid interface. We constructed a patterned wall featuring adjustable nonuniformity, which was accomplished by modifying the interaction between NR and the wall, noting that the resulting nonuniformity limits both the translational and rotational diffusion of NR, evident from decreases in diffusion coefficients and exponents. By trajectory analysis, we categorized the diffusion modes of NRs near the patterned wall with varied nonuniformities into three types: Fickian diffusion, desorption-mediated flight, and in-plane diffusion. Furthermore, energy analysis based on the adsorption-desorption mechanism has demonstrated that the three diffusion states are driven by interactions between the NR and the wall, which are primarily influenced by rotational diffusion. These results could significantly deepen the understanding of anisotropic nanoparticle interfacial diffusion and would provide new insights into the transport mechanisms of nanoparticles within confined environments.

Hidden Markov modeling of single-particle diffusion with stochastic tethering

The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a recent experiment, here we analyze the problem of particles undergoing two-dimensional Brownian motion with transient tethering to the surface. We model the problem as a hidden Markov model where the physical position is observed and the tethering state is hidden. We develop an alternating maximization algorithm to infer the hidden state of the particle and estimate the physical parameters of the system. The crux of our method is a saddle-point-like approximation, which involves finding the most likely sequence of hidden states and estimating the physical parameters from it. Extensive numerical tests demonstrate that our algorithm reliably finds the model parameters and is insensitive to the initial guess. We discuss the different regimes of physical parameters and the algorithm's performance in these regimes. We also provide a free software implementation of our algorithm.

Intermittent random walks under stochastic resetting

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. We demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. We calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, we prove that the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. Moreover, we demonstrate the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition.

Anomalous lateral diffusion of lipids during the fluid/gel phase transition of a lipid membrane

A lipid membrane undergoes a phase transition from fluid to gel phase upon changing external thermodynamic conditions, such as decreasing temperature and increasing pressure. Extremophilic organisms face the challenge of preventing this deleterious phase transition. The main focus of their adaptive strategy is to facilitate effective temperature sensing through sensor proteins, relying on the drastic changes in packing density and membrane fluidity during the phase transition. Although the changes in packing density parameters due to the fluid/gel phase transition are studied in detail, the impact on membrane fluidity is less explored in the literature. Understanding the lateral diffusive dynamics of lipids in response to temperature, particularly during the fluid/gel phase transition, is albeit crucial. Here we have simulated the phase transition of a single component lipid membrane composed of dipalmitoylphosphatidylcholine (DPPC) lipids using a coarse-grained (CG) model and studied the changes of the structural and dynamical properties. It is observed that near the phase transition point, both fluid and gel phase domains coexist together. The dynamics remains highly non-Gaussian for a long time even when the mean square displacement reaches the Fickian regime at a much earlier time. This Fickian yet non-Gaussian diffusion (FnGD) is a characteristic of a highly heterogeneous system, previously observed for the lateral diffusion of lipids in raft mimetic membranes having liquid-ordered and liquid-disordered phases co-existing together. We have analyzed the molecular trajectories and calculated the jump-diffusion of the lipids, stemming from sudden jump translations, using a translational jump-diffusion (TJD) approach. An overwhelming contribution of the jump-diffusion of the lipids is observed suggesting anomalous diffusion of lipids during fluid/gel phase transition of the membrane. These results are important in unravelling the intricate nature of lipid diffusion during the phase transition of the membrane and open up a new possibility of investigating the most significant change of membrane properties during phase transition, which can be effectively sensed by proteins.

Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping

In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.

Different glassy characteristics are related to either caging or dynamical heterogeneity

Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.

Universal to nonuniversal transition of the statistics of rare events during the spread of random walks

Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e^{-|x|^{β}} (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.

Tracking of Protein Adsorption on Poly(l-lactic acid) Film Surfaces: The Role of Molar Mass

Poly(l-lactic acid) (PLLA) has been extensively utilized as a biomaterial for various biomedical applications. The first and one of the most critical steps upon contact with biological fluids is the adsorption of proteins on the material's surface. Understanding the behavior of protein adsorption is vital for guiding the synthesis and preparation of PLLA for biomedical purposes. In this study, total internal reflection fluorescence microscopy was employed to investigate the adsorption of human serum albumin (HSA) on PLLA films with different molar masses. We found that molar mass affects HSA adsorption in such a way that it affects only the adsorption rate constants, but not the desorption rate constants. Additionally, we observed that HSA adsorption is spatially heterogeneous and exhibits many strong binding sites regardless of the molar mass of the PLLA films. We found that the free volume of PLLA plays a crucial role in determining its water uptake capacity and surface hydration, consequently impacting the adsorption of HSA.

Numerical simulations of confined Brownian-yet-non-Gaussian motion

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.

Non-Gaussian Diffusion Near Surfaces

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

Modeling Interfacial Interaction between Gas Molecules and Semiconductor Metal Oxides: A New View Angle on Gas Sensing

With the development of internet of things and artificial intelligence electronics, metal oxide semiconductor (MOS)-based sensing materials have attracted increasing attention from both fundamental research and practical applications. MOS materials possess intrinsic physicochemical properties, tunable compositions, and electronic structure, and are particularly suitable for integration and miniaturization in developing chemiresistive gas sensors. During sensing processes, the dynamic gas-solid interface interactions play crucial roles in improving sensors' performance, and most studies emphasize the gas-MOS chemical reactions. Herein, from a new view angle focusing more on physical gas-solid interactions during gas sensing, basic theory overview and latest progress for the dynamic process of gas molecules including adsorption, desorption, and diffusion, are systematically summarized and elucidated. The unique electronic sensing mechanisms are also discussed from various aspects including molecular interaction models, gas diffusion mechanism, and interfacial reaction behaviors, where structure-activity relationship and diffusion behavior are overviewed in detail. Especially, the surface adsorption-desorption dynamics are discussed and evaluated, and their potential effects on sensing performance are elucidated from the gas-solid interfacial regulation perspective. Finally, the prospect for further research directions in improving gas dynamic processes in MOS gas sensors is discussed, aiming to supplement the approaches for the development of high-performance MOS gas sensors.

Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.

How Stickiness Can Speed Up Diffusion in Confined Systems

The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating microchannels. Our results are confirmed by numerical calculations and Monte Carlo simulations.

Oxygen Ion Implantation Improving Cell Adhesion on Titanium Surfaces through Increased Attraction of Fibronectin PHSRN Domain

Mechanistic understanding of fibronectin (FN) adsorption which determines cell adhesion on cell-implant interfaces is significant for improving the osteoconduction and soft-tissue healing of implants. Here, it is shown that the adsorption behavior of FN on the titanium oxide surface (TiO₂ ) is highly relative to its Pro-His-Ser-Arg-Asn (PHSRN) peptide. FN lacking PHSRN fails to bind to surfaces, resulting in inhibited cell adhesion and spreading. Molecular dynamics simulation shows higher affinity and greater adsorption energy of PHSRN peptide with TiO₂ surface due to the stronger hydrogen bonds formed by the serine and arginine residues with O ion of the substrate. Finally, by increasing O content in TiO₂ surfaces through O ion-beam implantation, improving the cell adhesion, cell differentiation, and the subsequent biomineralization on titanium implant is realized. This study reveals the vital role of PHSRN in FN-mediated cell adhesion on implant surfaces, providing a promising new target for further tissue integration and implant success.

Rotational dynamics and transition mechanisms of surface-adsorbed proteins

The exquisite organization exhibited by hybrid biomolecular–inorganic materials in nature has inspired the development of synthetic analogues for numerous applications. Nevertheless, a mechanistic picture of the energetic controls and response dynamics leading to organization is lacking. Here, we pair high-speed atomic force microscopy with machine learning and Monte Carlo simulations to analyze the rotational dynamics of rod-like proteins on a crystal lattice, simultaneously quantifying the orientational energy landscape and transition probabilities between energetically favorable orientations. Although rotations largely follow Brownian diffusion, proteins often make large jumps in orientation, thus rapidly overcoming barriers that usually inhibit rotation. Moreover, the rotational dynamics can be tuned via protein size and solution chemistry, providing tools for controlling biomolecular assembly at inorganic interfaces.

Assembly of biomolecules at solid–water interfaces requires molecules to traverse complex orientation-dependent energy landscapes through processes that are poorly understood, largely due to the dearth of in situ single-molecule measurements and statistical analyses of the rotational dynamics that define directional selection. Emerging capabilities in high-speed atomic force microscopy and machine learning have allowed us to directly determine the orientational energy landscape and observe and quantify the rotational dynamics for protein nanorods on the surface of muscovite mica under a variety of conditions. Comparisons with kinetic Monte Carlo simulations show that the transition rates between adjacent orientation-specific energetic minima can largely be understood through traditional models of in-plane Brownian rotation across a biased energy landscape, with resulting transition rates that are exponential in the energy barriers between states. However, transitions between more distant angular states are decoupled from barrier height, with jump-size distributions showing a power law decay that is characteristic of a nonclassical Levy-flight random walk, indicating that large jumps are enabled by alternative modes of motion via activated states. The findings provide insights into the dynamics of biomolecules at solid–liquid interfaces that lead to self-assembly, epitaxial matching, and other orientationally anisotropic outcomes and define a general procedure for exploring such dynamics with implications for hybrid biomolecular–inorganic materials design.

Enhanced Facilitated Diffusion of Membrane-Associating Proteins under Symmetric Confinement

The facilitated surface diffusion of transiently adsorbing molecules in a planar confined microenvironment (i.e., slit-like confinement) is highly relevant to biological phenomena, such as extracellular signaling, as well as numerous biotechnology systems. Here, we studied the surface diffusion of individual proteins confined between two symmetric lipid bilayer membranes, under a continuum of confinement heights, using single-molecule tracking and convex lens-induced confinement as well as hybrid, kinetic Monte Carlo simulations of a generalized continuous time random walk process. Surface diffusion was observed to vary non-monotonically with confinement height, exhibiting a maximum at a height of ∼750 nm, where diffusion was nearly 40% greater than that for a semi-infinite system. This demonstrated that planar confinement can, in fact, increase surface diffusion, qualitatively validating previous theoretical predictions. Simulations reproduced the experimental results and suggested that confinement enhancement of surface diffusion for symmetric systems is limited to cases where the adsorbate exhibits weak surface sticking.

Motion of an active particle with dynamical disorder

We propose a model for investigating the motion of a single active particle in a heterogeneous environment where the heterogeneity may arise due to crowding, conformational fluctuations and/or slow rearrangement of the surroundings. Describing the active particle in terms of the Ornstein-Uhlenbeck process (OUP) and incorporating heterogeneity in a thermal bath using two separate models, namely "diffusing diffusivity" and "switching diffusion", we explore the essential dynamical properties of the particle for its one-dimensional motion. In addition, we show how the dynamical behavior is controlled by dynamical variables associated with active noise such as strength and persistence time. Our model is relevant in the context of single particle dynamics in a crowded environment, driven by activity.

The competing influence of surface roughness, hydrophobicity, and electrostatics on protein dynamics on a self-assembled monolayer

Surface morphology, in addition to hydrophobic and electrostatic effects, can alter how proteins interact with solid surfaces. Understanding the heterogeneous dynamics of protein adsorption on surfaces with varying roughness is experimentally challenging. In this work, we use single-molecule fluorescence microscopy to study the adsorption of α-lactalbumin protein on the glass substrate covered with a self-assembled monolayer (SAM) with varying surface concentrations. Two distinct interaction mechanisms are observed: localized adsorption/desorption and continuous-time random walk (CTRW). We investigate the origin of these two populations by simultaneous single-molecule imaging of substrates with both bare glass and SAM-covered regions. SAM-covered areas of substrates are found to promote CTRW, whereas glass surfaces promote localized motion. Contact angle measurements and atomic force microscopy imaging show that increasing SAM concentration results in both increasing hydrophobicity and surface roughness. These properties lead to two opposing effects: increasing hydrophobicity promotes longer protein flights, but increasing surface roughness suppresses protein dynamics resulting in shorter residence times. Our studies suggest that controlling hydrophobicity and roughness, in addition to electrostatics, as independent parameters could provide a means to tune desirable or undesirable protein interactions with surfaces.

Single-molecule photocatalytic dynamics at individual defects in two-dimensional layered materials

The insightful comprehension of in situ catalytic dynamics at individual structural defects of two-dimensional (2D) layered material, which is crucial for the design of high-performance catalysts via defect engineering, is still missing. Here, we resolved single-molecule trajectories resulted from photocatalytic activities at individual structural features (i.e., basal plane, edge, wrinkle, and vacancy) in 2D layered indium selenide (InSe) in situ to quantitatively reveal heterogeneous photocatalytic dynamics and surface diffusion behaviors. The highest catalytic activity was found at vacancy in a four-layer InSe, up to ~30× higher than that on the basal plane. Moreover, lower adsorption strength of reactant and slower dissociation/diffusion rates of product were found at more photocatalytic active defects. These distinct dynamic properties are determined by lattice structures/electronic energy levels of defects and layer thickness of supported InSe. Our findings shed light on the fundamental understanding of photocatalysis at defects and guide the rational defect engineering.

Single-Molecule Dynamics Reflect IgG Conformational Changes Associated with Ion-Exchange Chromatography

Conformational changes of antibodies and other biologics can decrease the effectiveness of pharmaceutical separations. Hence, a detailed mechanistic picture of antibody-stationary phase interactions that occur during ion-exchange chromatography (IEX) can provide critical insights. This work examines antibody conformational changes and how they perturb antibody motion and affect ensemble elution profiles. We combine IEX, three-dimensional single-protein tracking, and circular dichroism spectroscopy to investigate conformational changes of a model antibody, immunoglobulin G (IgG), as it interacts with the stationary phase as a function of salt conditions. The results indicate that the absence of salt enhances electrostatic attraction between IgG and the stationary phase, promotes surface-induced unfolding, slows IgG motion, and decreases elution from the column. Our results reveal previously unreported details of antibody structural changes and their influence on macroscale elution profiles.

Super-resolution fluorescence imaging of extracellular environments

The extracellular matrix (ECM) is an important biophysical environment that plays a role in a number of physiological processes. The ECM is highly dynamic, with changes occurring as local, nanoscale, physicochemical variations in physical confinement and chemistry from the perspective of biological molecules. The length and time scale of ECM dynamics are challenging to measure with current spectroscopic techniques. Super-resolution fluorescence microscopy has the potential to probe local, nanoscale, physicochemical variations in the ECM. Here, we review super-resolution imaging and analysis methods and their application to study model nanoparticles and biomolecules within synthetic ECM hydrogels and the brain extracellular space (ECS). We provide a perspective of future directions for the field that can move super-resolution imaging of the ECM towards more biomedically-relevant samples. Overall, super-resolution imaging is a powerful tool that can increase our understanding of extracellular environments at new spatiotemporal scales to reveal ECM processes at the molecular-level.

Non-Arrhenius kinetics and slowed-diffusion mechanism of molecular aggregation of a rhodamine dye on colloidal particles

The non-covalent association is important for many fields of science, including processes in living systems. This work elucidates the mechanism of rhodamine 123 molecular aggregation in dispersions of a layered silicate and explains the mystery of the slow kinetics of this process. Chemometric analysis of thousands of spectra recorded by stopped-flow visible spectroscopy identified two parallel diffusion processes described by a two-phase exponential function. The slow and fast processes followed the super-Arrhenius kinetics and were assigned to lateral (surface) diffusion and inter-particle diffusion of dye cations, respectively. This work, supported by a large amount of data and their in-depth analysis, provides the first evidence of how these processes coexist together and provides quantitative analysis of their dependence on the reaction conditions. The implications of this work can be crucial for understanding the mechanism of the non-covalent association of adsorbed molecules in nature.

Single-Molecule Study of Thermomyces lanuginosus Lipase in a Detergency Application System Reveals Diffusion Pattern Remodeling by Surfactants and Calcium

Lipases comprise one of the major enzyme classes in biotechnology with applications within, e.g., baking, brewing, biocatalysis, and the detergent industry. Understanding the mechanisms of lipase function and regulation is therefore important to facilitate the optimization of their function by protein engineering. Advances in single-molecule studies in model systems have provided deep mechanistic insights on lipase function, such as the existence of functional states, their dependence on regulatory cues, and their correlation to activity. However, it is unclear how these observations translate to enzyme behavior in applied settings. Here, single-molecule tracking of individual Thermomyces lanuginosus lipase (TLL) enzymes in a detergency application system allowed real-time direct observation of spatiotemporal localization, and thus diffusional behavior, of TLL enzymes on a lard substrate. Parallelized imaging of thousands of individual enzymes allowed us to observe directly the existence and quantify the abundance and interconversion kinetics between three diffusional states that we recently provided evidence to correlate with function. We observe redistribution of the enzyme's diffusional pattern at the lipid-water interface as well as variations in binding efficiency in response to surfactants and calcium, demonstrating that detergency effectors can drive the sampling of lipase functional states. Our single-molecule results combined with ensemble activity assays and enzyme surface binding efficiency readouts allowed us to deconvolute how application conditions can significantly alter protein functional dynamics and/or surface binding, both of which underpin enzyme performance. We anticipate that our results will inspire further efforts to decipher and integrate the dynamic nature of lipases, and other enzymes, in the design of new biotechnological solutions.

Brownian Dynamics Simulations of Proteins in the Presence of Surfaces: Long-Range Electrostatics and Mean-Field Hydrodynamics

Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian dynamics simulations can be carried out with the approximation of rigid body solutes moving through a continuum solvent. This allows the precomputation of interaction potential grids for the solutes, thereby allowing the computationally efficient calculation of forces. However, hydrodynamic and long-range electrostatic interactions cannot be fully treated with grid-based approaches alone. Here, we develop a treatment of both hydrodynamic and electrostatic interactions to include the presence of surfaces by modeling grid-based and long-range interactions. We describe its application to simulate the self-association and many-molecule adsorption of the well-characterized protein hen egg-white lysozyme to mica-like and silica-like surfaces. We find that the computational model can recover a number of experimental observables of the adsorption process and provide insights into their determinants. The computational model is implemented in the Simulation of Diffusional Association (SDA) software package.

Polarization-resolved single-molecule tracking reveals strange dynamics of fluorescent tracers through a deep rubbery polymer network

Tracking the movement of fluorescent single-molecule (SM) tracers has provided several new insights into the local structure and dynamics in complex environments such as soft materials and biological systems. However, SM tracking (SMT) remains unreliable at molecular length scales, as the localization error (LE) of SM trajectories (∼30-50 nm) is considerably larger than the size of molecular tracers (∼1-2 nm). Thus, instances of tracer (im)mobility in heterogeneous media, which provide indicators for underlying anomalous-transport mechanisms, remain obscured within the realms of SMT. Since the translation of passive tracers in an isotropic media is associated with fast dipolar rotation, we propose that authentic pauses within the LE can be revealed by probing the hindrance of SM reorientational dynamics. Here, we demonstrate how polarization-resolved SMT (PR-SMT) can provide emission anisotropy at each super-localized position, thereby revealing the tumbling propensity of SMs during random walks. For rhodamine 6G tracers undergoing heterogeneous transport in a hydrated polyvinylpyrrolidone (PVP) network, analysis of PR-SMT trajectories enabled us to discern instances of genuine immobility and localized motion within the LE. Our investigations on 100 SMs in (plasticized) PVP films reveal a wide distribution of dwell times and pause frequencies, demonstrating that most probes intermittently experience complete translational and rotational immobilization. This indicates that tracers serendipitously encounter compact, rigid polymer cavities during transport, implying the existence of nanoscale glass-like domains sparsely distributed in a predominantly deep-rubbery polymer network far above the glass transition.

Faster Surface Ligation Reactions Improve Immobilized Enzyme Structure and Activity

During integration into materials, the inactivation of enzymes as a result of their interaction with nanometer size denaturing "hotspots" on surfaces represents a critical challenge. This challenge, which has received far less attention than improving the long-term stability of enzymes, may be overcome by limiting the exploration of surfaces by enzymes. One way this may be accomplished is through increasing the rate constant of the surface ligation reaction and thus the probability of immobilization with reactive surface sites (i.e., ligation efficiency). Here, the connection between ligation reaction efficiency and the retention of enzyme structure and activity was investigated by leveraging the extremely fast reaction of strained trans-cyclooctene (sTCOs) and tetrazines (Tet). Remarkably, upon immobilization via Tet-sTCO chemistry, carbonic anhydrase (CA) retained 77% of its solution-phase activity, while immobilization via less efficient reaction chemistries, such as thiol-maleimide and azide-dibenzocyclooctyne, led to activity retention of only 46% and 27%, respectively. Dynamic single-molecule fluorescence tracking methods further revealed that longer surface search distances prior to immobilization (>0.5 μm) dramatically increased the probability of CA unfolding. Notably, the CA distance to immobilization was significantly reduced through the use of Tet-sTCO chemistry, which correlated with the increased retention of structure and activity of immobilized CA compared to the use of slower ligation chemistries. These findings provide an unprecedented insight into the role of ligation reaction efficiency in mediating the exploration of denaturing hotspots on surfaces by enzymes, which, in turn, may have major ramifications in the creation of functional biohybrid materials.

Nanoconfinement between Graphene Walls Suppresses the Near-Wall Diffusion of the Ionic Liquid [BMIM][PF6]

We identify two distinct regimes for the diffusion of the ionic liquid [BMIM][PF₆] confined between parallel graphene walls using molecular dynamics simulations. Within 2 nm of the wall, the cations and anions form a well-defined layered structure. In this region, the in-plane diffusion coefficients are suppressed when compared to their bulk values and increase monotonically with the distance away from the wall. Beyond 2 nm from the wall, the density profile and in-plane diffusion coefficients recover their bulk values. The channel-averaged in-plane diffusion coefficients increase monotonically with wall separation and recover the bulk values at a separation of 15 nm. A simple semianalytical model is proposed that mirrors this trend. The results also highlight the importance of applying a finite-size correction to molecular dynamics-predicted diffusion coefficients of confined liquids, which may otherwise be unusually larger than their bulk values.

Revealing the dynamic adsorption and diffusion of peptide amphiphile on supported lipid bilayer by single molecule experiment and simulation

Dynamic adsorption and diffusion of peptide amphiphiles (PAs) with different numbers of alkyl tails on supported lipid bilayers (SLBs) were investigated by single molecule tracking experiment and molecule dynamic simulation. Experimental results show two distinct populations of PAs with different residence time. Residence time of adsorbed PAs increases with the increase of the alkyl tails, whereas diffusion coefficient monotonically decreases with rising the number of alkyl tails and also decreases with increasing the mobility of SLBs. All-atom molecule dynamic simulation results prove that the adsorption and diffusion of PAs on SLB surface are mainly determined by interactions between PAs and SLBs and also the intrinsic mobility of PAs in aqueous solution. The electrostatic interactions and the mobility of PAs are two dominated but contradictory coefficients for the adsorption and diffusion of PAs. By increasing the alkyl tails, the mobility of PAs decreases while the electrostatic property does not change significantly, resulting in the increase of residence time and decrease of diffusivity of PAs. Additionally, for the PAs with large number of alkyl tails (≥ 3 alkyl tails), steric hindrance of alkyl tails leads to the decrease of adsorption probability of PAs on SLB surface. These findings lay the groundwork for guiding the design of PAs with high cell affinity, potentially useful for efficient drug delivery.

Nanoparticle Tracking to Probe Transport in Porous Media

From the granular and fractured subsurface environment to highly engineered polymer membranes used in pharmaceutical purification, porous materials are ubiquitous in nature and industrial applications. In particular, porous media are used extensively in processes including water treatment, pharmaceutical sterilization, food/beverage processing, and heterogeneous catalysis, where hindered mass transport is either essential to the process or a necessary but undesirable limitation. Unfortunately, there are currently no universal models capable of predicting mass transport based on a description of the porous material because real porous materials are complex and because many coupled dynamic mechanisms (e.g., adsorption, steric effects, hydrodynamic effects, electrostatic interactions, etc.) give rise to the observed macroscopic transport phenomena.While classical techniques, like nuclear magnetic resonance and dynamic light scattering, provide useful information about mass transport in porous media at the ensemble level, they provide limited insight into the microscopic mechanisms that give rise to complex phenomena such as anomalous diffusion, hindered pore-space accessibility, and unexpected retention under flow, among many others. To address this issue, we have developed refractive index matching imaging systems, combined with single-particle tracking methods, allowing the direct visualization of single-particle motion within a variety of porous materials.In this Account, we summarize our recent efforts to advance the understanding of nanoparticle transport in porous media using single-particle tracking methods in both fundamental and applied scenarios. First, we describe the basic principles for two-dimensional and three-dimensional single-particle tracking in porous materials. Then, we provide concrete examples of nanoparticle transport in porous materials from two perspectives: (1) understanding fundamental elementary particle transport processes in porous media, including pore accessibility and cavity escape, which limit transport in porous media, and (2) facilitating applications in industrial processes, e.g., by understanding the mechanisms of particle fouling and remobilization in filtration membranes. Finally, we provide an outlook of opportunities associated with investigating other types of mass transport in confined environments using single-particle tracking methods, including electrophoretic and self-propelled motion.

Surface hopping propagator: An alternative approach to diffusion-influenced reactions

Dynamics of a particle diffusing in a confinement can be seen a sequence of bulk-diffusion-mediated hops on the confinement surface. Here, we investigate the surface hopping propagator that describes the position of the diffusing particle after a prescribed number of encounters with that surface. This quantity plays the central role in diffusion-influenced reactions and determines their most common characteristics such as the propagator, the first-passage time distribution, and the reaction rate. We derive explicit formulas for the surface hopping propagator and related quantities for several Euclidean domains: half-space, circular annuli, circular cylinders, and spherical shells. These results provide the theoretical ground for studying diffusion-mediated surface phenomena. The behavior of the surface hopping propagator is investigated for both "immortal" and "mortal" particles.

Complex Nanoparticle Diffusional Motion in Liquid-Cell Transmission Electron Microscopy

Liquid-cell transmission electron microscopy (LCTEM) is a powerful in situ videography technique that has the potential to allow us to observe solution-phase dynamic processes at the nanoscale, including imaging the diffusion and interaction of nanoparticles. Artefactual effects imposed by the irradiated and confined liquid-cell vessel alter the system from normal "bulk-like" behavior in multiple ways. These artefactual LCTEM effects will leave their fingerprints in the motion behavior of the diffusing objects, which can be revealed through careful analysis of the object-motion trajectories. Improper treatment of the motion data can lead to erroneous descriptions of the LCTEM system's conditions. Here, we advance our anomalous diffusion object-motion analysis (ADOMA) method to extract a detailed description of the liquid-cell system conditions during any LCTEM experiment by applying a multistep analysis of the data and treating the x/y vectors of motion independently and in correlation with each other and with the object's orientation/angle.

Large Deviations for Continuous Time Random Walks

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.

Review and reproducibility of forming adsorbed layers from solvent washing of melt annealed films

Recent studies suggest chain adsorption in the melt may be responsible for a number of property changes in thin films by making correlations between the residual adsorbed layer thickness h_ads(t) measured after a given solvent washing procedure as a function of annealing time t of the film at an elevated temperature prior to this solvent rinse. This procedure, frequently called "Guiselin's experiment", refers to the thought experiment proposed in a 1992 theoretical treatment by Guiselin that assumed chain segments in contact with the surface are irreversibly adsorbed whereby unadsorbed chains could be washed away by solvent without disturbing the adsorbed substrate contact points in the melt. In the present work, we review this recent literature, identifying and experimentally testing a common protocol for forming adsorbed layers h_ads(t) from solvent washing melt films. We find h_ads(t) curves to be far less reproducible and reliable than implied in the literature, strongly dependent on solvent washing and substrate cleaning conditions, and annealing at elevated temperatures is unnecessary as densification of films sitting at room temperature makes the glassy film harder to wash off, leaving behind h_ads of comparable thickness. This review also summarizes literature understanding developed over several decades of study on polymer adsorption in solution, which experimentally demonstrated that polymer chains in solution are highly mobile, diffusing and exchanging on the surface even in the limit of strong adsorption, contradicting Guiselin's assumption. Preformed adsorbed layers of different thicknesses h_ads are shown to not affect the average glass transition temperature or physical aging of 30 nm thick films. In summary, a number of open questions and implications are discussed related to thin films and polymer nanocomposites.

Modeling of adsorption flux in nickel-contaminated synthetic simulated wastewater in the batch reactor

In the present investigation, physico-chemical characterization of composite material revealed the presence of fluffy surface structure with crystalline look and negatively charged surface functional groups. The study of adsorption flux by using dimensionless numbers φ (2.62), N_k (62.68) and λ (1.17 × 10^-5) proved that adsorption of nickel ions on the surface of composite material was mostly film diffusion-limited with maximum surface area coverage coupled with weakened surface tension. The results of intraparticle diffusivity and Boyd plot model showed that at the onset of process, film diffusion was the primary mechanism involved and at the later stage intraparticle diffusion played a critical role as rate governing step. The values of film (0.65 × 10^-8 cm² sec^-1) and pore diffusivity (1.8 × 10^-12 cm² sec^-1) coefficients showed that the adsorption process is dependent upon two different types of diffusion namely film and pore diffusion. Overall, transport and reshuffling mechanism had no substantial role in adsorption dynamics of nickel ions on the surface of composite material. Sorption isotherm and kinetics modeling showed higher values of regression coefficients for Langmuir isotherm (R² = 0.99) and pseudo-second-order kinetic model (R² = 0.99) compared to other models. This showed that sorption of nickel followed monolayer coverage with chemisorption at optimized process parameters like pH 6, biosorbent dose 0.1 g/L, temperature 50 °C, agitation rate180 rpm, adsorbate concentration100 mg/L and contact time 60 minutes. The positive value of enthalpy of adsorption (ΔH = + 10.41 kJ/mole) and entropy (ΔS = +58.19 J/mol K) showed that binding of nickel ions on the surface of the composite material was endothermic with improved randomness at solid-liquid interface. The negative value of (ΔG = -6.4 to -8.67 kJ/mol) showed spontaneous nature of nickel adsorption on composite material in the liquid phase.

Diffusion behavior of peptide amphiphiles containing different numbers of alkyl tails at a hydrophobic solid-liquid interface: single molecule tracking investigation

Using the single molecule tracking technique, the diffusion behavior of peptide amphiphiles (PAs) with different numbers of alkyl tails at a hydrophobic solid-liquid interface has been investigated. The effect of the number of alkyl tails of PAs on molecular trajectories at the hydrophobic solid-liquid interface has been systematically studied. PA molecules display an intermittent motion consisting of immobilization and hopping processes, which has been well simulated by the continuous time random walk (CTRW) model. The results reveal that the hydrophobic interaction between the PAs and hydrophobic surface plays an important role in the diffusion behavior of PAs. Increasing the number of alkyl tails in PAs systematically reduces the mobility of PAs on the hydrophobic surface. Moreover, the diffusion behavior of PAs at the hydrophobic interface also shows pH dependence. A decrease in pH is beneficial to the motion of all PAs on the hydrophobic surface, which can be ascribed to the protonation of PAs in acidic solutions. Therefore, the hydrophobic interaction is crucial to the transport of peptide amphiphiles at hydrophobic interfaces which would be important for the design of peptides in biological applications.

Temporally Anticorrelated Subdiffusion in Water Nanofilms on Silica Suggests Near-Surface Viscoelasticity

Single-molecule tracking was used to probe the local rheology of interfacial water. Fluorescent rhodamine molecules were tracked on silica surfaces as a function of ambient relative humidity, which controlled the thickness of condensed water nanofilms. At low humidity, the molecules exhibited confined diffusion in the vicinity of isolated adsorption sites characterized by a broad distribution of binding stiffness constants; subsequent chemical or physical surface passivation selectively eliminated stiffer binding sites. At increased humidity, molecularly thin water films condensed, permitting near-surface transport of rhodamine molecules. Motion was subdiffusive, with an anomalous exponent increasing with the nanofilm thickness. Molecular trajectories were temporally anticorrelated, ergodic, but also featured transient binding and intermittent diffusion. Statistical modeling demonstrated that this complex motion in water nanofilms had the characteristics of fractional Brownian motion combined with a continuous-time random walk. This was consistent with diffusion within viscoelastic nanofilms, suggesting persistent molecular structuring in the vicinity of the silica surface.

Diffusion dynamics of a single collapsed homopolymer globule at the solid-liquid interface

Contradictive to the conventional wisdom that a collapsed polymer globule in poor solvents adsorb on surfaces in a way analogous to the spreading of a liquid droplet, here we have shown via single molecule measurements that a single poly(N-isoporpylacrylamide) (PNIPAM) globule can jump from one spot to another as an elastic nonadhesive ball even on a hydrophobic polystyrene surface. The molecular weight dependence of the effective surface diffusion coefficient measured for the adsorbed globule suggested that it exhibited mostly a similar globular conformation to that in the bulk solution. Both the displacement and waiting time distributions of the adsorbed globules were found to follow a power-law decay rather than an exponential process, suggesting a broad distribution of binding energies due to the difference in degree of globule deformation. These effects together reflect a character of the viscoelasticity even in a single-chain globule in dilute solutions. Our findings also demonstrate that it is not the single-chain globule but the inter-globule aggregates at high concentration that lead to irreversible adsorption on the surface, which provides novel dynamics and mechanisms of how a thermosensitive polymer adsorbs on the hydrophobic surface above its lower critical solution temperature.

Polymer Free Volume Effects on Protein Dynamics in Polystyrene Revealed by Single-Molecule Spectroscopy

Protein-polymer interactions are critical to applications ranging from biomedical devices to chromatographic separations. The mechanistic relationship between the microstructure of polymer chains and protein interactions is challenging to quantify and not well studied. Here, single-molecule microscopy is used to compare the dynamics of two model proteins, α-lactalbumin and lysozyme, at the interface of uncharged polystyrene with varied molecular weights. The two proteins exhibit different surface interaction mechanisms despite having a similar size and structure. α-Lactalbumin exhibits interfacial adsorption-desorption with residence times that depend on polymer molecular weight. Lysozyme undergoes a continuous time random walk at the polystyrene surface with residence times that also depend on the molecular weight of polystyrene. Single-molecule observables suggest that the hindered continuous time random walk dynamics displayed by lysozyme are determined by the polystyrene free volume, a finding supported by thermal annealing and solvent quality studies. Hindered dynamics are dominated by short-range hydrophobic interactions where the contributions of electrostatic forces are negligible. This work establishes a relationship between the microscale structure (i.e., free volume) of polystyrene polymer chains to nanoscale interfacial protein dynamics.

Anomalous protein kinetics on low-fouling surfaces

In this work, protein-surface interactions were probed in terms of adsorption and desorption of a model protein, bovine serum albumin, on a low-fouling surface with single-molecule localization microscopy. Single-molecule experiments enable precise determination of both adsorption and desorption rates. Strikingly the experimental data show anomalous desorption kinetics, evident as a surface dwell time that exhibits a power-law distribution, i.e. a heavy-tailed rather than the expected exponential distribution. As a direct consequence of this heavy-tailed distribution, the average desorption rate depends upon the time scale of the experiment and the protein surface concentration does not reach equilibrium. Further analysis reveals that the observed anomalous desorption emerges due to the reversible formation of a small fraction of soluble protein multimers (small oligomers), such that each one desorbs from the surface with a different rate. The overall kinetics can be described by a series of elementary reactions, yielding simple scaling relations that predict experimental observations. This work reveals a mechanistic origin for anomalous desorption kinetics that can be employed to interpret observations where low-protein fouling surfaces eventually foul when in long-term contact with protein solutions. The work also provides new insights that can be used to define design principles for non-fouling surfaces and to predict their performance.

Packets of Diffusing Particles Exhibit Universal Exponential Tails

Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function P(X,t) of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of transport in random media. By extending the large deviations approach for a continuous time random walk, we uncover a general universal behavior for the decay of the density. It is found that fluctuations in the number of steps of the random walker, performed at finite time, lead to exponential decay (with logarithmic corrections) of P(X,t). This universal behavior also holds for short times, a fact that makes experimental observations readily achievable.

Protein adsorption measurements on low fouling and ultralow fouling surfaces: A critical comparison of surface characterization techniques

Ultralow protein fouling behavior is a common target for new high-performance materials. Ultralow fouling is often defined based on the amount of irreversibly adsorbed protein (< 5 ng cm^-2) measured by a surface ensemble averaging method. However, protein adsorption at solid interfaces is a dynamic process involving multiple steps, which may include adsorption, desorption, and irreversible protein denaturation. In order to better optimize the performance of antifouling surfaces, it is imperative to fully understand how proteins interact with surfaces, including kinetics of adsorption and desorption, conformation, stability, and amount of adsorbed proteins. Defining ultralow fouling surfaces based on a measurement at or near the limit of detection of a surface-averaged measurement may not capture all of this behavior. Single-molecule microscopy techniques can resolve individual protein-surface interactions with high temporal and spatial resolution. This information can be used to tune the properties of surfaces to better resist protein adsorption. In this work, we demonstrate how combining surface plasmon resonance, X-ray photoelectron spectroscopy, atomic force microscopy, and single-molecule localization microscopy provides a more complete picture of protein adsorption on low fouling and ultralow fouling polyelectrolyte multilayer and polymer brush surfaces, over different regimes of protein concentration. In this case, comparing the surfaces using surface plasmon resonance alone is insufficient to rank their resistance to protein adsorption. Our results suggest a revision of the accepted definition of ultralow fouling surfaces is timely: with the advent of time-resolved studies of protein adsorption kinetics at the single-molecule level, it is neither necessary nor sufficient to rely on a surface averaging techniques to qualify ultralow fouling surfaces. Since protein adsorption is a dynamic process, understanding how surface properties affect the kinetics of protein adsorption will enable the design of future generations of advanced antifouling materials. STATEMENT OF SIGNIFICANCE: The design of ultralow fouling surfaces is often optimized based on a single surface-averaging technique measuring the amount of irreversibly adsorbed protein. This work provides a critical comparison of alternative techniques for evaluating protein adsorption on low fouling and ultralow fouling surfaces, and demonstrates how additional information about the dynamics of protein-surface interactions at the interface can be obtained by application of single-molecule microscopy. This approach could be used to better elucidate mechanisms of protein resistance and design principles for advanced ultralow fouling materials.

The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated

The motion of the confined doxorubicin drug molecule exhibits an interesting combination of anomalous diffusion features.