Nanoscale topography influences polymer surface diffusion

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.

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.

Simulation study on the effect of polydisperse nanoparticles on polymer diffusion in crowded environments

The diffusion of polymer chains in a crowded environment with large and small immobile, attractive nanoparticles (NPs) is studied using Langevin dynamics simulations. For orderly distributed NPs on the simple cubic lattice, our results show that the diffusion of polymer chains is dependent on the NP-NP distance or lattice distance d. At low d where NPs are placed closely, subdiffusion occurs at a sufficiently high polydispersity of NPs, PD. Both the apparent diffusion coefficient and subdiffusion exponent of polymer chains decrease with increasing PD, attributed to the adsorption of polymers on NP clusters formed by larger NPs. At large d, normal diffusion is always observed, and the diffusion coefficient increases with increasing PD. The reason is that, at high PD, the difference between single large NP adsorption and double large NP adsorption is reduced, which increases the exchange of a polymer between the two adsorption states. Finally, the impact of size polydispersity of NPs on the diffusion of polymer chains in a crowded environment with randomly distributed NPs is also investigated. The results show that the position disorder of NPs enhances the subdiffusion of the system.

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.

Simulation Study on the Mechanism of Intermediate Subdiffusion of Diffusive Particles in Crowded Systems

The intermediate subdiffusion of diffusive particles in crowded systems is studied for two model systems: the continuous time random walk (CTRW) model and the obstruction-binding model. For the CTRW model with an arbitrarily given longest waiting time τmax, we find that the diffusive particle exhibits subdiffusion below τmax and recovers normal diffusion above τmax. For the obstruction-binding model with randomly distributed attractive obstacles, the diffusion of the diffusive particle is dependent on the binding energy and the density of obstacles. Interestingly, diffusion curves for different binding strengths can be overlapped by rescaling the simulation time, indicating that the diffusive particle in the obstruction-binding model can change from the intermediate subdiffusion to the normal diffusion at a long-term simulation scale. The results of the two model systems show that the diffusive particles only exhibit intermediate subdiffusion below the longest waiting time. Therefore, long timescale subdiffusion would only be observed in the CTRW model with an infinitely long waiting time and in the obstruction-binding model with an infinitely large binding strength.

Revealing molecular diffusion dynamics in polymer microspheres by optical resonances

Understanding the diffusion of small molecules in polymer microsystems is of great interest in diverse fundamental and industrial research. Despite the rapidly advancing optical imaging and spectroscopic techniques, entities under investigation are usually limited to flat films or bulky samples. We demonstrate a route to in situ detection of diffusion dynamics in polymer micro-objects by means of optical whispering-gallery mode resonances. Through mode tracking, interactions between solvent molecules and polymer microspheres, including sorption, diffusion, and swelling can be quantitatively analyzed. A turning point of mode response is observed, while the diffusion exceeds the sub-wavelength-thick outermost layer as the radial extent of resonances and starts penetrating the inner core. The estimated solubility in the glassy polymer is consistent with the predicted value using Flory-Huggins theory. Besides, the non-Fickian contribution is analyzed in such a glassy polymer-penetrant system. Our work represents a high-precision and label-free approach to describing characteristics in diffusion dynamics.

A prediction model for nanoparticle diffusion behavior in fibrous materials considering steric and hydrodynamic resistances

Precise prediction of the hindered diffusion behavior of electroneutral particles in fibrous media plays a critical role in the development of drugs, polymer membranes, and porous electrodes. However, the random microstructure and unknown coupling relationship of multiple resistance mechanisms lead to the lack of a universal prediction model. In this work, a dual-resistance model is proposed by reconstructed pore-scale simulations, which presents the coexistence of steric and hydrodynamic resistances in the multiplication form. The simulation results show that the relationship between steric resistance and structural parameters (porosity, fiber radius, and particle radius) is exponential, while that for hydrodynamic resistance is polynomial. The dominant diffusion resistance is found to change from hydrodynamic to steric resistance with a decrease in porosity. The fluorescent polystyrene microsphere diffusivity in a series of SiO₂ fibrous media is determined by single-particle tracking experiments, quantitatively confirming the dual-resistance model. The present model can be used for rapid diffusivity prediction and fibrous membrane and drug design.

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.

Novel Diffusion Mechanism of Polymers Pinned to an Attractive Impurity

Actual substrates unavoidably possess, to some extent, defects and dirt, which motivate understanding the impact due to their presence. The presence of a substrate naturally breaks symmetries. Additionally, it effectively reduces spatial dimensionality, which favors fluctuation-dominated behavior, but it also provides a multitude of possible interactions. We show evidence of novel behavior in the case of polymer mass transport at a crystalline substrate when a single attractive impurity is present. Specifically, we introduce a model system describing how an attractive impurity pins adsorbed polymers on a substrate. We propose a novel mechanism to explain the size scaling dependence of the diffusion coefficient as D∼N−3/2 for polymers with N monomers. Additionally, the size dependence of the diffusion coefficient scales can be described as D∼N−δ, with δ=1.51 as determined from extensive simulations.

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.

Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels

We present a numerical study on the effect of hydrodynamic interactions (HI) on the diffusion of inert point tracer particles in several fixed random structures. As expected, the diffusion is hampered by the extra hydrodynamic friction introduced by the obstacle network. However, a non-trivial effect due to HI appears in the analysis of the van-Hove displacement probability close to the percolation threshold, where tracers diffuse through critical fractal paths. We show that the tracer dynamics can be split up into short and long jumps, the latter being ruled by either exponential or Gaussian van Hove distribution tails. While at short time HI slow down the tracer diffusion, at long times, hydrodynamic interactions with the obstacles increase the probability of longer jumps, which circumvent the traps of the labyrinth more easily. Notably, the relation between the anomalous diffusion exponent and the fractal dimension of the critical (intricate) paths is greater than one, which implies that the long-time (long-jump) diffusion is mildly superdiffuse. A possible reason for such a hastening of the diffusion along the network corridors is the hydrodynamically induced mobility anisotropy, which favours displacements parallel to the walls, an effect which has already been experimentally observed in collagen gels.

A simulation study on the subdiffusion of polymer chains in crowded environments containing nanoparticles

Polymer chains in crowded environments often show subdiffusive behavior. We adopt molecular dynamics simulations to study the conditions for the subdiffusion of polymer chains in crowded environments containing randomly distributed, immobile, attractive nanoparticles (NPs). The attraction is strong enough to adsorb polymer chains on NPs. The results show that subdiffusion occurs at a low concentration of polymer chains (c_p). A transition from subdiffusion to normal diffusion is observed when c_p exceeds the transition concentration , which increases with increasing concentration of NPs while decreases with increasing size of NPs. The high concentration and small size of NPs exert a big effect on the subdiffusion of polymer chains. The subdiffusive behavior of polymer chains can be attributed to the strong adsorption of polymer chains on the attractive NPs. For the subdiffusion case, polymer chains are adsorbed strongly on multiple NPs, and they diffuse via the NP-exchange diffusion mechanism. However for the normal diffusion case, polymer chains are either free or weakly adsorbed on one or a few NPs, and they diffuse mainly via the adsorption-and-desorption diffusion mechanism.

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.

Lateral diffusion of single poly(ethylene oxide) chains on the surfaces of glassy and molten polymer films

Fluorescence correlation spectroscopy was used to show that the temperature-dependent diffusion coefficient of poly(ethylene oxide) (PEO) adsorbed on polystyrene and different poly(alkyl methacrylate) (PAMA) films in aqueous solution exhibited a maximum close to (but below) the surface glass transition temperature, T_gs, of the film. This elevated diffusion was observed over a small range of temperatures below T_gs for these surfaces, and at other temperatures, the diffusion was similar to that on silicon, although the diffusion coefficient for PEO on polystyrene at temperatures above T_gs did not completely decrease to that on silicon, in contrast to the PAMA surfaces. It is concluded that the enhanced surface mobility of the films near the surface glass transition temperature induces conformational changes in the adsorbed PEO. The origin of this narrow and dramatic increase in diffusion coefficient is not clear, but it is proposed that it is caused by a coupling of a dominant capillary mode in the liquid surface layer with the polymer. Friction force microscopy experiments also demonstrate an unexpected increase in friction at the same temperature as the increase in diffusion coefficient.

Diffusion of colloidal particles in model porous media

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.

Dynamics of long-term protein aggregation on low-fouling surfaces

Understanding the mechanisms of protein interactions with solid surfaces is critical to predict how proteins affect the performance of materials in biological environments. Low-fouling and ultra-low fouling surfaces are often evaluated in short-term protein adsorption experiments, where 'short-term' is defined as the time required to reach an initial apparent or pseudo-equilibrium, which is usually less than 600 s. However, it has long been recognized that these short-term observations fail to predict protein adsorption behavior in the long-term, characterized by irreversible accumulation of protein on the surface. This important long-term behavior is frequently ignored or attributed to slow changes in surface chemistry over time-such as oxidation-often with little or no experimental evidence. Here, we report experiments measuring protein adsorption on "low-fouling" and "ultralow-fouling" surfaces using single-molecule localization microscopy to directly probe protein adsorption and desorption. The experiments detect protein adsorption for thousands of seconds, enabling direct observation of both short-term (reversible adsorption) and long-term (irreversible adsorption leading to accumulation) protein-surface interactions. By bridging the gap between these two time scales in a single experiment, this work enables us to develop a single mathematical model that predicts behavior in both temporal regimes. The experimental data in combination with the resulting model provide several important insights: (1) short-term measurements of protein adsorption using ensemble-averaging methods may not be sufficient for designing antifouling materials; (2) all investigated surfaces eventually foul when in long-term contact with protein solutions; (3) fouling can occur through surface-induced oligomerization of proteins which may be a distinct step from irreversible adsorption; and (4) surfaces can be designed to reduce oligomerization or the adsorption of oligomers, to prevent or delay fouling.

100th Anniversary of Macromolecular Science Viewpoint: Enabling Advances in Fluorescence Microscopy Techniques

In the past few decades there has been a revolution in the field of optical microscopy with emerging capabilities such as super-resolution and single-molecule fluorescence techniques. Combined with the classical advantages of fluorescence imaging, such as chemical labeling specificity, and noninvasive sample preparation and imaging, these methods have enabled significant advances in our polymer community. This Viewpoint discusses several of these capabilities and how they can uniquely offer information where other characterization techniques are limited. Several examples are highlighted that demonstrate the ability of fluorescence microscopy to understand key questions in polymer science such as single-molecule diffusion and orientation, 3D nanostructural morphology, and interfacial and multicomponent dynamics. Finally, we briefly discuss opportunities for further advances in techniques that may allow them to make an even greater contribution in polymer science.

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.

Estimating and leveraging protein diffusion on ion-exchange resin surfaces

Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed protein, accelerating molecular recognition, and informing the fundamentals of adsorption. In the case of ion-exchange chromatographic beads with small, tortuous pores, where the existence of surface diffusion is often not recognized, slow mass transfer can result in lower resin capacity utilization. We demonstrate that accounting for and exploiting protein surface diffusion can alleviate the mass-transfer limitations on multiple significant length scales. Although the surface diffusivity has previously been shown to correlate with ionic strength (IS) and binding affinity, we show that the dependence is solely on the binding affinity, irrespective of pH, IS, and resin ligand density. Different surface diffusivities give rise to different protein distributions within the resin, as characterized using confocal microscopy and small-angle neutron scattering (length scales of micrometer and nanometer, respectively). The binding dependence of surface diffusion inspired a protein-loading approach in which the binding affinity, and hence the surface diffusivity, is modulated by varying IS. Such gradient loading increased the protein uptake efficiency by up to 43%, corroborating the importance of protein surface diffusion in protein transport in ion-exchange chromatography.

Inconsistency of Diffusion and Relaxation of Ring Polymers Adsorbed on Rough Surfaces

We explore the diffusion and relaxation dynamics of a single ring polymer strongly adsorbed on rough surfaces with different roughnesses by means of molecular dynamics simulations. Our simulations demonstrate that on rough surfaces the intrachain topological constraint deriving from the closed architecture induces the inconsistency of diffusion and relaxation of ring polymers. When the lateral chain size is larger than the obstacle distance (2R_g∥,r > d), the ring closure induces the polymers to anchor on a single obstacle and dramatically reduces their diffusivity, where R_g∥,r and d are the lateral components of the mean-square radius of gyration and the obstacle distance, respectively. However, the single obstacle anchoring has no effect on the relaxation of ring polymers, which implies a deviation between the diffusion and the relaxation. With the lateral chain size beyond twice of the obstacle distance (R_g∥,r > d), the ring polymers are totally confined in the array of obstacles and can only diffuse through hopping over the obstacles, resulting in an exponential reduction of their diffusion coefficient. However, the relaxation of ring polymers mainly depends on their rotating reptation and satisfies the reptation-like dynamics, which means that the diffusion and the relaxation are nearly irrelevant. This inconsistency between the diffusion and relaxation is a unique property of adsorbed ring polymers, which would be meaningful to understand the physical nature of polymers with ring closure and significant to develop the corresponding applications.

Influence of Oligonucleotide Grafting Density on Surface-Mediated DNA Transport and Hybridization

Adsorption of soluble DNA to surfaces decorated with complementary DNA plays an important role in many bionanotechnology applications, and previous studies have reported complex dependencies of the surface density of immobilized DNA on hybridization. While these effects have been speculatively ascribed to steric or electrostatic effects, the influence of surface-mediated molecular transport (i.e., intermittent "hopping diffusion") has not been fully appreciated. Here, single-molecule tracking and Förster resonance energy transfer (FRET) were employed to characterize the mobility and the hybridization efficiency of adsorbed ssDNA oligonucleotides ("target") at solid-liquid interfaces exhibiting surface-immobilized ssDNA ("probe") over a wide range of surface grafting densities. Two distinct regimes were observed, with qualitatively different transport and hybridization behaviors. At dilute grafting density, only 1-3% of target molecules were observed to associate with probes (i.e., to hybridize). Adsorbing target molecules often searched unsuccessfully and "flew", via desorption-mediated diffusion, to secondary locations before hybridizing. In contrast, at high probe grafting density, approximately 20% of target DNA hybridized to immobilized probes, and almost always in the vicinity of initial adsorption. Moreover, following a dehybridization event, target molecules rehybridized at high probe density, but rehybridization was infrequent in the dilute density regime. Interestingly, the intermittent interfacial transport of mobile target molecules was suppressed by the presence of immobilized probe DNA, presumably due to an increased probability of readsorption following each "hop". Together, these findings suggested that many salient effects of grafting density on surface-mediated DNA hybridization can be directly related to the mechanisms of surface-mediated intermittent diffusion.

Slow polymer diffusion on brush-patterned surfaces in aqueous solution

A model system for the investigation of diffusional transport in compartmentalized nanosystems is described. Arrays of "corrals" enclosed within poly[oligo(ethylene glycol)methyl ether methacrylate] (POEGMA) "walls" were fabricated using double-exposure interferometric lithography to deprotect aminosilane films protected by a nitrophenyl group. In exposed regions, removal of the nitrophenyl group enabled attachment of an initiator for the atom-transfer radical polymerization of end-grafted POEGMA (brushes). Diffusion coefficients for poly(ethylene glycol) in these corrals were obtained by fluorescence correlation spectroscopy. Two modes of surface diffusion were observed: one which is similar to diffusion on the unpatterned surface and a very slow mode of surface diffusion that becomes increasingly important as confinement increases. Diffusion within the POEGMA brushes does not significantly contribute to the results.

Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels

Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity", fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.

Recent advances in optical microscopic methods for single-particle tracking in biological samples

With the rapid development of optical microscopic techniques, explorations on the chemical and biological properties of target objects in biological samples at single-molecule/particle level have received great attention recently. In the past decades, various powerful techniques have been developed for single-particle tracking (SPT) in biological samples. In this review, we summarize the commonly used optical microscopic methods for SPT, such as total internal reflection fluorescence microscopy (TIRFM), super-resolution fluorescence microscopy (SRM), dark-field optical microscopy (DFM), total internal reflection scattering microscopy (TIRSM), and differential interference contrast microscopy (DICM). We then discuss the image processing and data analysis methods, including particle localization, trajectory reconstruction, and diffusion behavior analysis. The application of SPT on the cell membrane, within the cell, and the cellular invading process of viruses are introduced. Finally, the challenges and prospects of optical microscopic technologies for SPT are delineated.

Roughness of Transmembrane Helices Reduces Lipid Membrane Dynamics

The dynamics of cellular membranes is primarily determined by lipid species forming a bilayer. Proteins are considered mainly as effector molecules of diverse cellular processes. In addition to large assemblies of proteins, which were found to influence properties of fluid membranes, biological membranes are densely populated by small, highly mobile proteins. However, little is known about the effect of such proteins on the dynamics of membranes. Using synthetic peptides, we demonstrate that transmembrane helices interfere with the mobility of membrane components by trapping lipid acyl chains on their rough surfaces. The effect is more pronounced in the presence of cholesterol, which segregates from the rough surface of helical peptides. This may contribute to the formation or stabilization of membrane heterogeneities. Since roughness is a general property of helical transmembrane segments, our results suggest that, independent of their size or cytoskeleton linkage, integral membrane proteins affect local membrane dynamics and organization.

Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data

We employ Bayesian statistics using the nested-sampling algorithm to compare and rank multiple models of ergodic diffusion (including anomalous diffusion) as well as to assess their optimal parameters for in silico-generated and real time-series. We focus on the recently-introduced model of Brownian motion with "diffusing diffusivity"-giving rise to widely-observed non-Gaussian displacement statistics-and its comparison to Brownian and fractional Brownian motion, also for the time-series with some measurement noise. We conduct this model-assessment analysis using Bayesian statistics and the nested-sampling algorithm on the level of individual particle trajectories. We evaluate relative model probabilities and compute best-parameter sets for each diffusion model, comparing the estimated parameters to the true ones. We test the performance of the nested-sampling algorithm and its predictive power both for computer-generated (idealised) trajectories as well as for real single-particle-tracking trajectories. Our approach delivers new important insight into the objective selection of the most suitable stochastic model for a given time-series. We also present first model-ranking results in application to experimental data of tracer diffusion in polymer-based hydrogels.

From a Protein's Perspective: Elution at the Single-Molecule Level

Column chromatography is a widely used analytical technique capable of identifying and isolating a desired chemical species from a more complicated mixture. Despite the method's prevalence, theoretical descriptions have not advanced to accommodate today's common analyte, proteins. Proteins are increasingly used as biologics, a term that refers to biological pharmaceuticals, and present new complexities for chromatographic separation. Large variations in surface charge, chemistry, and structure among protein analytes expose the limits in the current theoretical framework's ability to predict the efficiency of a column without empirical data. The bottleneck created by empirical optimization is a strong motivation for a renewed effort to achieve an in-depth understanding of the range of interactions that occur between a protein analyte and the stationary phase that together enable its selective separation from other constituents of a mixture. The physical and chemical processes that dictate the amount of time an analyte spends in the column are often abstracted by theory and treated as statistical distributions. Until recently, these distributions could not be mapped experimentally as traditional experimental techniques could not reveal underlying heterogeneity in structure, charge, and dynamics. Aligning the latest experimental and theoretical advances is thus a hurdle to be overcome so that significant progress can be made toward a predictive chromatographic theory. In this Account, we detail the work of the Landes Lab in developing single-molecule techniques that refine the stochastic theory of chromatography as a first step toward predictive chromatographic column design. We provide a brief review of the development of stochastic theory and establish a mathematical framework to put the discussed physical chemistry in context. We describe our investigations of three pertinent phenomena: mobile/stationary phase exchange, adsorption/desorption kinetics, and hindered diffusion. We highlight experimental evidence that points to nonuniform behavior. Then, we describe our work in developing single-molecule techniques that can evaluate these effects on a protein-by-protein basis. We highlight two developments: fast imaging via super temporal-resolved microscopy (STReM) and visualizing diffusion within pores via a combination of fluorescence correlation spectroscopy and super-resolution optical fluctuation imaging (fcsSOFI). Both methods offer new ways to study chromatographic elution at the single-protein level. Such methods can identify the rare heterogeneities that prevent efficient separations and advance the field closer to predictively optimized protein separations.

Interfacial Properties and Hopping Diffusion of Small Nanoparticle in Polymer/Nanoparticle Composite with Attractive Interaction on Side Group

The diffusion dynamics of fullerene (C 60 ) in unentangled linear atactic polystyrene (PS) and polypropylene (PP) melts and the structure and dynamic properties of polymers in interface area are investigated by performing all-atom molecular dynamics simulations. The comparison of the results in two systems emphasises the influence of local interactions exerted by polymer side group on the diffusion dynamics of the nanoparticle. In the normal diffusive regime at long time scales, the displacement distribution function (DDF) follows a Gaussian distribution in PP system, indicating a normal diffusion of C 60 . However, we observe multiple peaks in the DDF curve for C 60 diffusing in PS melt, which indicates a diffusion mechanism of hopping of C 60 . The attractive interaction between C 60 and phenyl ring side groups are found to be responsible for the observed hopping diffusion. In addition, we find that the C 60 is dynamically coupled with a subsection of a tetramer on PS chain, which has a similar size with C 60 . The phenyl ring on PS chain backbone tends to have a parallel configuration in the vicinity of C 60 surface, therefore neighbouring phenyl rings can form chelation effect on the C 60 surface. Consequently, the rotational dynamics of phenyl ring and the translational diffusion of styrene monomers are found to be slowed down in this interface area. We hope our results can be helpful for understanding of the influence of the local interactions on the nanoparticle diffusion dynamics and interfacial properties in polymer/nanoparticle composites.

Effects of surface roughness on the self-diffusion dynamics of a single polymer

We employ molecular dynamics simulations to simulate the diffusion dynamics of a single polymer adsorbed on surfaces with different roughnesses, which are characterized by the separation distance between obstacles and the height of obstacles. Our simulations demonstrate that for strong adsorption and when the confinement of obstacles is strong enough for all chains, the scaling exponent α of the diffusion coefficient on the chain length exhibits three cases with increase of the height of obstacles: a Rouse plateau with α ≈ -1 (the lateral motion of the polymer chains is free), a reptationlike plateau with α ≈ -1.5 (the polymer chains can hardly stride over the obstacles in the perpendicular direction) and a transition from the Rouse plateau to the reptationlike plateau with -1.5 < α < -1 (the obstacles hinder the lateral motion of the polymer chains). However, with increase of the separation distance between obstacles, the confinement from the obstacles exhibits a decrease (more lateral motions of the polymer chains are allowed), which results in a higher plateau (no longer separate reptationlike dynamics). Our results clarify the effects of surface roughness on the diffusion mechanism of polymer chains strongly adsorbed on solid surfaces in dilute solutions and the resulting transition mechanism from the Rouse scaling to the reptationlike scaling, which is significant for the understanding of the physical nature and the development of the corresponding applications.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?

Three-Dimensional Tracking of Interfacial Hopping Diffusion

Theoretical predictions have suggested that molecular motion at interfaces-which influences processes including heterogeneous catalysis, (bio)chemical sensing, lubrication and adhesion, and nanomaterial self-assembly-may be dominated by hypothetical "hops" through the adjacent liquid phase, where a diffusing molecule readsorbs after a given hop according to a probabilistic "sticking coefficient." Here, we use three-dimensional (3D) single-molecule tracking to explicitly visualize this process for human serum albumin at solid-liquid interfaces that exert varying electrostatic interactions on the biomacromolecule. Following desorption from the interface, a molecule experiences multiple unproductive surface encounters before readsorption. An average of approximately seven surface collisions is required for the repulsive surfaces, decreasing to approximately two and a half for surfaces that are more attractive. The hops themselves are also influenced by long-range interactions, with increased electrostatic repulsion causing hops of longer duration and distance. These findings explicitly demonstrate that interfacial diffusion is dominated by biased 3D Brownian motion involving bulk-surface coupling and that it can be controlled by influencing short- and long-range adsorbate-surface interactions.

Modulation of collective cell behaviour by geometrical constraints

Intracellular and extracellular mechanical forces play a crucial role during tissue growth, modulating nuclear shape and function and resulting in complex collective cell behaviour. However, the mechanistic understanding of how the orientation, shape, symmetry and homogeneity of cells are affected by environmental geometry is still lacking. Here we investigate cooperative cell behaviour and patterns under geometric constraints created by topographically patterned substrates. We show how cells cooperatively adopt their geometry, shape, positioning of the nucleus and subsequent proliferation activity. Our findings indicate that geometric constraints induce significant squeezing of cells and nuclei, cytoskeleton reorganization, drastic condensation of chromatin resulting in a change in the cell proliferation rate and the anisotropic growth of cultures. Altogether, this work not only demonstrates complex non-trivial collective cellular responses to geometrical constraints but also provides a tentative explanation of the observed cell culture patterns grown on different topographically patterned substrates. These findings provide important fundamental knowledge, which could serve as a basis for better controlled tissue growth and cell-engineering applications.

Suppression of CIP4/Par6 attenuates TGF-β1-induced epithelial-mesenchymal transition in NRK-52E cells

Transforming growth factor-β (TGF-β) induces epithelial-mesenchymal transition (EMT) primarily via a Smad-dependent mechanism. However, there are few studies available on TGF-β-induced EMT through the activation of non-canonical pathways. In this study, the Cdc42-interacting protein-4 (CIP4)/partitioning-defective protein 6 (Par6) pathway was investigated in TGF-β1-stimulated NRK-52E cells. Rat NRK-52E cells were obtained and stimulated with TGF-β1. The expression levels of E-cadherin, α-smooth muscle actin (α-SMA) and CIP4 were then examined by western blot analyses. Rat NRK-52E cells were transfected with Par6 or CIP4 small interfering RNA (siRNA), and scrambled siRNA as controls. The cells were incubated with 20 ng/ml of TGF-β1 for 72 h in order to observe the effects of Par6 and CIP4 silencing. Confocal fluorescence microscopy was also applied to reveal the expression and distribution of E-cadherin, α-SMA, Par6 and CIP4. The results demonstrated that E-cadherin expression was decreased, and α-SMA expression was increased in the TGF-β1-stimulated cells. Simultaneously, the increased expression of CIP4 and p-Par6 was confirmed by western blot analyses. The results of confocal fluorescence microscopy revealed that rat CIP4 exhibited cluster formations located adjacent to the cell periphery; however, as for the protein expression and distribution of Par6, there was no obvious difference between the control cells and cells exposed to TGF-β1. siRNA molecules capable of CIP4 and Par6 knockdown were used to demonstrate reversed TGF-β1-induced EMT. Moreover, CIP4 loss of function reversed the increase in p-Par6 protein expression in the TGF-β1-stimulated NRK-52E cells. A similar result was observed with the decreased CIP4 protein expression due to Par6 loss of function. Our data thus suggest that the CIP4/Par6 complex plays an important role in the occurrence of EMT in TGF-β1-stimulated NRK-52E cells. The underlying mechanisms are mediated, at least in part, through the upregulation of CIP4, which occurrs due to stimulation with TGF-β1; subsequently, CIP4 increases the phosphorylation of Par6, which accelerates the process of EMT.

Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media

Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency R_{n}, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

Diffusive dynamics of polymer chains in an array of nanoposts

The diffusion of the head, side, and middle segments in confined polymer chains displays different dynamics in different directions.

Nanoparticle diffusion in crowded and confined media

We identify distinct mechanisms controlling slowing of nanoparticle diffusion through complex media featuring both rigid geometrical confinement and soft mobile crowders. Towards this end, we use confocal microscopy and single particle tracking to probe the diffusion of 400 nm nanoparticles suspended in Newtonian water, in a Newtonian glycerol/water mixture, or in a non-Newtonian polymer solution through a model porous medium, a packed bed of microscale glass beads. The mobility of nanoparticles, as quantified by the long-time diffusion coefficient extracted from the particle mean-squared displacement, slows as the average pore size of the packed bed media decreases for both Newtonian and non-Newtonian solutions. The distribution of particle displacements is non-Gaussian, consistent with the spatial heterogeneity of the geometrical confinement imposed by the packed bed. The slowing of nanoparticle mobility in all solutions follows the predictions of models that describe hydrodynamic interactions with the packed bed. In non-Newtonian solutions, depletion interactions due to the polymers near the glass beads result in temporary adsorption of particles onto the bead surface, as indicated by a stretched-exponential distribution of residence times. Our results therefore suggest that the confined diffusive dynamics of nanoparticles in polymer solutions is controlled by two competing mechanisms: hydrodynamic interactions between particles and spatial obstacles, which dictate the long-time slowing of diffusion, and depletion interactions between particles and confining walls due to the macromolecules, which control transient adsorption and hence alter the statistics of the short-time motion.

Abnormal polymer transport in crowded attractive micropost arrays

We investigate polymer diffusion in a quasi-two-dimensional environment decorated with attractive cylindrical posts using Langevin dynamics simulation. We find that the polymer diffusivity has non-monotonic dependence on the post array density. This diffusive behavior strongly depends on the adsorption-desorption transition and the critical adsorption strength ε_c. For ε < ε_c, the polymer undergoes normal diffusion and the diffusivity decreases as the post density increases due to the reduction of the void volume. For ε > ε_c, polymer dynamics is strongly mediated by post adsorption, and we observe a regime where the polymer diffusivity increases as the post density increases. The polymer diffusivity reaches a maximum, which can be attributed to cross-post translation enabled by large polymer conformation fluctuations. We find both cross-post transport and polymer conformation fluctuations strongly depend on the post absorption strength and the chain length.

Surface Roughness Modulates Diffusion and Fibrillation of Amyloid-β Peptide

The presence of surfaces influences the kinetics of amyloid-β (Aβ) peptide fibrillation. Although it has been generally recognized that the fibrillation process can be assisted or accelerated by surface chemistry, the impact of surface topography, i.e., roughness, on peptide fibrillation is relatively little understood. Here we study the role of surface roughness on surface-mediated fibrillation using polymer coatings of varying roughness as well as polymer microparticles. Using single-molecule tracking, atomic force microscopy, and the thioflavin T fluorescence technique, we show that a rough surface decelerates the two-dimensional (2D) diffusion of peptides and retards the surface-mediated fibrillation. A higher degree of roughness that presents an obstacle to peptide diffusion is found to inhibit the fibrillation process.

Polymer Surface Transport Is a Combination of in-Plane Diffusion and Desorption-Mediated Flights

Previous studies of polymer motion at solid/liquid interfaces described the transport in the context of a continuous time random walk (CTRW) process, in which diffusion switches between desorption-mediated "flights" (i.e., hopping) and surface-adsorbed waiting-time intervals. However, it has been unclear whether the waiting times represented periods of complete immobility or times during which molecules engaged in a different (e.g., slower or confined) mode of interfacial transport. Here we designed high-throughput, single-molecule tracking measurements to address this question. Specifically, we studied polymer dynamics on either chemically homogeneous or nanopatterned surfaces (hexagonal diblock copolymer films) with chemically distinct domains, where polymers were essentially excluded from the low-affinity domains, eliminating the possibility of significant continuous diffusion in the absence of desorption-mediated flights. Indeed, the step-size distributions on homogeneous surfaces exhibited an additional diffusive mode that was missing on the chemically heterogeneous nanopatterned surfaces, confirming the presence of a slow continuous mode due to 2D in-plane diffusion. Kinetic Monte Carlo simulations were performed to test this model and, with the theoretical in-plane diffusion coefficient of D_2D = 0.20 μm²/s, we found a good agreement between simulations and experimental data on both chemically homogeneous and nanopatterned surfaces.

Probing Non-Gaussianity in Confined Diffusion of Nanoparticles

Confined diffusion is ubiquitous in nature. Ever since the "anomalous yet Brownian" motion was observed, the non-Gaussianity in confined diffusion has been unveiled as an important issue. In this Letter, we experimentally investigate the characteristics and source of non-Gaussian behavior in confined diffusion of nanoparticles suspended in polymer solutions. A time-varied and size-dependent non-Gaussianity is reported based on the non-Gaussian parameter and displacement probability distribution, especially when the nanoparticle's size is smaller than the typical polymer mesh size. This non-Gaussianity does not vanish even at the long-time Brownian stage. By inspecting the displacement autocorrelation, we observe that the nanoparticle-structure interaction, indicated by the anticorrelation, is limited in the short-time stage and makes little contribution to the non-Gaussianity in the long-time stage. The main source of the non-Gaussianity can therefore be attributed to hopping diffusion that results in an exponential probability distribution with the large displacements, which may also explain certain processes dominated by rare events in the biological environment.