Imaging Fluorescence-Correlation Spectroscopy for Measuring Fast Surface Diffusion at Liquid/Solid Interfaces

Fast Diffusion Characterization by Multiphoton Excited Fluorescence Recovery while Photobleaching

Multiphoton-excited fluorescence recovery while photobleaching (FRWP) is demonstrated as a method for quantitative measurements of rapid molecular diffusion over microsecond to millisecond timescales. Diffusion measurements are crucial in assessing molecular mobility in cell biology, materials science, and pharmacology. Optical and fluorescence microscopy techniques enable non-invasive rapid analysis of molecular diffusion but can be challenging for systems with diffusion coefficients exceeding ∼100 μm2/s. As an example, fluorescence recovery after photobleaching (FRAP) operates on the implicit assumption of a comparatively fast photobleaching step prior to a relatively slow recovery and is not generally applicable for systems exhibiting substantial recovery during photobleaching. These challenges are exacerbated in multiphoton excitation by the lower excitation efficiency and competing effects from local heating. Herein, beam-scanning FRWP with patterned line-bleach illumination is introduced as a technique that addresses FRAP limitations and further extends its application range by measuring faster diffusion events. In FRWP, the recovery of fluorescence is continuously probed after each pass of a fast-scanning mirror, and the upper bound of measurable diffusion rates is, therefore, only limited by the mirror scanning frequency. A theoretical model describing transient fluctuations in fluorescence intensity arising as a result of combined contributions from photobleaching and localized photothermal effect is introduced along with a mathematical framework for quantifying fluorescence intensity temporal curves and recovering room-temperature diffusion coefficients. FRWP is then tested by characterization of normal diffusion of rhodamine-labeled bovine serum albumin, green fluorescence protein, and immunoglobulin G molecules in aqueous solutions of varying viscosity.

Peroxisome biogenesis initiated by protein phase separation

Peroxisomes are organelles that carry out β-oxidation of fatty acids and amino acids. Both rare and prevalent diseases are caused by their dysfunction1. Among disease-causing variant genes are those required for protein transport into peroxisomes. The peroxisomal protein import machinery, which also shares similarities with chloroplasts2, is unique in transporting folded and large, up to 10 nm in diameter, protein complexes into peroxisomes3. Current models postulate a large pore formed by transmembrane proteins4; however, so far, no pore structure has been observed. In the budding yeast Saccharomyces cerevisiae, the minimum transport machinery includes the membrane proteins Pex13 and Pex14 and the cargo-protein-binding transport receptor, Pex5. Here we show that Pex13 undergoes liquid-liquid phase separation (LLPS) with Pex5-cargo. Intrinsically disordered regions in Pex13 and Pex5 resemble those found in nuclear pore complex proteins. Peroxisomal protein import depends on both the number and pattern of aromatic residues in these intrinsically disordered regions, consistent with their roles as 'stickers' in associative polymer models of LLPS5,6. Finally, imaging fluorescence cross-correlation spectroscopy shows that cargo import correlates with transient focusing of GFP-Pex13 and GFP-Pex14 on the peroxisome membrane. Pex13 and Pex14 form foci in distinct time frames, suggesting that they may form channels at different saturating concentrations of Pex5-cargo. Our findings lead us to suggest a model in which LLPS of Pex5-cargo with Pex13 and Pex14 results in transient protein transport channels7.

Simulating stochastic adsorption of diluted solute molecules at interfaces

This report uses Monte Carlo simulations to connect stochastic single-molecule and ensemble surface adsorption of molecules from dilute solutions. Monte Carlo simulations often use a fundamental time resolution to simulate each discrete step for each molecule. The adsorption rate obtained from such a simulation surprisingly contains an error compared to the results obtained from the traditional method. Simulating adsorption kinetics is interesting in many processes, such as mass transportation within cells, the kinetics of drug-receptor interactions, membrane filtration, and other general reaction kinetics in diluted solutions. Thus, it is important to understand the origin of the disagreement and find a way to correct the results. This report reviews the traditional model, explains the single-molecule simulations, and introduces a method to correct the results of adsorption rate. For example, one can bin finer time steps into time steps of interest to simulate the fractal diffusion or simply introduce a correction factor for the simulations. Then two model systems, self-assembled monolayer (SAM) and biosensing on the patterned surface, are simulated to check the accuracy of the equations. It is found that the adsorption rate of SAM is highly dependent on the conditions and the uncertainty is large. However, the biosensing system is relatively accurate. This is because the concentration gradient near the interface varies significantly with reaction conditions for SAMs while relatively stable for the biosensing system.

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.

A new metric for relating macroscopic chromatograms to microscopic surface dynamics: the distribution function ratio (DFR)

Heterogeneous stationary phase chemistry causes chromatographic tailing that lowers separation efficiency and complicates optimizing mobile phase conditions. Model-free metrics are attractive for assessing optimal separation conditions due to the low quantity of information required, but often do not reveal underlying mechanisms that cause tailing, for example, heterogeneous retention modes. We report a new metric, which we call the Distribution Function Ratio (DFR), based on a graphical comparison between the chromatogram and Gaussian cumulative distribution functions, achieving correspondence to ground truth surface dynamics with a single chromatogram. Using a Monte Carlo framework, we show that the DFR can predict the prevalence of heterogeneous retention modes with high precision when the relative desorption rate between modes is known, as in during surface dynamics experiments. Ground truth comparisons reveal that the DFR outperforms both the asymmetry factor and skewness by yielding a one-to-one correspondence with heterogeneous retention mode prevalence over a broad range of experimentally realistic values. Perhaps of more value, we illustrate that the DFR, when combined with the asymmetry factor and skewness, can estimate microscopic surface dynamics, providing valuable insights into surface chemistry using existing chromatographic instrumentation. Connecting ensemble results to microscopic quantities through the lens of simulation establishes a new chemistry-driven route to measuring and advancing separations.

Computationally-efficient spatiotemporal correlation analysis super-resolves anomalous diffusion

Anomalous diffusion dynamics in confined nanoenvironments govern the macroscale properties and interactions of many biophysical and material systems. Currently, it is difficult to quantitatively link the nanoscale structure of porous media to anomalous diffusion within them. Fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) has been shown to extract nanoscale structure and Brownian diffusion dynamics within gels, liquid crystals, and polymers, but has limitations which hinder its wider application to more diverse, biophysically-relevant datasets. Here, we parallelize the least-squares curve fitting step on a GPU improving computation times by up to a factor of 40, implement anomalous diffusion and two-component Brownian diffusion models, and make fcsSOFI more accessible by packaging it in a user-friendly GUI. We apply fcsSOFI to simulations of the protein fibrinogen diffusing in polyacrylamide of varying matrix densities and super-resolve locations where slower, anomalous diffusion occurs within smaller, confined pores. The improvements to fcsSOFI in speed, scope, and usability will allow for the wider adoption of super-resolution correlation analysis to diverse research topics.

Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy

Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. Here, we report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four-point space-time correlation function demonstrates a growing dynamic correlation length, ξ, upon cooling of the liquid toward the glass transition temperature. ξ as a function of the relaxation time τ are in good agreement with Adam-Gibbs theory, inhomogeneous mode-coupling theory and random first-order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near-surface layer with order of magnitude shorter relaxation time than inside the bulk.

Single Particle Tracking: From Theory to Biophysical Applications

After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.

Confocal Raman Microscopy Investigation of Molecular Transport into Individual Chromatographic Silica Particles

Porous silica is used as a support in a variety of separation processes, including chromatographic separation and solid-phase extraction. The resolution and efficiency of these applications is significantly impacted by the kinetics of partitioning and molecular transport into the interior of the porous particles. Molecular transport in porous silica has been explored previously by measuring chromatographic elution profiles, but such measurements are limited to relatively low retention conditions, where within-particle molecular transport must be inferred from elution profiles of solutes emerging from a packed column. In this work, a measurement of within-particle molecular transport is carried out using confocal Raman microscopy to probe the time-dependent accumulation of pyrene from an aqueous mobile phase into the center of individual C₁₈-chromatographic particles. The measured time constants for pyrene accumulation were much slower than diffusion-limited transport of solute in solution to the particle surface. Furthermore, the accumulation into the center of the particle did not show a time-lag characteristic of slow-transport into the particle interior. The exponential rise of pyrene concentration is, however, consistent with first-order Langmuir adsorption kinetics at low surface coverages. The linear dependence of the time-constant on particle radius indicates an adsorption barrier near the outer boundary of the particle, where the accumulation rate depends on flux across the boundary (proportional to the particle area) to satisfy the within-particle capacity at equilibrium (proportional to the particle volume). The pyrene accumulation kinetics into the porous particle, expressed as a heterogeneous rate constant, were nearly 50-times faster than the pyrene adsorption rate at a planar C₁₈-functionalized silica surface, which demonstrates the impact of multiple surface encounters within the porous structure leading to much greater capture efficiency compared to a planar surface. Monte Carlo simulations of within-particle pyrene diffusion, with the adsorption efficiency estimated from the planar-surface adsorption rate, predict a diffusion-to-capture distance within the porous particle that is within 40% of that observed in the radial dependence of the pyrene within-particle accumulation results.

Probing Heterogeneity and Bonding at Silica Surfaces through Single-Molecule Investigation of Base-Mediated Linkage Failure

The nature of silica surfaces is relevant to many chemical systems, including heterogeneous catalysis and chromatographies utilizing functionalized-silica stationary phases. Surface linkages must be robust to achieve wide and reliable applicability. However, silyl ether-silica support linkages are known to be susceptible to detachment when exposed to basic conditions. We use single-molecule spectroscopy to examine the rate of surface linkage failure upon exposure to base at a variety of deposition conditions. Kinetic analysis elucidates the role of thermal annealing and addition of blocking layers in increasing stability. Critically, it was found that successful surface modification strategies alter the rate at which base molecules approach the silica surface as opposed to reducing surface linkage reactivity. Our results also demonstrate that the innate structural diversity of the silica surface is likely the cause of observed heterogeneity in surface-linkage disruption kinetics.

Tracking Bulk and Interfacial Diffusion Using Multiplex Coherent Anti-Stokes Raman Scattering Correlation Spectroscopy

Multiplex coherent anti-Stokes Raman scattering correlation spectroscopy (CARS-CS) is shown as a label-free, chemically specific approach for monitoring the molecular mobility of particles in solution and at interfaces on the millisecond time scale. The CARS spectral range afforded by broadband excitation facilitates a quantitative measurement for the number of particles in the focal volume, whereas the autocorrelation of spectral data elucidates dynamic events, such as diffusion. The measured diffusion coefficients for polymer beads ranging from 100 nm to 1.1 μm in diameter are on the order of 10(-8)-10(-9) cm(2)/s, in good agreement with predicted Stokes-Einstein values. Diffusion at different interfaces shows particles are fastest in bulk medium, marginally slower at the liquid/glass interface, and 1.5-2 times slower rate at the air/liquid interface. Multivariate curve resolution analysis of distinct spectral features in multiplex CARS measurement distinguishes different composition lipid vesicles in a mixture diffusing through the focal volume. The observed diffusion is consistent with results obtained from single particle tracking experiments. This work demonstrates the utility of multiplex CARS correlation spectroscopy for monitoring particle diffusion from different chemical species across diverse interfaces.

Fluorescence correlation spectroscopy in thin films at reflecting substrates as a means to study nanoscale structure and dynamics at soft-matter interfaces

Structure and dynamics at soft-matter interfaces play an important role in nature and technical applications. Optical single-molecule investigations are noninvasive and capable to reveal heterogeneities at the nanoscale. In this work we develop an autocorrelation function (ACF) approach to retrieve tracer diffusion parameters obtained from fluorescence correlation spectroscopy (FCS) experiments in thin liquid films at reflecting substrates. This approach then is used to investigate structure and dynamics in 100-nm-thick 8CB liquid crystal films on silicon wafers with five different oxide thicknesses. We find a different extension of the structural reorientation of 8CB at the solid-liquid interface for thin and for thick oxide. For the thin oxides, the perylenediimide tracer diffusion dynamics in general agrees with the hydrodynamic modeling using no-slip boundary conditions with only a small deviation close to the substrate, while a considerably stronger decrease of the interfacial tracer diffusion is found for the thick oxides.

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.

Spatially Multiplexed Imaging: Fluorescence Correlation Spectroscopy for Efficient Measurement of Molecular Diffusion at Solid-Liquid Interfaces

Fluorescence correlation spectroscopy (FCS) has become an important technique for the characterization of molecular dynamics, especially at interfaces. Fluorescence correlation spectroscopy provides both temporal and spatial resolution for measuring fast processes at equilibrium through analysis of noise in fluorescence intensities from the statistical fluctuations in a small number of molecules. The small molecular populations produce very low-level fluorescence signals, where time-averaging the fluorescence autocorrelation function is needed to generate reasonable signal-to-noise (S/N) ratios. Recently imaging cameras have been adapted to FCS measurements of molecular dynamics at interfaces (membranes and surfaces) through the use of electron-multiplying charge-coupled device (EM-CCD) detectors for acquisition of fluorescence from addressable areas on the detector. This approach provides a major advantage over traditional focused-spot FCS by allowing electronic control over the location and area of the acquired region on the sample surface. Imaging-FCS can also provide a spatial multiplexing advantage through its ability to measure intensity data from larger areas in parallel with no loss of time resolution. In this work, this multiplexing advantage is exploited to determine molecular diffusion rates from the simultaneous measurement of multiple areas on a surface, the autocorrelation traces from which are averaged to improve the S/N ratio. As proof of concept, the diffusion of 1,1'-dioctadecyl-3,3,3'3'-tetramethylindocarbocyanine perchlorate (DiI) on a C18-modified interface was measured using this multiplexed method and compared to autocorrelation data acquired from a single spot. Due to the slow thermal recovery of the EM-CCD that inhibits fast time-averaging, spatial multiplexing in imaging-FCS provides an eightyfold time savings to reach the same S/N ratio as multiple (time-averaged) measurements from a single spot.

Variable surface transport modalities on functionalized nylon films revealed with single molecule spectroscopy

Functionalization of separation membranes with ion-exchange ligands allows control of the surface mobility of protein molecules facilitating optimized membrane design.

Characterization of Porous Materials by Fluorescence Correlation Spectroscopy Super-resolution Optical Fluctuation Imaging

Porous materials such as cellular cytosol, hydrogels, and block copolymers have nanoscale features that determine macroscale properties. Characterizing the structure of nanopores is difficult with current techniques due to imaging, sample preparation, and computational challenges. We produce a super-resolution optical image that simultaneously characterizes the nanometer dimensions of and diffusion dynamics within porous structures by correlating stochastic fluctuations from diffusing fluorescent probes in the pores of the sample, dubbed here as "fluorescence correlation spectroscopy super-resolution optical fluctuation imaging" or "fcsSOFI". Simulations demonstrate that structural features and diffusion properties can be accurately obtained at sub-diffraction-limited resolution. We apply our technique to image agarose hydrogels and aqueous lyotropic liquid crystal gels. The heterogeneous pore resolution is improved by up to a factor of 2, and diffusion coefficients are accurately obtained through our method compared to diffraction-limited fluorescence imaging and single-particle tracking. Moreover, fcsSOFI allows for rapid and high-throughput characterization of porous materials. fcsSOFI could be applied to soft porous environments such hydrogels, polymers, and membranes in addition to hard materials such as zeolites and mesoporous silica.

Tuning the Flight Length of Molecules Diffusing on a Hydrophobic Surface

Transport at solid-liquid interfaces is critical to self-assembly, biosensing, and heterogeneous catalysis, but surface diffusion remains difficult to characterize and rationally manipulate, due to the inherent heterogeneity of adsorption on solid surfaces. Using single-molecule tracking, we characterized the diffusion of a fluorescent long-chain surfactant on a hydrophobic surface, which involved periods of confinement alternating with bulk-mediated "flights". The concentration of methanol in solution was varied to tune the strength of the hydrophobic surface-molecule interaction. The frequency of confinement had a nonmonotonic dependence on methanol concentration that reflected the relative influence of anomalously strong adsorption sites. By carefully accounting for the effect of this surface heterogeneity, we demonstrated that flight lengths increased monotonically as the hydrophobic attraction decreased, in agreement with theoretical predictions for bulk-mediated surface diffusion. The theory provided an accurate description of surface diffusion, despite the system being heterogeneous, and can be leveraged to optimize molecular search and assembly processes.

Fluorescence Recovery after Photobleaching and Single-Molecule Tracking Measurements of Anisotropic Diffusion within Identical Regions of a Cylinder-Forming Diblock Copolymer Film

This work demonstrates ensemble and single-molecule diffusion measurements within identical regions of a cylinder-forming polystyrene-poly(ethylene oxide) diblock copolymer (PS-b-PEO) film using fluorescence recovery after photobleaching (FRAP) and single-molecule tracking (SMT). A PS-b-PEO film (∼4 μm thick) with aligned cylindrical PEO microdomains containing 10 μM sulforhodamine B (SRB) was prepared by directional solvent-vapor penetration (SVP) of 1,4-dioxane. The ensemble diffusion behavior of SRB in the microdomains was assessed in FRAP studies of circular photobleached regions (∼7 μm in diameter). The SRB concentration was subsequently reduced by additional photobleaching, and the diffusion of individual SRB molecules was explored using SMT in the identical area (∼16 × 16 μm(2)). The FRAP data showed anisotropic fluorescence recovery, yielding the average microdomain orientation. The extent of fluorescence recovery observed (∼90%) demonstrated long-range microdomain connectivity, while the recovery time dependence provided an ensemble measurement of the SRB diffusion coefficient within the cylindrical microdomains. The SMT data exhibited one-dimensional diffusion of individual SRB molecules along the SVP direction across the entire film thickness, as consistent with the FRAP results. Importantly, the average of the single-molecule diffusion coefficients was close to the value obtained from FRAP in the identical area. In some cases, SMT offered smaller diffusion coefficients than FRAP, possibly due to contributions from SRB molecules confined within short PEO microdomains. The implementation of FRAP and SMT measurements in identical areas provides complementary information on molecular diffusion with minimal influence of sample heterogeneity, permitting direct comparison of ensemble and single-molecule diffusion behavior.