New fluorescence correlation spectroscopy enabling direct observation of spatiotemporal dependence of diffusion constants as an evidence of anomalous transport in extracellular matrices

Simulation Studies of Dynamical Heterogeneity in a Dense Two-Dimensional Dimer-Solvent System with Obstacles

A coarse-grained model of a two-dimensional colloidal suspension was designed. The model was athermal and, in addition, a lattice approximation was introduced. It consisted of solvent (monomer) molecules, dimer molecules, and immobile impenetrable obstacles that introduced additional heterogeneity into the system. Dynamic properties were determined by a Monte Carlo simulation using the dynamic lattice liquid simulation algorithm. It is shown that there is a range of obstacle concentrations in which different diffusion characteristics were observed for dimers and solvents. In the system studied, it is possible to define the ranges of concentrations of individual components (solvent, dimers, and obstacles), in which the nature of the movement of dimers and solvents is different (normal diffusion vs. subdiffusion). The ratio of diffusion coefficients of solvent molecules and dimers for short times does not depend on the concentration of obstacles, while for long times, the ratio increases but remains independent of the concentration of the dimer.

Mechanobiology of 3D cell confinement and extracellular crowding

Cells and tissues are often under some level of confinement, imposed by the microenvironment and neighboring cells, meaning that there are limitations to cell size, volume changes, and fluid exchanges. 3D cell culture, increasingly used for both single cells and organoids, inherently impose levels of confinement absent in 2D systems. It is thus key to understand how different levels of confinement influences cell survival, cell function, and cell fate. It is well known that the mechanical properties of the microenvironment, such as stiffness and stress relaxation, are important in activating mechanosensitive pathways, and these are responsive to confinement conditions. In this review, we look at how low, intermediate, and high levels of confinement modulate the activation of known mechanobiology pathways, in single cells, organoids, and tumor spheroids, with a specific focus on 3D confinement in microwells, elastic, or viscoelastic scaffolds. In addition, a confining microenvironment can drastically limit cellular communication in both healthy and diseased tissues, due to extracellular crowding. We discuss potential implications of extracellular crowding on molecular transport, extracellular matrix deposition, and fluid transport. Understanding how cells sense and respond to various levels of confinement should inform the design of 3D engineered matrices that recapitulate the physical properties of tissues.

Segmented fluorescence correlation spectroscopy (FCS) on a commercial laser scanning microscope

Performing accurate Fluorescence Correlation Spectroscopy (FCS) measurements in cells can be challenging due to cellular motion or other intracellular processes. In this respect, it has recently been shown that analysis of FCS data in short temporal segments (segmented FCS) can be very useful to increase the accuracy of FCS measurements inside cells. Here, we demonstrate that segmented FCS can be performed on a commercial laser scanning microscope (LSM), even in the absence of the dedicated FCS module. We show how data can be acquired on a Leica SP8 confocal microscope and then exported and processed with a custom software in MATLAB. The software performs segmentation of the data to extract an average ACF and measure the diffusion coefficient in specific subcellular regions. First of all, we measure the diffusion of fluorophores of different size in solution, to show that good-quality ACFs can be obtained in a commercial LSM. Next, we validate the method by measuring the diffusion coefficient of GFP in the nucleus of HeLa cells, exploiting variations of the intensity to distinguish between nucleoplasm and nucleolus. As expected, the measured diffusion coefficient of GFP is slower in the nucleolus relative to nucleoplasm. Finally, we apply the method to HeLa cells expressing a PARP1 chromobody to measure the diffusion coefficient of PARP1 in different subcellular regions. We find that PARP1 diffusion is slower in the nucleolus compared to the nucleoplasm.

Resonance Light-Scattering Correlation Spectroscopy and Its Application in Analytical Chemistry for Life Science

Resonance light-scattering correlation spectroscopy (RLSCS) is a new single-particle detection method with its working principle being like fluorescence correlation spectroscopy (FCS). RLSCS is obtained by autocorrelation function analysis on the measured fluctuation of the resonance light scattering (RLS) intensity occurring within a subfemtoliter volume when a single nanoparticle (such as gold nanoparticles (NPs) or silver (SNPs)) freely diffuses through the volume. The RLSCS technique can detect such parameters as concentration, diffusion coefficient (translation and rotation), etc. Compared with the FCS technique, the correlated fluorescence intensity signal in RLSCS is replaced with the RLS signal of the nanoparticles, overcoming some limits of the fluorescent probes such as photobleaching under high-intensity or long-term illumination. In this Account, we showcase RLSCS methods, theoretical models at different optical configurations, and some key applications. First, the RLSCS optical detection system was constructed based on the confocal optics, its theoretical model was proposed, and the diffusion behaviors of the nanoparticles in the solution were studied including the rotational and translational diffusion. And, methods were developed to measure the concentration, size, aspect ratio, and size distribution of the NPs. Second, based on the RLSCS methods, some detection strategies were developed for homogeneous DNA detection, immunoassay, apoptosis assay, self-thermophoresis of the nanomotor, and quantitative assay in single living cells. Meanwhile, a new fluorescence/scattering cross-correlation spectroscopy (FSCCS) method was proposed for monitoring the molecule-particle interaction. This method enriched the conventional fluorescence/fluorescence cross-correlation spectroscopy (FCCS) method. Third, using the EMCCD with high sensitivity and rapid response as an optical detector, two temporospatially resolved scattering correlation spectroscopy methods and their theoretical models were developed: total internal reflection (TIR) configuration-based spatially resolved scattering correlation spectroscopy (SRSCS) and dark-field illumination-based scattering correlation spectroscopy (DFSCS). These methods extended single-spot confocal RLSCS to imaging RLSCS, which makes RLSCS have the ability for multiple channel detection with temporospatial resolution. The method was successfully used for investigating the dynamic behaviors of gold NPs in live cells and obtained its temporospatial concentration distribution and diffusion behaviors. The final section of this Account outlines future directions in the development of RLSCS.

Diffusion of hydrophilic to hydrophobic forms of Nile red in aqueous C12EO10 gels by variable area fluorescence correlation spectroscopy

Solute diffusion within lyotropic liquid crystal gels prepared from a series of water and decaethylene glycol monododecyl ether (C₁₂EO₁₀) mixtures was explored by variable area fluorescence correlation spectroscopy. Aqueous C₁₂EO₁₀ gels were prepared in concentrations ranging from 55 : 45 to 70 : 30 wt% of surfactant and water. Small angle X-ray scattering revealed that these gels comprise hexagonal mesophases of cylindrical micelles. Micelle spacing was found to decrease with increasing C₁₂EO₁₀ concentration. Three different Nile red (NR) dyes were employed as model solutes and were separately doped into the gels at nanomolar levels. These include a hydrophilic form of NR incorporating an anionic sulfonate group (NRSO₃^-), a hydrophobic form incorporating a fourteen-carbon alkane tail (NRC₁₄), and commercial NR as an intermediate case. FCS data acquired from the gels revealed that NRSO₃^- diffused primarily in 3D. Its diffusion coefficient exhibited a monotonic decrease with increasing gel concentration and micelle packing density, consistent with confinement of its motions by its exclusion from the micelle cores. NRC₁₄ exhibited the smallest diffusion coefficient, most likely due to its larger size and enhanced interactions with the micelle cores. NR yielded an intermediate diffusion coefficient and the most anomalous behavior of the three dyes, attributable to its facile partitioning between core and corona regions, and greater participation by 1D diffusion. The results of these studies afford an improved understanding of molecular mass transport through soft-matter nanomaterials like those being developed for use in drug delivery and membrane based chemical separations.

The BrightEyes-TTM as an open-source time-tagging module for democratising single-photon microscopy

Fluorescence laser-scanning microscopy (LSM) is experiencing a revolution thanks to new single-photon (SP) array detectors, which give access to an entirely new set of single-photon information. Together with the blooming of new SP LSM techniques and the development of tailored SP array detectors, there is a growing need for (i) DAQ systems capable of handling the high-throughput and high-resolution photon information generated by these detectors, and (ii) incorporating these DAQ protocols in existing fluorescence LSMs. We developed an open-source, low-cost, multi-channel time-tagging module (TTM) based on a field-programmable gate array that can tag in parallel multiple single-photon events, with 30 ps precision, and multiple synchronisation events, with 4 ns precision. We use the TTM to demonstrate live-cell super-resolved fluorescence lifetime image scanning microscopy and fluorescence lifetime fluctuation spectroscopy. We expect that our BrightEyes-TTM will support the microscopy community in spreading SP-LSM in many life science laboratories.

Quantitative evaluation of macromolecular crowding environment based on translational and rotational diffusion using polarization dependent fluorescence correlation spectroscopy

Macromolecular crowding (MMC) in cells is a hot topic in biology; therefore, well-characterized measurement standards for the evaluation of the nano-environment in MMC solutions are necessary. We propose to use polarization-dependent fluorescence correlation spectroscopy (Pol-FCS) for evaluation of macromolecular crowding in solutions. Pol-FCS can simultaneously measure the relaxation times of rotational and translational diffusion of fluorescent molecules at the same position, even in living cells with low damage. In this report, the differences in the nano-environment among solutions of small molecules, gels, and MMC solutions were evaluated by comparing their rotational and translational diffusion using Pol-FCS. Moreover, this method could distinguish the phase shift in the polyethylene glycol solution. Finally, we separately evaluated the nano-environment in the cytosol and nucleus of living cells in different cell lines and cell cycles. We expect this evaluation method to be useful in characterizing the nano-environment in MMC studies. In addition, the proposed method may be useful for other nano-environments such as liquid-liquid phase separation.

How Do Surface Properties of Nanoparticles Influence Their Diffusion in the Extracellular Matrix? A Model Study in Matrigel Using Polymer-Grafted Nanoparticles

Diffusion of nanomedicines inside the extracellular matrix (ECM) has been identified as a key factor to achieve homogeneous distribution and therefore therapeutic efficacy. Here, we sought to determine the impact of nanoparticles' (NPs) surface properties on their ability to diffuse in the ECM. As model nano-objects, we used a library of gold nanoparticles grafted with a versatile polymethacrylate corona, which enabled the surface properties to be modified. To accurately recreate the features of the native ECM, diffusion studies were carried out in a tumor-derived gel (Matrigel). We developed two methods to evaluate the diffusion ability of NPs inside this model gel: an easy-to-implement one based on optical monitoring and another one using small-angle X-ray scattering (SAXS) measurements. Both enabled the determination of the diffusion coefficients of NPs and comparison of the influence of their various surface properties, while the SAXS technique also allowed to monitor the NPs' structure as they diffused inside the gel. Positive charges and hydrophobicity were found to particularly hinder diffusion, and the different results suggested on the whole the presence of NPs-matrix interactions, therefore underlying the importance of the ECM model. The accuracy of the tumor-derived gels used in this study was evidenced by in vivo experiments involving intratumoral injections of NPs on mice, which showed that diffusion patterns in the peripheral tumor tissues were quite similar to the ones obtained within the chosen ECM model.

Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy

The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant-matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap's length scale is also accessed. On the other hand, by tuning the pH value, the diffusant-matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.

Molecular transport in systems containing binding obstacles

We studied the movement of particles in crowded environments by means of extensive Monte Carlo simulations. The dynamic lattice liquid model was employed for this purpose. It is based on the cooperative movement concept and allows the study of systems at high densities. The cooperative model of molecular transport is assumed: the motion of all moving particles is highly correlated. The model is supposed to mimic lateral motion in a membrane and therefore the system is two-dimensional with moving objects and traps placed on a triangular lattice. In our study the interaction (binding) of traps with moving particles was assumed. The conditions in which subdiffusive motion appeared in the system were analysed. The influence of the strength of binding on the dynamic percolation threshold was also shown. The differences in the dynamics compared to systems with impenetrable obstacles and with systems without correlation in motion were presented and discussed. It was shown that in the case of correlated motion the influence of deep traps is similar to that of impenetrable obstacles. If the traps are shallow a recovery to normal diffusion was observed for longer time periods.

Anomalous Diffusion in Inverted Variable-Lengthscale Fluorescence Correlation Spectroscopy

Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of the resulting autocorrelation data is model dependant. Two recently introduced strategies, however, can help move toward a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length scales and 2) their inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion, and diffusing diffusivity) in variable-length-scale FCS. We show that, when used in concert, length-scale variation and data inversion permit us to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.

Pathways for creation and annihilation of nanoscale biomembrane domains reveal alpha and beta-toxin nanopore formation processes

Raft-like functional domains with putative sizes of 20–200 nm and which are evolving dynamically are believed to be the most crucial regions in cellular membranes which determine cell signaling and various functions of cells.

Spot variation fluorescence correlation spectroscopy by data post-processing

Spot variation fluorescence correlation spectroscopy (SV-FCS) is a variant of the FCS techniques which may give useful information about the structural organisation of the medium in which the diffusion takes place. We show that the same results can be obtained by post-processing the photon count data from ordinary FCS measurements. By using this method, one obtains the fluorescence autocorrelation functions for sizes of confocal volume, which are effectively smaller than that of the initial FCS measurement. The photon counts of the initial experiment are first transformed into smooth intensity trace using kernel smoothing method or to a piecewise-continuous intensity trace using binning and then a non-linear transformation is applied to this trace. The result of this transformation mimics the photon count rate in an experiment performed with a smaller confocal volume. The applicability of the method is established in extensive numerical simulations and directly supported in in-vitro experiments. The procedure is then applied to the diffusion of AlexaFluor647-labeled streptavidin in living cells.

The Secreted Signaling Protein Wnt3 Is Associated with Membrane Domains In Vivo: A SPIM-FCS Study

Wnt3 is a morphogen that activates the Wnt signaling pathway and regulates a multitude of biological processes ranging from cell proliferation and cell fate specification to differentiation over embryonic induction to neural patterning. Recent studies have shown that the palmitoylation of Wnt3 by Porcupine, a membrane-bound O-acyltransferase, plays a significant role in the intracellular membrane trafficking of Wnt3 and subsequently, its secretion in live zebrafish embryos, where chemical inhibition of Porcupine reduced the membrane-bound and secreted fractions of Wnt3 and eventually led to defective brain development. However, the membrane distribution of Wnt3 in cells remains not fully understood. Here, we determine the membrane organization of functionally active Wnt3-EGFP in cerebellar cells of live transgenic zebrafish embryos and the role of palmitoylation in its organization using single plane illumination microscopy-fluorescence correlation spectroscopy (SPIM-FCS), a multiplexed modality of FCS, which generates maps of molecular dynamics, concentration, and interaction of biomolecules. The FCS diffusion law was applied to SPIM-FCS data to study the subresolution membrane organization of Wnt3. We find that at the plasma membrane in vivo, Wnt3 is associated with cholesterol-dependent domains. This association reduces with increasing concentrations of Porcupine inhibitor (C59), confirming the importance of palmitoylation of Wnt3 for its association with cholesterol-dependent domains. Reduction of membrane cholesterol also results in a decrease of Wnt3 association with cholesterol-dependent domains in live zebrafish. This demonstrates for the first time, to our knowledge, in live vertebrate embryos that Wnt3 is associated with cholesterol-dependent domains.

A user's guide for characterizing plasma membrane subdomains in living cells by spot variation fluorescence correlation spectroscopy

Due to the intrinsic molecular Brownian agitation within plasma membrane and the vast diversity of membrane components, it is expected that the plasma membrane organization is highly heterogeneous with the formation of local complex multicomponent assemblies of lipids and proteins on different time scales. Still, deciphering this lateral organization on living cells and on the appropriate length and temporal scales has been challenging but is crucial to advance our knowledge on the biological function of the plasma membrane. Among the methodological developments based on biophotonics, the spot variation FCS (svFCS), a fluorescent correlation spectroscopy (FCS)-based method, has allowed the significant progress in the characterization of cell membrane lateral organization at the suboptical level, including to providing compelling evidence for the in vivo existence of lipid-dependent nanodomains. The aim of this chapter is to serve as a guide for setting and applying the svFCS methodology to study the plasma membrane of both adherent and nonadherent cell types.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

The diffusion of macromolecules in cells and in complex fluids is often found to deviate from simple Fickian diffusion. One explanation offered for this behavior is that molecular crowding renders diffusion anomalous, where the mean-squared displacement of the particles scales as 〈r(2)〉∝t(α) with α < 1. Unfortunately, methods such as fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP) probe diffusion only over a narrow range of lengthscales and cannot directly test the dependence of the mean-squared displacement (MSD) on time. Here we show that variable-lengthscale FCS (VLS-FCS), where the volume of observation is varied over several orders of magnitude, combined with a numerical inversion procedure of the correlation data, allows retrieving the MSD for up to five decades in time, bridging the gap between diffusion experiments performed at different lengthscales. In addition, we show that VLS-FCS provides a way to assess whether the propagator associated with the diffusion is Gaussian or non-Gaussian. We used VLS-FCS to investigate two systems where anomalous diffusion had been previously reported. In the case of dense cross-linked agarose gels, the measured MSD confirmed that the diffusion of small beads was anomalous at short lengthscales, with a cross-over to simple diffusion around ≈1 μm, consistent with a caged diffusion process. On the other hand, for solutions crowded with marginally entangled dextran molecules, we uncovered an apparent discrepancy between the MSD, found to be linear, and the propagators at short lengthscales, found to be non-Gaussian. These contradicting features call to mind the "anomalous, yet Brownian" diffusion observed in several biological systems, and the recently proposed "diffusing diffusivity" model.

High Current Ionic Diode Using Homogeneously Charged Asymmetric Nanochannel Network Membrane

A high current ionic diode is achieved using an asymmetric nanochannel network membrane (NCNM) constructed by soft lithography and in situ self-assembly of nanoparticles with uniform surface charge. The asymmetric NCNM exhibits high rectified currents without losing a rectification ratio because of its ionic selectivity gradient and differentiated electrical conductance. Asymmetric ionic transport is analyzed with diode-like I-V curves and visualized via fluorescent dyes, which is closely correlated with ionic selectivity and ion distribution according to variation of NCNM geometries.

Fluorescence Correlation Spectroscopy: A Tool to Study Protein Oligomerization and Aggregation In Vitro and In Vivo

Fluorescence correlation spectroscopy (FCS) is a highly sensitive analytical technique used to measure dynamic molecular parameters, such as diffusion time (from which particle size can be calculated), conformation, and concentration of fluorescent molecules. It has been particularly powerful in characterizing size distributions in molecular associations (e.g., dimer/multimer formation) both in well-behaved thermodynamically equilibrated systems in vitro as well as in more complex environments in vivo. Protein aggregation reactions like amyloid formation, in contrast, are complex, often involving a series of uniquely structured aggregation intermediates appearing at different time scales. Nonetheless, FCS can be used in appropriate cases to characterize the early stages of some aggregation reactions. Here are described step-by-step protocols and experimental procedures for the study of molecular complex formation in aggregation systems as observed in simple buffer systems, cell extracts, and living cells. The methods described are illustrated with examples from studies of the self-assembly of huntingtin fragments, but in principle can be adapted for any aggregating system.

A straightforward approach for gated STED-FCS to investigate lipid membrane dynamics

Recent years have seen the development of multiple technologies to investigate, with great spatial and temporal resolution, the dynamics of lipids in cellular and model membranes. One of these approaches is the combination of far-field super-resolution stimulated-emission-depletion (STED) microscopy with fluorescence correlation spectroscopy (FCS). STED-FCS combines the diffraction-unlimited spatial resolution of STED microscopy with the statistical accuracy of FCS to determine sub-millisecond-fast molecular dynamics with single-molecule sensitivity. A unique advantage of STED-FCS is that the observation spot for the FCS data recordings can be tuned to sub-diffraction scales, i.e. <200 nm in diameter, in a gradual manner to investigate fast diffusion of membrane-incorporated labelled entities. Unfortunately, so far the STED-FCS technology has mostly been applied on a few custom-built setups optimised for far-red fluorescent emitters. Here, we summarise the basics of the STED-FCS technology and highlight how it can give novel details into molecular diffusion modes. Most importantly, we present a straightforward way for performing STED-FCS measurements on an unmodified turnkey commercial system using a time-gated detection scheme. Further, we have evaluated the STED-FCS performance of different commonly used green emitting fluorescent dyes applying freely available, custom-written analysis software.

Particle transport through hydrogels is charge asymmetric

Transport processes within biological polymer networks, including mucus and the extracellular matrix, play an important role in the human body, where they serve as a filter for the exchange of molecules and nanoparticles. Such polymer networks are complex and heterogeneous hydrogel environments that regulate diffusive processes through finely tuned particle-network interactions. In this work, we present experimental and theoretical studies to examine the role of electrostatics on the basic mechanisms governing the diffusion of charged probe molecules inside model polymer networks. Translational diffusion coefficients are determined by fluorescence correlation spectroscopy measurements for probe molecules in uncharged as well as cationic and anionic polymer solutions. We show that particle transport in the charged hydrogels is highly asymmetric, with diffusion slowed down much more by electrostatic attraction than by repulsion, and that the filtering capability of the gel is sensitive to the solution ionic strength. Brownian dynamics simulations of a simple model are used to examine key parameters, including interaction strength and interaction range within the model networks. Simulations, which are in quantitative agreement with our experiments, reveal the charge asymmetry to be due to the sticking of particles at the vertices of the oppositely charged polymer networks.

Fluorescent correlation spectroscopy measurements with adaptive optics in the intercellular space of spheroids

In this study we demonstrate the use of adaptive optics to correct the biasing effects of optical aberrations when measuring the dynamics of molecules diffusing between cells in multicellular spheroids. Our results indicate that, on average, adaptive optics leads to a reduction of the 3D size of the point spread function that is statistically significant in terms of measured number of molecules and diffusion time. The sensorless approach, which uses the molecular brightness as optimization metric, is validated in a complex, highly heterogeneous, biological environment. This work paves the way towards the design of accurate diffusion measurements of molecules in thick biological specimens.

Single molecule confocal fluorescence lifetime correlation spectroscopy for accurate nanoparticle size determination

Experimental procedure in confocal single molecule fluorescence lifetime correlation spectroscopy to determine the excitation power and molecular or particulate concentration under which the application of an unmodified model autocorrelation function is justified.

Measurement of biomolecular diffusion in extracellular matrix condensed by fibroblasts using fluorescence correlation spectroscopy

The extracellular matrix (ECM) comprises the heterogeneous environment outside of cells in a biological system. The ECM is dynamically organized and regulated, and many biomolecules secreted from cells diffuse throughout the ECM, regulating a variety of cellular processes. Therefore, investigation of the diffusive behaviors of biomolecules in the extracellular environment is critical. In this study, we investigated the diffusion coefficients of biomolecules of various sizes, measuring from 1 to 10 nm in radius, by fluorescence correlation spectroscopy in contracted collagen gel caused by fibroblasts, a traditional culture model of dynamic rearrangement of collagen fibers. The diffusion coefficients of the biomolecules in control collagen gel without cells decreased slightly as compared to those in solution, while the diffusion coefficients of biomolecules in the contracted gel at the cell vicinity decreased dramatically. Additionally, the diffusion coefficients of biomolecules were inversely correlated with molecular radius. In collagen gels populated with fibroblasts, the diffusion coefficient at the cell vicinity clearly decreased in the first 24 h of culture. Furthermore, molecular diffusion was greatly restricted, with a central focus on the populated cells. By using the obtained diffusion coefficients of biomolecules, we calculated the collagen fiber condensation ratio by fibroblasts in the cell vicinity at 3 days of culture to represent a 52-fold concentration. Thus, biomolecular diffusion is restricted in the vicinity of the cells where collagen fibers are highly condensed.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Revisiting point FRAP to quantitatively characterize anomalous diffusion in live cells

Fluorescence recovery after photobleaching (FRAP) is widely used to interrogate diffusion and binding of proteins in live cells. Herein, we apply two-photon excited FRAP with a diffraction limited bleaching and observation volume to study anomalous diffusion of unconjugated green fluorescence protein (GFP) in vitro and in cells. Experiments performed on dilute solutions of GFP reveal that reversible fluorophore bleaching can be mistakenly interpreted as anomalous diffusion. We derive a reaction-diffusion FRAP model that includes reversible photobleaching, and demonstrate that it properly accounts for these photophysics. We then apply this model to investigate the diffusion of GFP in HeLa cells and polytene cells of Drosophila larval salivary glands. GFP exhibits anomalous diffusion in the cytoplasm of both cell types and in HeLa nuclei. Polytene nuclei contain optically resolvable chromosomes, permitting FRAP experiments that focus separately on chromosomal or interchrosomal regions. We find that GFP exhibits anomalous diffusion in chromosomal regions but diffuses normally in regions devoid of chromatin. This observation indicates that obstructed transport through chromatin and not crowding by macromolecules is a source of anomalous diffusion in polytene nuclei. This behavior is likely true in other cells, so it will be important to account for this type of transport physics and for reversible photobleaching to properly interpret future FRAP experiments on DNA-binding proteins.

Fluorescence correlation spectroscopy: past, present, future

In recent years fluorescence correlation spectroscopy (FCS) has become a routine method for determining diffusion coefficients, chemical rate constants, molecular concentrations, fluorescence brightness, triplet state lifetimes, and other molecular parameters. FCS measures the spatial and temporal correlation of individual molecules with themselves and so provides a bridge between classical ensemble and contemporary single-molecule measurements. It also provides information on concentration and molecular number fluctuations for nonlinear reaction systems that complement single-molecule measurements. Typically implemented on a fluorescence microscope, FCS samples femtoliter volumes and so is especially useful for characterizing small dynamic systems such as biological cells. In addition to its practical utility, however, FCS provides a window on mesoscopic systems in which fluctuations from steady states not only provide the basis for the measurement but also can have important consequences for the behavior and evolution of the system. For example, a new and potentially interesting field for FCS studies could be the study of nonequilibrium steady states, especially in living cells.

Physiological environment induces quick response - slow exhaustion reactions

In vivo environments are highly crowded and inhomogeneous, which may affect reaction processes in cells. In this study we examined the effects of intracellular crowding and an inhomogeneity on the behavior of in vivo reactions by calculating the spectral dimension (d(s)), which can be translated into the reaction rate function. We compared estimates of anomaly parameters obtained from fluorescence correlation spectroscopy (FCS) data with fractal dimensions derived from transmission electron microscopy (TEM) image analysis. FCS analysis indicated that the anomalous property was linked to physiological structure. Subsequent TEM analysis provided an in vivo illustration; soluble molecules likely percolate between intracellular clusters, which are constructed in a self-organizing manner. We estimated a cytoplasmic spectral dimension d(s) to be 1.39 ± 0.084. This result suggests that in vivo reactions initially run faster than the same reactions in a homogeneous space; this conclusion is consistent with the anomalous character indicated by FCS analysis. We further showed that these results were compatible with our Monte-Carlo simulation in which the anomalous behavior of mobile molecules correlates with the intracellular environment, leading to description as a percolation cluster, as demonstrated using TEM analysis. We confirmed by the simulation that the above-mentioned in vivo like properties are different from those of homogeneously concentrated environments. Additionally, simulation results indicated that crowding level of an environment might affect diffusion rate of reactant. Such knowledge of the spatial information enables us to construct realistic models for in vivo diffusion and reaction systems.

Spot variation fluorescence correlation spectroscopy allows for superresolution chronoscopy of confinement times in membranes

Resolving the dynamical interplay of proteins and lipids in the live-cell plasma membrane represents a central goal in current cell biology. Superresolution concepts have introduced a means of capturing spatial heterogeneity at a nanoscopic length scale. Similar concepts for detecting dynamical transitions (superresolution chronoscopy) are still lacking. Here, we show that recently introduced spot-variation fluorescence correlation spectroscopy allows for sensing transient confinement times of membrane constituents at dramatically improved resolution. Using standard diffraction-limited optics, spot-variation fluorescence correlation spectroscopy captures signatures of single retardation events far below the transit time of the tracer through the focal spot. We provide an analytical description of special cases of transient binding of a tracer to pointlike traps, or association of a tracer with nanodomains. The influence of trap mobility and the underlying binding kinetics are quantified. Experimental approaches are suggested that allow for gaining quantitative mechanistic insights into the interaction processes of membrane constituents.

Near-critical fluctuations and cytoskeleton-assisted phase separation lead to subdiffusion in cell membranes

We address the relationship between membrane microheterogeneity and anomalous subdiffusion in cell membranes by carrying out Monte Carlo simulations of two-component lipid membranes. We find that near-critical fluctuations in the membrane lead to transient subdiffusion, while membrane-cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, we present a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion.

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.

Fluorescence lifetime probe for solvent microviscosity utilizing anilinonaphthalene sulfonate

The correlation between the fluorescent dynamics of excited anilinonaphthalene sulfonate (ANS) and the microviscosity of solvent molecules surrounding ANS is investigated by time-resolved fluorescence spectroscopy. ANS has been widely used to probe the local hydrophobicity due to the drastic change in its intensity. It is revealed that the fluorescence lifetime from the charge transfer (CT) state of ANS sensitively reflects the microviscosity. The higher sensitivity of 2,6-ANS than of 1,8-ANS demonstrates that the spatial freedom of the rotating phenylamino group in the photoexcited ANS is an important factor that determines the sensitivity. As an application, the measurements of the microviscosity of water in biologically important systems, such as hyaluronan, gellan gum, and gelatin aqueous solutions are also presented. The present results suggest that the fluorescence lifetime of ANS enables the estimation of the solvent microviscosity and provide a useful probe molecule for fluorescence lifetime imaging microscopy.

Diffusion and partitioning of fluorescent lipid probes in phospholipid monolayers

The pressure-dependent diffusion and partitioning of single lipid fluorophores in DMPC and DPPC monolayers were investigated with the use of a custom-made monolayer trough mounted on a combined fluorescence correlation spectroscopy (FCS) and wide-field microscopy setup. It is shown that lipid diffusion, which is essential for the function of biological membranes, is heavily influenced by the lateral pressure and phase of the lipid structure. Both of these may change dynamically during, e.g., protein adsorption and desorption processes. Using FCS, we measured lipid diffusion coefficients over a wide range of lateral pressures in DMPC monolayers and fitted them to a free-area model as well as the direct experimental observable mean molecular area. FCS measurements on DPPC monolayers were also performed below the onset of the phase transition (Pi < 5 mN/m). At higher pressures, FCS was not applicable for measuring diffusion coefficients in DPPC monolayers. Single-molecule fluorescence microscopy and differential scanning calorimetry clearly showed that this was due to heterogeneous partitioning of the lipid fluorophores in condensed phases. The results were compared with dye partitioning in giant lipid vesicles. These findings are significant in relation to the application of lipid fluorophores to study diffusion in both model systems and biological systems.

Measuring diffusion of lipid-like probes in artificial and natural membranes by raster image correlation spectroscopy (RICS): use of a commercial laser-scanning microscope with analog detection

The heterogeneity in composition and interaction within the cellular membrane translates into a wide range of diffusion coefficients of its constituents. Therefore, several complementary microfluorimetric techniques such as fluorescence correlation spectroscopy (FCS), fluorescence recovery after photobleaching (FRAP) and single-particle tracking (SPT) have to be applied to explore the dynamics of membrane components. The recently introduced raster image correlation spectroscopy (RICS) offers a much wider dynamic range than each of these methods separately and allows for spatial mapping of the dynamic properties. RICS is implemented on a confocal laser-scanning microscope (CLSM), and the wide dynamic range is achieved by exploiting the inherent time information carried by the scanning laser beam in the generation of the confocal images. The original introduction of RICS used two-photon excitation and photon counting detection. However, most CLSM systems are based on one-photon excitation with analog detection. Here we report on the performance of such a commercial CLSM (Zeiss LSM 510 META) in the study of the diffusion of the fluorescent lipid analog 1,1'-dioctadecyl-3,3,3',3'-tetramethyl-indodicarbocyanine perchlorate (DiI-C(18)(5)) both in giant unilamellar vesicles and in the plasma membrane of living oligodendrocytes, i.e., the myelin-producing cells of the central nervous system. It is shown that RICS on a commercial CLSM with analog detection allows for reliable results in the study of membrane diffusion by removal of unwanted correlations introduced by the analog detection system. The results obtained compare well with those collected by FRAP and FCS.

Anisotropic diffusion of fluorescently labeled ATP in rat cardiomyocytes determined by raster image correlation spectroscopy

A series of experimental data points to the existence of profound diffusion restrictions of ADP/ATP in rat cardiomyocytes. This assumption is required to explain the measurements of kinetics of respiration, sarcoplasmic reticulum loading with calcium, and kinetics of ATP-sensitive potassium channels. To be able to analyze and estimate the role of intracellular diffusion restrictions on bioenergetics, the intracellular diffusion coefficients of metabolites have to be determined. The aim of this work was to develop a practical method for determining diffusion coefficients in anisotropic medium and to estimate the overall diffusion coefficients of fluorescently labeled ATP in rat cardiomyocytes. For that, we have extended raster image correlation spectroscopy (RICS) protocols to be able to discriminate the anisotropy in the diffusion coefficient tensor. Using this extended protocol, we estimated diffusion coefficients of ATP labeled with the fluorescent conjugate Alexa Fluor 647 (Alexa-ATP). In the analysis, we assumed that the diffusion tensor can be described by two values: diffusion coefficient along the myofibril and that across it. The average diffusion coefficients found for Alexa-ATP were as follows: 83 ± 14 μm²/s in the longitudinal and 52 ± 16 μm²/s in the transverse directions (n = 8, mean ± SD). Those values are ∼2 (longitudinal) and ∼3.5 (transverse) times smaller than the diffusion coefficient value estimated for the surrounding solution. Such uneven reduction of average diffusion coefficient leads to anisotropic diffusion in rat cardiomyocytes. Although the source for such anisotropy is uncertain, we speculate that it may be induced by the ordered pattern of intracellular structures in rat cardiomyocytes.