Anisotropic diffusion in mitral cell dendrites revealed by fluorescence correlation spectroscopy

Fluorescence Correlation Spectroscopy and Phase Separation

A quantitative understanding of the forces controlling the assembly and functioning of biomolecular condensates requires the identification of phase boundaries at which condensates form as well as the determination of tie-lines. Here, we describe in detail how Fluorescence Correlation Spectroscopy (FCS) provides a versatile approach to estimate phase boundaries of single-component and multicomponent solutions as well as insights about the transport properties of the condensate.

High rates of calcium-free diffusion in the cytosol of living cells

Calcium (Ca²⁺) is a universal second messenger that participates in the regulation of innumerous physiological processes. The way in which local elevations of the cytosolic Ca²⁺ concentration spread in space and time is key for the versatility of the signals. Ca²⁺ diffusion in the cytosol is hindered by its interaction with proteins that act as buffers. Depending on the concentrations and the kinetics of the interactions, there is a large range of values at which Ca²⁺ diffusion can proceed. Having reliable estimates of this range, particularly of its highest end, which corresponds to the ions free diffusion, is key to understand how the signals propagate. In this work, we present the first experimental results with which the Ca²⁺-free diffusion coefficient is directly quantified in the cytosol of living cells. By means of fluorescence correlation spectroscopy experiments performed in Xenopus laevis oocytes and in cells of Saccharomyces cerevisiae, we show that the ions can freely diffuse in the cytosol at a higher rate than previously thought.

Quantification of native mRNA dynamics in living neurons using fluorescence correlation spectroscopy and reduction-triggered fluorescent probes

RNA localization in subcellular compartments is essential for spatial and temporal regulation of protein expression in neurons. Several techniques have been developed to visualize mRNAs inside cells, but the study of the behavior of endogenous and nonengineered mRNAs in living neurons has just started. In this study, we combined reduction-triggered fluorescent (RETF) probes and fluorescence correlation spectroscopy (FCS) to investigate the diffusion properties of activity-regulated cytoskeleton-associated protein (Arc) and inositol 1,4,5-trisphosphate receptor type 1 (Ip3r1) mRNAs. This approach enabled us to discriminate between RNA-bound and unbound fluorescent probes and to quantify mRNA diffusion parameters and concentrations in living rat primary hippocampal neurons. Specifically, we detected the induction of Arc mRNA production after neuronal activation in real time. Results from computer simulations with mRNA diffusion coefficients obtained in these analyses supported the idea that free diffusion is incapable of transporting mRNA of sizes close to those of Arc or Ip3r1 to distal dendrites. In conclusion, the combined RETF-FCS approach reported here enables analyses of the dynamics of endogenous, unmodified mRNAs in living neurons, affording a glimpse into the intracellular dynamics of RNA in live cells.

Fluorescence correlation spectroscopy experiments to quantify free diffusion coefficients in reaction-diffusion systems: The case of Ca^{2+} and its dyes

Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca^{2+}) and single-wavelength dyes that increase their fluorescence upon Ca^{2+} binding. We validate the approach with experiments performed in aqueous solutions containing Ca^{2+} and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.

FCS experiments to quantify Ca2+ diffusion and its interaction with buffers

Ca²⁺ signals are ubiquitous. One of the key factors for their versatility is the variety of spatio-temporal distributions that the cytosolic Ca²⁺ can display. In most cell types Ca²⁺ signals not only depend on Ca²⁺ entry from the extracellular medium but also on Ca²⁺ release from internal stores, a process which is in turn regulated by cytosolic Ca²⁺ itself. The rate at which Ca²⁺ is transported, the fraction that is trapped by intracellular buffers, and with what kinetics are thus key features that affect the time and spatial range of action of Ca²⁺ signals. The quantification of Ca²⁺ diffusion in intact cells is quite challenging because the transport rates that can be inferred using optical techniques are intricately related to the interaction of Ca²⁺ with the dye that is used for its observation and with the cellular buffers. In this paper, we introduce an approach that uses Fluorescence Correlation Spectroscopy (FCS) experiments performed at different conditions that in principle allows the quantification of Ca²⁺ diffusion and of its reaction rates with unobservable (non-fluorescent) Ca²⁺ buffers. To this end, we develop the necessary theory to interpret the experimental results and then apply it to FCS experiments performed in a set of solutions containing Ca²⁺, a single wavelength Ca²⁺ dye, and a non-fluorescent Ca²⁺ buffer. We show that a judicious choice of the experimental conditions and an adequate interpretation of the fitting parameters can be combined to extract information on the free diffusion coefficient of Ca²⁺ and of some of the properties of the unobservable buffer. We think that this approach can be applied to other situations, particularly to experiments performed in intact cells.

Ca(2+)-BK channel clusters in olfactory receptor neurons and their role in odour coding

Olfactory receptor neurons (ORNs) have high-voltage-gated Ca(2+) channels whose physiological impact has remained enigmatic since the voltage-gated conductances in this cell type were first described in the 1980s. Here we show that in ORN somata of Xenopus laevis tadpoles these channels are clustered and co-expressed with large-conductance potassium (BK) channels. We found approximately five clusters per ORN and twelve Ca(2+) channels per cluster. The action potential-triggered activation of BK channels accelerates the repolarization of action potentials and shortens interspike intervals during odour responses. This increases the sensitivity of individual ORNs to odorants. At the level of mitral cells of the olfactory bulb, odour qualities have been shown to be coded by first-spike-latency patterns. The system of Ca(2+) and BK channels in ORNs appears to be important for correct odour coding because the blockage of BK channels not only affects ORN spiking patterns but also changes the latency pattern representation of odours in the olfactory bulb.

Fluorescence correlation spectroscopy: principles and applications

Fluorescence correlation spectroscopy (FCS) is used to study the movements and the interactions of biomolecules at extremely dilute concentrations, yielding results with good spatial and temporal resolutions. Using a number of technical developments, FCS has become a versatile technique that can be used to study a variety of sample types and can be advantageously combined with other methods. Unlike other fluorescence-based techniques, the analysis of FCS data is not based on the average intensity of the fluorescence emission but examines the minute intensity fluctuations caused by spontaneous deviations from the mean at thermal equilibrium. These fluctuations can result from variations in local concentrations owing to molecular mobility or from characteristic intermolecular or intramolecular reactions of fluorescently labeled biomolecules present at low concentrations. Here, we provide a basic introduction to FCS, including its technical development and theoretical basis, experimental setup of an FCS system, adjustment of a setup, data acquisition, and analysis of FCS measurements. Finally, the application of FCS to the study of lipid bilayer membranes and to living cells is discussed.

Defining the subcellular interface of nanoparticles by live-cell imaging

Understanding of nanoparticle-bio-interactions within living cells requires knowledge about the dynamic behavior of nanomaterials during their cellular uptake, intracellular traffic and mutual reactions with cell organelles. Here, we introduce a protocol of combined kinetic imaging techniques that enables investigation of exemplary fluorochrome-labelled nanoparticles concerning their intracellular fate. By time-lapse confocal microscopy we observe fast, dynamin-dependent uptake of polystyrene and silica nanoparticles via the cell membrane within seconds. Fluorescence recovery after photobleaching (FRAP) experiments reveal fast and complete exchange of the investigated nanoparticles at mitochondria, cytoplasmic vesicles or the nuclear envelope. Nuclear translocation is observed within minutes by free diffusion and active transport. Fluorescence correlation spectroscopy (FCS) and raster image correlation spectroscopy (RICS) indicate diffusion coefficients of polystyrene and silica nanoparticles in the nucleus and the cytoplasm that are consistent with particle motion in living cells based on diffusion. Determination of the apparent hydrodynamic radii by FCS and RICS shows that nanoparticles exert their cytoplasmic and nuclear effects mainly as mobile, monodisperse entities. Thus, a complete toolkit of fluorescence fluctuation microscopy is presented for the investigation of nanomaterial biophysics in subcellular microenvironments that contributes to develop a framework of intracellular nanoparticle delivery routes.

Monitoring and quantifying dynamic physiological processes in live neurons using fluorescence recovery after photobleaching

The direct visualization of subcellular dynamic processes is often hampered by limitations in the resolving power achievable with conventional microscopy techniques. Fluorescence recovery after photobleaching has emerged as a highly informative approach to address this challenge, permitting the quantitative measurement of the movement of small organelles and proteins in living functioning cells, and offering detailed insights into fundamental cellular phenomena of physiological importance. In recent years, its implementation has benefited from the increasing availability of confocal microscopy systems and of powerful labeling techniques based on genetically encoded fluorescent proteins or other chemical markers. In this review, we present fluorescence recovery after photobleaching and related techniques in the context of contemporary neurobiological research and discuss quantitative and semi-quantitative approaches to their interpretation.

Direct measurement of diffusion in olfactory cilia using a modified FRAP approach

The diffusion coefficient of fluorescein in detached cilia of Xenopus laevis olfactory receptor neurons was measured using spatially-resolved FRAP, where the dye along half of the ciliary length was photobleached and its spatiotemporal fluorescence redistribution recorded. Fitting a one-dimensional numerical simulation of diffusion and photobleaching for 35 cilia resulted in a mean value of the diffusion coefficient and thus a reduction by a factor of compared to free diffusion in aqueous solution.

Multiphoton fluorescence recovery after photobleaching in bounded systems

Multiphoton fluorescence recovery after photobleaching (MP-FRAP) is a laser microscopy technique used to measure diffusion coefficients of macromolecules in biological systems. The three-dimensional resolution and superior depth penetration within scattering samples offered by MP-FRAP make it an important tool for investigating both in vitro and in vivo systems. However, biological systems frequently confine diffusion within solid barriers, and to date the effect of such barriers on the measurement of absolute diffusion coefficients via MP-FRAP has not been studied. We have used Monte Carlo simulations of diffusion and MP-FRAP to understand the effect of barriers of varying geometries and positions relative to the two-photon focal volume. Furthermore, we supply ranges of barrier positions within which MP-FRAP can confidently be employed to measure accurate diffusion coefficients. Finally, we produce two new MP-FRAP models that can produce accurate diffusion coefficients in the presence of a single plane boundary or parallel infinite plane boundaries positioned parallel to the optical axis, up to the resolution limit of the multiphoton laser scanning microscope.

A microfluidic device to establish concentration gradients using reagent density differences

Microfabrication has become widely utilized to generate controlled microenvironments that establish chemical concentration gradients for a variety of engineering and life science applications. To establish microfluidic flow, the majority of existing devices rely upon additional facilities, equipment, and excessive reagent supplies, which together limit device portability as well as constrain device usage to individuals trained in technological disciplines. The current work presents our laboratory-developed bridged μLane system, which is a stand-alone device that runs via conventional pipette loading and can operate for several days without need of external machinery or additional reagent volumes. The bridged μLane is a two-layer polydimethylsiloxane microfluidic device that is able to establish controlled chemical concentration gradients over time by relying solely upon differences in reagent densities. Fluorescently labeled Dextran was used to validate the design and operation of the bridged μLane by evaluating experimentally measured transport properties within the microsystem in conjunction with numerical simulations and established mathematical transport models. Results demonstrate how the bridged μLane system was used to generate spatial concentration gradients that resulted in an experimentally measured Dextran diffusivity of (0.82 ± 0.01) × 10(-6) cm(2)/s.

Fluorescence correlation spectroscopy: criteria for analysis in complex systems

We have evaluated the effect of varying three key parameters for Fluorescence Correlation Spectroscopy analysis, first in the context of a one species/one environment system, and then in a complex system composed of two species, or conversely, two environments. We establish experimentally appropriate settings for the (1) minimum lag time, (2) maximum lag time, and (3) averaging times over which an autocorrelation is carried out, as a function of expected diffusion decay time for a particular solute, and show that use of appropriate settings plays a critical role in recovering accurate and reliable decay times and resulting diffusion constants. Both experimental and simulated data were used to show that for a complex binary system, to extract accurate diffusion constants for both species, decay times must be bounded by adequate minimum and maximum lag times as dictated by the fast and slow diffusing species, respectively. We also demonstrate that even when constraints on experimental conditions do not permit achieving the necessary lag time limits for both of the species in a binary system, the accuracy of the recovered diffusion constant for the one species whose autocorrelation function is fully time-resolved is unaffected by uncertainty in fitting introduced by the presence of the second species.

Resolution in the ApoTome and the confocal laser scanning microscope: comparison

The essential feature of the confocal laser scanning microscope (cLSM) is the generation of optical sections by the removal of out-of-focus light. About ten years ago, structured illumination microscopy (SIM) was introduced as an alternative method for obtaining optical sections from biological specimens. Here we compare the resolution of the ApoTome (commercial SIM by Zeiss) to that achieved by a cLSM (Zeiss LSM 510). If fluorescent beads are used as test objects, then the ApoTome will achieve a lower axial resolution than the cLSM. In contrast to that, its lateral resolution scores slightly better. If subresolution homogeneous fluorescent layers are used as test objects, then the ApoTome will achieve a higher axial resolution than the cLSM. The ApoTome's axial resolution is homogeneous over the field-of-view while that of the cLSM changes markedly. Finally, the anisotropy of the ApoTome's resolution was found to be negligible for standard applications while its capability to resolve fine structures within stained tissue slices is limited to one or two cell layers and thus worse than in the cLSM.

Microscale diffusion properties of the cartilage pericellular matrix measured using 3D scanning microphotolysis

Chondrocytes, the cells in articular cartilage, are enclosed within a pericellular matrix (PCM) whose composition and structure differ from those of the extracellular matrix (ECM). Since the PCM surrounds each cell, molecules that interact with the chondrocyte must pass through the pericellular environment. A quantitative understanding of the diffusional properties of the PCM may help in elucidating the regulatory role of the PCM in controlling transport to and from the chondrocyte. The diffusivities of fluorescently labeled 70 kDa and 500 kDa dextrans were quantified within the PCM of porcine articular cartilage using a newly developed mathematical model of scanning microphotolysis (SCAMP). SCAMP is a rapid line photobleaching method that accounts for out-of-plane bleaching attributable to high magnification. Data were analyzed by a best-fit comparison to simulations generated using a discretization of the diffusion-reaction equation in conjunction with the microscope-specific three-dimensional excitation and detection profiles. The diffusivity of the larger molecule (500 kDa dextran) was significantly lower than that of the smaller molecule (70 kDa dextran), and values were consistent with those reported previously using standard techniques. Furthermore, for both dextran sizes, the diffusion coefficient was significantly lower in the PCM than in the ECM; however, this difference was not detected in early-stage arthritic tissue. We have successfully modified the SCAMP technique to measure diffusion coefficients within the small volume of the PCM using confocal laser scanning microscopy. Our results support the hypothesis that diffusivity within the PCM of healthy articular cartilage is lower than that within the ECM, presumably due to differences in proteoglycan content.

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.

Effect of cholesterol on diffusion in surfactant bilayers

Biological membranes consist of lipid bilayers with liquid-ordered and liquid-disordered phases. It is believed that cholesterol controls the size of the microdomains in the liquid-ordered phase and thereby affects the mobility as well as the permeability of the membrane. We study this process in a model system consisting of the nonionic surfactant C(12)E(5) and water in the lamellar phase. We measure the diffusion of fluorescent probe molecules (rhodamine B) by fluorescence correlation spectroscopy. For different surfactant to water ratios, we measure how the molecular mobility varies with the amount of cholesterol added. We find that a reduction of the diffusion coefficient is already detectable at a molar ratio of 8 mol % cholesterol.

Fluorescence correlation spectroscopy simulations of photophysical phenomena and molecular interactions: a molecular dynamics/monte carlo approach

Fluorescence correlation spectroscopy (FCS) is being applied increasingly to study diffusion and interactions of fluorescently labeled macromolecules in complex biological systems. Fluctuations in detected fluorescence, deltaF(t), are expressed as time-correlation functions, G(tau), and photon-count histograms, P(k;DeltaT). Here, we developed a generalized simulation approach to compute G(tau) and P(k;DeltaT) for complex systems with arbitrary geometry, photophysics, diffusion, and macromolecular interactions. G(tau) and P(k;DeltaT) were computed from deltaF(t) generated by a Brownian dynamics simulation of single-molecule trajectories followed by a Monte Carlo simulation of fluorophore excitation and detection statistics. Simulations were validated by comparing analytical and simulated G(tau) and P(k;DeltaT) for diffusion of noninteracting fluorophores in a three-dimensional Gaussian excitation and detection volume. Inclusion of photobleaching and triplet-state relaxation produced significant changes in G(tau) and P(k;DeltaT). Simulations of macromolecular interactions and complex diffusion were done, including transient fluorophore binding to an immobile matrix, cross-correlation analysis of interacting fluorophores, and anomalous sub- and superdiffusion. The computational method developed here is generally applicable for simulating FCS measurements on systems complicated by fluorophore interactions or molecular crowding, and experimental protocols for which G(tau) and P(k;DeltaT) cannot be computed analytically.

Optimizing detection of tissue anisotropy by fluorescence recovery after photobleaching

Fluorescence recovery after photobleaching (FRAP) has been widely used to measure fluid flow and diffusion in gels and tissues. It has not been widely used in detection of tissue anisotropy. This may be due to a lack of applicable theory, or due to inherent limitations of the method. We discuss theoretical aspects of the relationship between anisotropy of tissue structure and anisotropy of diffusion coefficients, with special regard to the size of the tracer molecule used. We derive a semi-mechanistic formula relating the fiber volume fraction and ratio of fiber and tracer molecule diameters to the expected anisotropy of the diffusion coefficients. This formula and others are tested on simulated random walks through random simulated and natural media. We determine bounds on the applicability of FRAP for detection of tissue anisotropy, and suggest minimum tracer sizes for detection of anisotropy in tissues of different composition (fiber volume fraction and fiber diameter). We find that it will be easier to detect anisotropy in monodisperse materials than in polydisperse materials. To detect mild anisotropy in a tissue, such as cartilage, which has a low fiber fraction would require a tracer molecule so large that it would be difficult to deliver to the tissue. We conclude that FRAP can be used to detect tissue anisotropy when the tracer molecule is sufficiently large relative to the fiber diameter, volume fraction, and degree of polydispersivity, and when the anisotropy is sufficiently pronounced.

Diffusional anisotropy in collagenous tissues: fluorescence imaging of continuous point photobleaching

Molecular transport in avascular collagenous tissues such as articular cartilage occurs primarily via diffusion. The presence of ordered structures in the extracellular matrix may influence the local transport of macromolecules, leading to anisotropic diffusion depending on the relative size of the molecule and that of extracellular matrix structures. Here we present what we believe is a novel photobleaching technique for measuring the anisotropic diffusivity of macromolecules in collagenous tissues. We hypothesized that macromolecular diffusion is anisotropic in collagenous tissues, depending on molecular size and the local organization of the collagen structure. A theoretical model and experimental protocol for fluorescence imaging of continuous point photobleaching was developed to measure diffusional anisotropy. Significant anisotropy was observed in highly ordered collagenous tissues such as ligament, with diffusivity ratios>2 along the fiber direction compared to the perpendicular direction. In less-ordered tissues such as articular cartilage, diffusional anisotropy was dependent on site in the tissue and size of the diffusing molecule. Anisotropic diffusion was also dependent on the size of the diffusing molecule, with greatest anisotropy observed for larger molecules. These findings suggest that diffusional transport of macromolecules is anisotropic in collagenous tissues, with higher rates of diffusion along primary orientation of collagen fibers.

Diffusion of spheres in isotropic and nematic suspensions of rods

Diffusion of a small tracer sphere (apoferritin) in isotropic and nematic networks [of fd virus] is discussed. For a tracer sphere that is smaller than the mesh size of the network, screened hydrodynamic interactions between the sphere and the network determine its diffusion coefficient. A theory is developed for such interactions as well as their relation to the long-time self-diffusion coefficient. Fluorescence correlation spectroscopy measurements on mixtures of apoferritin and fd virus are presented. The long-time self-diffusion coefficient of apoferritin is measured as a function of the fd-virus concentration, both in the isotropic and nematic state, in directions parallel and perpendicular to the nematic director. The hydrodynamic screening length of the fd-virus network as a function of fd concentration is obtained by combining these experimental data with the theory. Surprisingly, the screening length increases with increasing concentration in nematic networks. This is due to the increase in the degree of alignment, which apparently leads to a strong increase of the screening length. Hydrodynamic screening is thus strongly diminished by alignment. A self-consistent calculation of the screening length does not work at higher concentrations, probably due to the strong variation of the typical incident flow fields over the contour of a rod.

FCS cell surface measurements—Photophysical limitations and consequences on molecular ensembles with heterogenic mobilities

BACKGROUND

Fluorescence Correlation Spectroscopy is a powerful method to analyze densities and diffusive behavior of molecules in membranes, but effects of photodegradation can easily be overlooked.

METHOD

Based on experimental photophysical parameters, calculations were performed to analyze the consequences of photobleaching in fluorescence correlation spectroscopy (FCS) cell surface experiments, covering a range of standard measurement conditions.

RESULTS

Cumulative effects of photobleaching can be prominent, although an absolute majority of the fluorescent molecules would pass the laser excitation beam without being photo-bleached. Given a distribution of molecules on a cell surface with different diffusive properties, the fraction of molecules that is actually analyzed depends strongly on the excitation intensities and measurement times, as well as on the size of the reservoir of freely diffusing molecules. Both the slower and the faster diffusing molecules can be disfavored.

CONCLUSIONS

Apart from quantifying photobleaching effects, the calculations suggest that the effects can be used to extract additional information, for instance about the size of the reservoirs of free diffusion. By certain choices of measurement conditions, it may be possible to more specifically analyze certain species within a population, based on their different diffusive properties, different areas of free diffusion, or different kinetics of possible transient binding.

Fluorescence correlation spectroscopy diffusion laws to probe the submicron cell membrane organization

To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.

Extracellular space diffusion in central nervous system: anisotropic diffusion measured by elliptical surface photobleaching

Diffusion in the extracellular space (ECS) is crucial for normal central nervous system physiology. The determinants of ECS diffusion include viscous interactions with extracellular matrix/plasma membranes ("viscosity") and ECS geometry ("tortuosity"). To resolve viscosity versus tortuosity effects, we measured direction-dependent (anisotropic) diffusion in ECS in mouse spinal cord by photobleaching using an elliptical spot produced by a cylindrical lens in the excitation path. Anisotropic diffusion slowed fluorescence recovery when the long axis of the ellipse was parallel versus perpendicular to the direction of faster diffusion. A mathematical model was constructed to deduce diffusion coefficients (D(x), D(y)) from fluorescence recovery measured for parallel and perpendicular orientations of the long axis of the ellipse. Elliptical spot photobleaching was validated by photobleaching aqueous-phase fluorophores on a diffraction grating, where diffusion is one-dimensional. Measurement of the diffusion of 70 kDa FITC-dextran in spinal cord in living mice indicated that viscosity slows diffusion by approximately 1.8-fold compared with its diffusion in solution. ECS geometry hinders diffusion across (but not along) axonal fibers in spinal cord further by approximately fivefold. In cerebral cortex, however, approximately 50% of the hindrance to ECS diffusion comes from viscosity and approximately 50% from tortuosity. We suggest that the extracellular matrix might have evolved to facilitate rather than hinder diffusion even for large molecules.

Action potential backpropagation and multiglomerular signaling in the rat vomeronasal system

In the accessory olfactory bulb (AOB), sensory neurons expressing a given vomeronasal receptor (VR) gene send divergent projections to many glomeruli, and second-order neurons (mitral cells) link to multiple glomeruli via branched primary dendrites. We used calcium imaging and paired somadendritic patch-clamp recording to track backpropagated action potentials (APs) in rat AOB primary dendrites. In cells loaded with 150 microm Calcium Orange, somatic spikes elicited fluorescence transients over the entire primary dendritic tree, and the relative fluorescence increment DeltaF/F(0) increased along all branches from soma to glomeruli. Backpropagation was reliant on Na+ channels: in 1 microm TTX, somatic AP commands evoked dendritic Ca2+ transients that declined steeply with distance. In paired soma- dendritic whole-cell recordings, backpropagated APs were unattenuated up to approximately 200 microm from the soma, whereas subthreshold voltage transients decayed markedly. Computational modeling indicated that the large distal Ca2+ transients are consistent with active, not passive, backpropagation. Genetic tracing in the AOB has suggested homotypic connectivity with individual mitral cell dendritic arbors projecting only to glomeruli targeted by sensory neurons expressing the same VR gene. Non-decremental, non-dichotomous backpropagation in AOB primary dendrites ensures fast, reliable communication between mitral cells and their homotypic glomeruli, binding them into functional modules in accordance with their VR-coded inputs.

Sizing-up finite fluorescent particles with nanometer-scale precision by convolution and correlation image analysis

Determining the positions, shapes and sizes of finite living particles such as bacteria, mitochondria or vesicles is of interest in many biological processes. In fluorescence microscopy, algorithms that can simultaneously localize such particles as a function of time and determine the parameters of their shapes and sizes at the nanometer scale are not yet available. Here we develop two such algorithms based on convolution and correlation image analysis that take into account the position, orientation, shape and size of the object being tracked, and we compare the precision of the two algorithms using computer simulations. We show that the precision of both algorithms strongly depends on the object's size. In cases where the diameter of the object is larger than about four to five times the beam waist radius, the convolution algorithm gives a better precision than the correlation algorithm (it leads to more precise parameters), while for smaller object diameters, the correlation algorithm gives superior precision. We apply the convolution algorithm to sequences of confocal laser scanning micrographs of immobile Escherichia coli bacteria, and show that the centroid, the front end, the rear end, the left border and the right border of a bacterium can be determined with a signal-to-noise-dependent precision down to approximately 5 nm.

Reaction–diffusion models of development with state-dependent chemical diffusion coefficients

Reaction-diffusion models are widely used to model developmental processes. The great majority of current models invoke constant diffusion coefficients. However, the diffusion of metabolites or signals through tissues is frequently such that this assumption may reasonably be questioned. We consider several different physical mechanisms leading to effective diffusion coefficients in biological tissues which vary with the local conditions, including models in which juxtacrine signaling results in the diffusion of a signal in the absence of material transport. We develop a mathematical formalism for transforming local transport laws into diffusive terms. This procedure is appropriate when the typical length scale over which the concentrations change significantly is much greater than the dimensions of a cell. We review previous developmental models which considered the possibility of state-dependent diffusion coefficients. We also provide a few new motivating examples.

High- and low-mobility populations of HP1 in heterochromatin of mammalian cells

Heterochromatin protein 1 (HP1) is a conserved nonhistone chromosomal protein with functions in euchromatin and heterochromatin. Here we investigated the diffusional behaviors of HP1 isoforms in mammalian cells. Using fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP) we found that in interphase cells most HP1 molecules (50-80%) are highly mobile (recovery halftime: t(1/2) approximately 0.9 s; diffusion coefficient: D approximately 0.6-0.7 microm(2) s(-1)). Twenty to 40% of HP1 molecules appear to be incorporated into stable, slow-moving oligomeric complexes (t(1/2) approximately 10 s), and constitutive heterochromatin of all mammalian cell types analyzed contain 5-7% of very slow HP1 molecules. The amount of very slow HP1 molecules correlated with the chromatin condensation state, mounting to more than 44% in condensed chromatin of transcriptionally silent cells. During mitosis 8-14% of GFP-HP1alpha, but not the other isoforms, are very slow within pericentromeric heterochromatin, indicating an isoform-specific function of HP1alpha in heterochromatin of mitotic chromosomes. These data suggest that mobile as well as very slow populations of HP1 may function in concert to maintain a stable conformation of constitutive heterochromatin throughout the cell cycle.

Focal Volume Confinement by Submicrometer-Sized Fluidic Channels

Microfluidic channels with two lateral dimensions smaller than 1 microm were fabricated in fused silica for high-sensitivity single-molecule detection and fluorescence correlation spectroscopy. The effective observation volumes created by these channels are approximately 100 times smaller than observation volumes using conventional confocal optics and thus enable single-fluorophore detection at higher concentrations. Increased signal-to-noise ratios are also attained because the molecules are restricted to diffuse through the central regions of the excitation volume. Depending on the channel geometries, the effective dimensionality of diffusion is reduced, which is taken into account by simple solutions to diffusion models with boundaries. Driven by electrokinetic forces, analytes could be flowed rapidly through the observation volume, drastically increasing the rate of detection events and reducing data acquisition times. The statistical accuracy of single-molecule characterization is improved because all molecules are counted and contribute to the analysis. Velocities as high as 0.1 m/s were reached, corresponding to average molecular residence times in the observation volume as short as 10 micros. Applications of these nanofabricated devices for high-throughput, single-molecule detection in drug screening and genomic analysis are discussed.

A dynamic view of cellular processes by in vivo fluorescence auto- and cross-correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is becoming increasingly popular as a technique that aims at complementing live cell images with biophysical information. This article provides both a short overview over recent intracellular FCS applications and a practical guide for investigators, who are seeking to integrate FCS into live cell imaging to obtain information on particle mobility, local concentrations, and molecular interactions. A brief introduction to the principles of FCS is provided, particularly emphasizing practical aspects such as the choice of appropriate dyes and positioning of the measurement volume in the sample. Possibilities and limitations in extracting parameters from autocorrelation curves are discussed, and attention is drawn to potential artifacts, such as photobleaching and probe aggregation. The principle of dual-color cross-correlation is reviewed along with considerations for proper setup and adjustment. Practical implications of nonideal conditions including incomplete focus overlap and spectral cross-talk are considered. Recent examples of both auto- and cross-correlation applications demonstrate the potential of FCS for cell biology.