Ensemble and single particle fluorimetric techniques in concerted action to study the diffusion and aggregation of the glycine receptor α3 isoforms in the cell plasma membrane

The spatio-temporal membrane behavior of glycine receptors (GlyRs) is known to be of influence on receptor homeostasis and functionality. In this work, an elaborate fluorimetric strategy was applied to study the GlyR α3K and L isoforms. Previously established differential clustering, desensitization and synaptic localization of these isoforms imply that membrane behavior is crucial in determining GlyR α3 physiology. Therefore diffusion and aggregation of homomeric α3 isoform-containing GlyRs were studied in HEK 293 cells. A unique combination of multiple diffraction-limited ensemble average methods and subdiffraction single particle techniques was used in order to achieve an integrated view of receptor properties. Static measurements of aggregation were performed with image correlation spectroscopy (ICS) and, single particle based, direct stochastic optical reconstruction microscopy (dSTORM). Receptor diffusion was measured by means of raster image correlation spectroscopy (RICS), temporal image correlation spectroscopy (TICS), fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT). The results show a significant difference in diffusion coefficient and cluster size between the isoforms. This reveals a positive correlation between desensitization and diffusion and disproves the notion that receptor aggregation is a universal mechanism for accelerated desensitization. The difference in diffusion coefficient between the clustering GlyR α3L and the non-clustering GlyR α3K cannot be explained by normal diffusion. SPT measurements indicate that the α3L receptors undergo transient trapping and directed motion, while the GlyR α3K displays mild hindered diffusion. These findings are suggestive of differential molecular interaction of the isoforms after incorporation in the membrane.     

Single particle tracking. Analysis of diffusion and flow in two-dimensional systems.

Analysis of the trajectories of small particles at high spatial and temporal resolution using video enhanced contrast microscopy provides a powerful approach to characterizing the mechanisms of particle motion in living cells and in other systems. We present here the theoretical basis for the analysis of these trajectories for particles undergoing random diffusion and/or systematic transport at uniform velocity in two-dimensional systems. The single particle tracking method, based on observations of the trajectories of individual particles, is compared with methods that characterize the motions of a large collection of particles such as fluorescence photobleaching recovery. Determination of diffusion coefficients or transport velocities either from correlation of positions or of velocities of the particles is discussed. A result of practical importance is an analysis of the dependence of the expected statistical uncertainty of these determinations on the number of position measurements. This provides a way of judging the accuracy of the diffusion coefficients and transport velocities obtained using this approach.     

Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells.

The movements of E-cadherin, epidermal growth factor receptor, and transferrin receptor in the plasma membrane of a cultured mouse keratinocyte cell line were studied using both single particle tracking (SPT; nanovid microscopy) and fluorescence photobleaching recovery (FPR). In the SPT technique, the receptor molecules are labeled with 40 nm-phi colloidal gold particles, and their movements are followed by video-enhanced differential interference contrast microscopy at a temporal resolution of 33 ms and at a nanometer-level spatial precision. The trajectories of the receptor molecules obtained by SPT were analyzed by developing a method that is based on the plot of the mean-square displacement against time. Four characteristic types of motion were observed: (a) stationary mode, in which the microscopic diffusion coefficient is less than 4.6 x 10(-12) cm2/s; (b) simple Brownian diffusion mode; (c) directed diffusion mode, in which unidirectional movements are superimposed on random motion; and (d) confined diffusion mode, in which particles undergoing Brownian diffusion (microscopic diffusion coefficient between 4.6 x 10(-12) and 1 x 10(-9) cm2/s) are confined within a limited area, probably by the membrane-associated cytoskeleton network. Comparison of these data obtained by SPT with those obtained by FPR suggests that the plasma membrane is compartmentalized into many small domains 300-600 nm in diameter (0.04-0.24 microns2 in area), in which receptor molecules are confined in the time scale of 3-30 s, and that the long-range diffusion observed by FPR can occur by successive movements of the receptors to adjacent compartments. Calcium-induced differentiation decreases the sum of the percentages of molecules in the directed diffusion and the stationary modes outside of the cell-cell contact regions on the cell surface (which is proposed to be the percentage of E-cadherin bound to the cytoskeleton/membrane-skeleton), from approximately 60% to 8% (low- and high-calcium mediums, respectively).     

The effect of ligand affinity on integrins’ lateral diffusion in cultured cells

The role of ligand affinity in altering αPS2CβPS integrins’ lateral mobility was studied using single particle tracking (SPT) with ligand-functionalized quantum dots (QDs) and fluorescence recovery after photobleaching (FRAP) with fluorescent protein tagged integrins. Integrins are ubiquitous transmembrane proteins that are vital for numerous cellular functions, including bidirectional signaling and cell anchorage. Wild-type and high ligand affinity mutant (αPS2CβPS-V409D) integrins were studied in S2 cells. As measured by SPT, the integrin mobile fraction decreased by 22 % and had a 4× slower diffusion coefficient for αPS2CβPS-V409D compared to wild-type integrins. These differences are partially the result of αPS2CβPS-V409D integrins’ increased clustering. For the wild-type integrins, the average of all diffusion coefficients measured by SPT was statistically similar to the ensemble FRAP results. A 75 % slower average diffusion coefficient was measured by SPT compared to FRAP for αPS2CβPS-V409D integrins, and this may be the result of SPT measuring only ligand-bound integrins, in contrast all ligand-bound and ligand-unbound integrins are averaged in FRAP measurements. Specific binding of the ligand-functionalized QDs was 99 % for integrin expressing cells. The results prove that the ligand binding affinity affects the lateral dynamics of a subset of integrins based on the complementary SPT and FRAP data.     

Analysis of molecular diffusion by first-passage time variance identifies the size of confinement zones

The diffusion of receptors within the two-dimensional environment of the plasma membrane is a complex process. Although certain components diffuse according to a random walk model (Brownian diffusion), an overwhelming body of work has found that membrane diffusion is nonideal (anomalous diffusion). One of the most powerful methods for studying membrane diffusion is single particle tracking (SPT), which records the trajectory of a label attached to a membrane component of interest. One of the outstanding problems in SPT is the analysis of data to identify the presence of heterogeneity. We have adapted a first-passage time (FPT) algorithm, originally developed for the interpretation of animal movement, for the analysis of SPT data. We discuss the general application of the FPT analysis to molecular diffusion, and use simulations to test the method against data containing known regions of confinement. We conclude that FPT can be used to identify the presence and size of confinement within trajectories of the receptor LFA-1, and these results are consistent with previous reports on the size of LFA-1 clusters. The analysis of trajectory data for cell surface receptors by FPT provides a robust method to determine the presence and size of confined regions of diffusion.     

Shear‐induced diffusion of red blood cells measured with dynamic light scattering‐optical coherence tomography

Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering‐optical coherence tomography (DLS‐OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution‐constrained three‐dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS‐OCT to measure both RBC velocity and the shear‐induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear‐induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10^?6 mm². These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.      

Estimation of diffusion constants from single molecular measurement without explicit tracking

Background

Time course measurement of single molecules on a cell surface provides detailed information about the dynamics of the molecules that would otherwise be inaccessible. To extract the quantitative information, single particle tracking (SPT) is typically performed. However, trajectories extracted by SPT inevitably have linking errors when the diffusion speed of single molecules is high compared to the scale of the particle density.

Methods

To circumvent this problem, we develop an algorithm to estimate diffusion constants without relying on SPT. The proposed algorithm is based on a probabilistic model of the distance to the nearest point in subsequent frames. This probabilistic model generalizes the model of single particle Brownian motion under an isolated environment into the one surrounded by indistinguishable multiple particles, with a mean field approximation.

Results

We demonstrate that the proposed algorithm provides reasonable estimation of diffusion constants, even when other methods suffer due to high particle density or inhomogeneous particle distribution. In addition, our algorithm can be used for visualization of time course data from single molecular measurements.

Conclusions

The proposed algorithm based on the probabilistic model of indistinguishable Brownian particles provide accurate estimation of diffusion constants even in the regime where the traditional SPT methods underestimate them due to linking errors.

     

Quantifying Subpixel Accuracy: An Experimental Method for Measuring Accuracy in Image-Correlation-Based, Single-Particle Tracking

Single-particle tracking (SPT) is a range of powerful analysis techniques that measure particle motion from video microscopy image sequences. SPT is used to study the behavior of motor proteins and associated organelle transport within a cell. Many SPT algorithms deliver subpixel accurate measurements with noisy data corresponding to sub-10-nm resolution. Image-correlation techniques have been shown to be the most accurate method of tracking extended objects. However, to date, it has not been possible to determine the level of error when measuring the motion of an arbitrary particle with this method. In this article we derive a method for experimentally determining the accuracy of image-correlation-based SPT. We then apply this technique to a series of confocal fluorescence microscope image sequences of mitochondria, demonstrating the possibility of making measurements accurate to 5 nm when working with extended objects within live cells. In doing so we show that for particles with a low signal/noise ratio, the accuracy can vary by a factor of 2, corresponding to different particle shapes for a given signal/noise ratio. Use of the presented technique will allow researchers to quantify the accuracy of their measurements on a per-particle basis. This in turn will allow the selection of the most accurately tracked particles, helping to push the accuracy of spatial measurements well below the diffraction limit. This is particularly important for the study of molecular motors whose step size is a similar scale to these limits.     

Diffusion coefficient of the cyclic GMP analog 8-(fluoresceinyl)thioguanosine 3'',5'' cyclic monophosphate in the salamander rod outer segment.

Cyclic GMP (cGMP) is the intracellular messenger mediating phototransduction in retinal rods, with its longitudinal diffusion in the rod outer segment (ROS) likely to be a factor in determining light sensitivity. From the kinetics of cGMP-activated currents in the truncated ROS of the salamander (Ambystoma tigrinum), the cGMP diffusion coefficient was previously estimated to be approximately 60 x 10(-8) cm2 s-1. On the other hand, fluorescence measurements in intact salamander ROS using 8-(fluoresceinyl)thioguanosine 3',5'-cyclic monophosphate (Fl-cGMP) led to a diffusion coefficient for this compound of 1 x 10(-8) cm2 s-1; after corrections for differences in size and in binding to cellular components between cGMP and Fl-cGMP, this gave an upper limit of 11 x 10(-8) cm2 s-1 for the cGMP diffusion coefficient. To properly compare the two sets of measurements, we have examined the diffusion of Fl-cGMP in the truncated ROS. From the kinetics of Fl-cGMP-activated currents, we have obtained a diffusion coefficient of 3 x 10(-8) cm2 s-1 for this analog; the cGMP diffusion coefficient measured from the same truncated ROSs was approximately 80 x 10(-8) cm2 s-1. Thus, a factor of 27 appears appropriate for correcting differences in size and intracellular binding between cGMP and Fl-cGMP. Application of this correction factor to the Fl-cGMP diffusion coefficient measurements by Olson and Pugh (1993) gives a cGMP diffusion coefficient of approximately 30 x 10(-8) cm2 s-1, in reasonable agreement with the value measured from the truncated ROS.     

Diaphanous-1 affects the nanoscale clustering and lateral diffusion of receptor for advanced glycation endproducts (RAGE)

The interactions between the cytoplasmic protein diaphanous-1 (Diaph1) and the receptor for advanced glycation endproducts (RAGE) drive the negative consequences of RAGE signaling in several disease processes. Reported in this work is how Diaph1 affects the nanoscale clustering and diffusion of RAGE measured using super-resolution stochastic optical reconstruction microscopy (STORM) and single particle tracking (SPT). Altering the Diaph1 binding site has a different impact on RAGE diffusion compared to when Diaph1 expression is reduced in HEK293 cells. In cells with reduced Diaph1 expression (RAGE-Diaph1^?/?), the average RAGE diffusion coefficient is increased by 35%. RAGE diffusion is known to be influenced by the dynamics of the actin cytoskeleton. Actin labeling shows that a reduced Diaph1 expression leads to cells with reduced filopodia density and length. In contrast, when two RAGE amino acids that interact with Diaph1 are mutated (RAGE_RQ/AA), the average RAGE diffusion coefficient is decreased by 16%. Since RAGE diffusion is slowed when the interaction between Diaph1 and RAGE is disrupted, the interaction of the two proteins results in faster RAGE diffusion. In both RAGE_RQ/AA and RAGE-Diaph1^?/? cells the number and size of RAGE clusters are decreased compared to cells expressing RAGE and native concentrations of Diaph1. This work shows that Diaph1 has a role in affecting RAGE clusters and diffusion.     

Tracking bio‐molecules in live cells using quantum dots

Single particle tracking (SPT) techniques were developed to explore bio‐molecules dynamics in live cells at single molecule sensitivity and nanometer spatial resolution. Recent developments in quantum dots (Qdots) surface coating and bio‐conjugation schemes have made them most suitable probes for live cell applications. Here we review recent advancements in using quantum dots as SPT probes for live cell experiments. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Apparent subdiffusion inherent to single particle tracking

Subdiffusion and its causes in both in vivo and in vitro lipid membranes have become the focus of recent research. We report apparent subdiffusion, observed via single particle tracking (SPT), in a homogeneous system that only allows normal diffusion (a DMPC monolayer in the fluid state). The apparent subdiffusion arises from slight errors in finding the actual particle position due to noise inherent in all experimental SPT systems. A model is presented that corrects this artifact, and predicts the time scales after which the effect becomes negligible. The techniques and results presented in this paper should be of use in all SPT experiments studying normal and anomalous diffusion.     

Resolution of the conformational distribution and dynamics of a flexible molecule using frequency-domain fluorometry

We report the first resolution of both the conformational distribution and end-to-end diffusion coefficient of a flexible molecule. This molecular information was recovered using only the donor intensity decay in a single solvent at a single viscosity, as observed by the technique of frequency-domain fluorometry. This technique can be extended to measurements of structural fluctuations of biological macromolecules.     

Conformational changes and aggregation of alginic acid as determined by fluorescence correlation spectroscopy

Insight into the conformations and aggregation of alginic acid was gained by measuring its diffusion coefficient at very dilute concentrations using fluorescence correlation spectroscopy. Both the pH and ionic strength (I) had an important influence on the diffusion coefficient of the polysaccharide. For pH, three effects were isolated: (i) below pH 4, the charge density decreased causing increased aggregation; (ii) between pH 4 and 8, a molecular expansion was observed with increasing pH, whereas (iii) above pH 8 some dissociation of the polymer was observed. Increasing I from 0.001 to 0.1 M resulted in a ca. 20% increase in the diffusion coefficient. By coupling these measurements to molar mass determinations obtained by size exclusion chromatography and monomer size estimations determined from ab initio calculations, it was possible to determine the radii of gyration via de Gennes renormalization theory. From diffusion coefficients and radii of gyration obtained as a function of ionic strength, persistence lengths (total, electrostatic, and intrinsic) were calculated from the Benoit-Doty relationship.     

Lateral diffusion on tubular membranes: quantification of measurements bias

Single Particle Tracking (SPT) is a powerful technique for the analysis of the lateral diffusion of the lipid and protein components of biological membranes. In neurons, SPT allows the study of the real-time dynamics of receptors for neurotransmitters that diffuse continuously in and out synapses. In the simplest case where the membrane is flat and is parallel to the focal plane of the microscope the analysis of diffusion from SPT data is relatively straightforward. However, in most biological samples the membranes are curved, which complicates analysis and may lead to erroneous conclusions as for the mode of lateral diffusion. Here we considered the case of lateral diffusion in tubular membranes, such as axons, dendrites or the neck of dendritic spines. Monte Carlo simulations allowed us to evaluate the error in diffusion coefficient (D) calculation if the curvature is not taken into account. The underestimation is determined by the diameter of the tubular surface, the frequency of image acquisition and the degree of mobility itself. We found that projected trajectories give estimates that are 25 to 50% lower than the real D in case of 2D-SPT over the tubular surface. The use of 3D-SPT improved the measurements if the frequency of image acquisition was fast enough in relation to the mobility of the molecules and the diameter of the tube. Nevertheless, the calculation of D from the components of displacements in the axis of the tubular structure gave accurate estimate of D, free of geometrical artefacts. We show the application of this approach to analyze the diffusion of a lipid on model tubular membranes and of a membrane-bound GFP on neurites from cultured rat hippocampal neurons.     

Single-particle tracking of membrane protein diffusion in a potential: simulation, detection, and application to confined diffusion of CFTR Cl- channels

Confined diffusion of membrane receptors and lipids can result from intramembrane barriers, skeletal interactions, rafts, and other phenomena. We simulated single-particle diffusion in two dimensions in an arbitrary potential, V(r), based on summation of random and potential gradient-driven motions. Algorithms were applied and verified for detection of potential-driven diffusion, and for determination of V(r) from radial particle density distributions, taking into account experimental uncertainties in particle position and finite trajectory recording. Single-particle tracking (SPT) analysis of the diffusion of cystic fibrosis transmembrane conductance regulator (CFTR) Cl(-) channels in mammalian cells revealed confined diffusion with diffusion coefficient approximately 0.004 microm(2)/s. SPT data fitted closely to a springlike attractive potential, V(r) = kr(2), but not to other V(r) forms such as hard-wall or viscoelastic-like potentials. The "spring constant", k, determined from SPT data was 2.6 +/- 0.8 pN/microm, and not altered significantly by modulation of skeletal protein architecture by jasplakinolide. However, k was reduced by a low concentration of latrunculin, supporting the involvement of actin in the springlike tethering of CFTR. Confined diffusion of membrane proteins is likely a general phenomenon suitable for noninvasive V(r) analysis of force-producing mechanisms. Our data provide the first measurement of actin elasticity, to the best of our knowledge, that does not involve application of an external force.     

Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells

To probe the dynamics and size of lipid rafts in the membrane of living cells, the local diffusion of single membrane proteins was measured. A laser trap was used to confine the motion of a bead bound to a raft protein to a small area (diam < or = 100 nm) and to measure its local diffusion by high resolution single particle tracking. Using protein constructs with identical ectodomains and different membrane regions and vice versa, we demonstrate that this method provides the viscous damping of the membrane domain in the lipid bilayer. When glycosylphosphatidylinositol (GPI) -anchored and transmembrane proteins are raft-associated, their diffusion becomes independent of the type of membrane anchor and is significantly reduced compared with that of nonraft transmembrane proteins. Cholesterol depletion accelerates the diffusion of raft-associated proteins for transmembrane raft proteins to the level of transmembrane nonraft proteins and for GPI-anchored proteins even further. Raft-associated GPI-anchored proteins were never observed to dissociate from the raft within the measurement intervals of up to 10 min. The measurements agree with lipid rafts being cholesterol-stabilized complexes of 26 +/- 13 nm in size diffusing as one entity for minutes.     

Regulation Mechanism of the Lateral Diffusion of Band 3 in Erythrocyte Membranes by the Membrane Skeleton

Mechanisms that regulate the movement of a membrane spanning protein band 3 in erythrocyte ghosts were investigated at the level of a single or small groups of molecules using single particle tracking with an enhanced time resolution (0.22 ms). Two-thirds of band 3 undergo macroscopic diffusion: a band 3 molecule is temporarily corralled in a mesh of 110 nm in diameter, and hops to an adjacent mesh an average of every 350 ms. The rest (one-third) of band 3 exhibited oscillatory motion similar to that of spectrin, suggesting that these band 3 molecules are bound to spectrin. When the membrane skeletal network was dragged and deformed/translated using optical tweezers, band 3 molecules that were undergoing hop diffusion were displaced toward the same direction as the skeleton. Mild trypsin treatment of ghosts, which cleaves off the cytoplasmic portion of band 3 without affecting spectrin, actin, and protein 4.1, increased the intercompartmental hop rate of band 3 by a factor of 6, whereas it did not change the corral size and the microscopic diffusion rate within a corral. These results indicate that the cytoplasmic portion of band 3 collides with the membrane skeleton, which causes temporal confinement of band 3 inside a mesh of the membrane skeleton.     

Methods to measure the lateral diffusion of membrane lipids and proteins

In this chapter, we discuss methods to measure lateral mobility of membrane lipids and proteins using techniques based on the light microscope. These methods typically sample lateral mobility in very small, micron-sized regions of the membrane so that they can be used to measure diffusion in regions of single cells. The methods are based on fluorescence from the molecules of interest or from light scattered from particles attached to single or small groups of membrane lipids or proteins. Fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS) and Single particle tracking (SPT) are presented in that order. FRAP and FCS methodologies are described for a dedicated wide field microscope although many confocal microscopes now have software permitting these measurement to be made; nevertheless, the principles of the measurement are the same for a wide field or confocal microscope. SPT can be applied to trace the movements of single fluorescent molecules in membranes but this aspect will not be treated in detail.     

Lowering the barriers to random walks on the cell surface

We used fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT) techniques to compare diffusion of class I major histocompatibility complex molecules (MHC) on normal and alpha-spectrin-deficient murine erythroleukemia (MEL) cells. Because the cytoskeleton mesh acts as a barrier to lateral mobility of membrane proteins, we expected that diffusion of membrane proteins in alpha-spectrin-deficient MEL cells would differ greatly from that in normal MEL cells. In the event, diffusion coefficients derived from either FRAP or SPT analysis were similar for alpha-spectrin-deficient and normal MEL cells, differing by a factor of approximately 2, on three different timescales: tens of seconds, 1-10 s, and 100 ms. SPT analysis showed that the diffusion of most class I MHC molecules was confined on both cell types. On the normal MEL cells, the mean diagonal length of the confined area was 330 nm with a mean residency time of 40s. On the alpha-spectrin-deficient MEL cells, the mean diagonal length was 650 nm with a mean residency time of 45s. Thus there are fewer barriers to lateral diffusion on cytoskeleton mutant MEL cells than on normal MEL cells, but this difference does not strongly affect lateral diffusion on the scales measured here.