Detection of non-Brownian diffusion in the cell membrane in single molecule tracking

Multicolour single molecule imaging on cells using a supercontinuum source

Multicolour single molecule fluorescence imaging enables the study of multiple proteins in the membranes of living cells. We describe the use of a supercontinuum laser as the excitation source, show its comparability with multiplexed single-wavelength lasers and demonstrate that it can be used to study membrane proteins such as the ErbB receptor family. We discuss the benefits of white-light sources for single molecule fluorescence, in particular their ease of use and the freedom to use the most appropriate dye without being constrained by available laser wavelengths.

Single-molecule imaging of stochastic signaling events in living cells

Environmental changes result in signaling events at cell membranes. To develop the means to understand these events at the molecular level, it is essential to become familiar with the stochastic nature of signaling molecules in living cells. Using total internal reflection fluorescent microscopy (TIRFM), these signaling events can be directly observed at the single-molecule level. This article explains the basis of TIRFM and how it is set up. It then describes how to visualize cell membrane signaling events. It also explains how to prove that detected fluorescence is emitted from single dye molecules and how to analyze the data from TIRFM experiments.

Correlating anomalous diffusion with lipid bilayer membrane structure using single molecule tracking and atomic force microscopy

Anomalous diffusion has been observed abundantly in the plasma membrane of biological cells, but the underlying mechanisms are still unclear. In general, it has not been possible to directly image the obstacles to diffusion in membranes, which are thought to be skeleton bound proteins, protein aggregates, and lipid domains, so the dynamics of diffusing particles is used to deduce the obstacle characteristics. We present a supported lipid bilayer system in which we characterized the anomalous diffusion of lipid molecules using single molecule tracking, while at the same time imaging the obstacles to diffusion with atomic force microscopy. To explain our experimental results, we performed lattice Monte Carlo simulations of tracer diffusion in the presence of the experimentally determined obstacle configurations. We correlate the observed anomalous diffusion with obstacle area fraction, fractal dimension, and correlation length. To accurately measure an anomalous diffusion exponent, we derived an expression to account for the time-averaging inherent to all single molecule tracking experiments. We show that the length of the single molecule trajectories is critical to the determination of the anomalous diffusion exponent. We further discuss our results in the context of confinement models and the generating stochastic process.

Neurotrophin signaling via long-distance axonal transport

Neurotrophins are a family of target-derived growth factors that support survival, development, and maintenance of innervating neurons. Owing to the unique architecture of neurons, neurotrophins that act locally on the axonal terminals must convey their signals across the entire axon for subsequent regulation of gene transcription in the cell nucleus. This long-distance retrograde signaling, a motor-driven process that can take hours or days, has been a subject of intense interest. In the last decade, live-cell imaging with high sensitivity has significantly increased our capability to track the transport of neurotrophins, their receptors, and subsequent signals in real time. This review summarizes recent research progress in understanding neurotrophin-receptor interactions at the axonal terminal and their transport dynamics along the axon. We emphasize high-resolution studies at the single-molecule level and also discuss recent technical advances in the field.

Detecting and tracking nonfluorescent nanoparticle probes in live cells

Precisely imaging and tracking dynamic biological processes in live cells are crucial for both fundamental research in life sciences and biomedical applications. Nonfluorescent nanoparticles are emerging as important optical probes in live-cell imaging because of their excellent photostability, large optical cross sections, and low cytotoxicity. Here, we provide a review of recent development in optical imaging of nonfluorescent nanoparticle probes and their applications in dynamic tracking and biosensing in live cells. A brief discussion on cytotoxicity of nanoparticle probes is also provided.

Hierarchical mesoscale domain organization of the plasma membrane

Based on recent single-molecule imaging results in the living cell plasma membrane, we propose a hierarchical architecture of three-tiered mesoscale (2-300nm) domains to represent the fundamental functional organization of the plasma membrane: (i) membrane compartments of 40-300nm in diameter due to the partitioning of the entire plasma membrane by the actin-based membrane skeleton 'fence' and transmembrane protein 'pickets' anchored to the fence; (ii) raft domains (2-20nm); and (iii) dimers/oligomers and greater complexes of membrane-associated proteins (3-10nm). The basic molecular interactions required for the signal transduction function of the plasma membrane can be fundamentally understood and conveniently summarized as the cooperative actions of these mesoscale domains, where thermal fluctuations/movements of molecules and weak cooperativity play crucial roles.

Single molecule tracking studies of lower critical solution temperature transition behavior in poly(N-isopropylacrylamide)

Spatial and temporal heterogeneities in expanded and collapsed surface bound poly(N-isopropylacrylamide), pNIPAAm, films are studied by single molecule tracking (SMT) experiments. Tracking data are analyzed using both radius of gyration (R(g)) evolution and confinement level calculations to elucidate the range of behaviors displayed by single Rhodamine6G (R6G) molecules. Confined diffusion that is dictated by the free volume within surface tethered chains is observed with considerable dispersion among individual R6G molecules. Thus, the distribution of probe behavior reflects nanometer-scale information about the behavior of the probe-polymer system at temperatures above (T > T(LCST)) and below (T < T(LCST)) the lower critical solution temperature (LCST). In this context, confinement-level analysis and R(g) evolution both show a larger degree of confinement of the probe in pNIPAAm at T > T(LCST). Temperature-dependent changes in confinement are evidenced at T > T(LCST) by a higher percentage of confined steps, longer periods of confined events, and smaller area of confined zones, as well as a shift in the overall distribution of R(g) evolution paths and final R(g) distributions.

Relaxation properties in a diffusive model of k-mers with constrained movements on a triangular lattice

We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are k-mers that can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean-square displacement, the self-part of the van Hove correlation function, and the self-intermediate scattering function. We observe a considerable slowing of diffusion on a long-time scale when suppressing the rotational motion of k-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self-intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale τ(q(n)) is found to decrease with the wave vector q(n) according to a simple power law. Furthermore, the slowing of the dynamics with density ρ(0) is consistent with the scaling law 1/τ(q(n);ρ(0))∝(ρ(c)-ρ(0))(ϰ), with the same exponent ϰ=3.34±0.12 for all wave vectors q(n). The density ρ(c) is approximately equal to the closest packing limit, θ(CPL)≲1, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient D(s) scales with the same power-law exponent and critical density.

Transmembrane helices can induce domain formation in crowded model membranes

We studied compositionally heterogeneous multi-component model membranes comprised of saturated lipids, unsaturated lipids, cholesterol, and α-helical TM protein models using coarse-grained molecular dynamics simulations. Reducing the mismatch between the length of the saturated and unsaturated lipid tails reduced the driving force for segregation into liquid-ordered (l(o)) and liquid-disordered (l(d)) lipid domains. Cholesterol depletion had a similar effect, and binary lipid mixtures without cholesterol did not undergo large-scale phase separation under the simulation conditions. The phase-separating ternary dipalmitoyl-phosphatidylcholine (DPPC)/dilinoleoyl-PC (DLiPC)/cholesterol bilayer was found to segregate into l(o) and l(d) domains also in the presence of a high concentration of ΤΜ helices. The l(d) domain was highly crowded with TM helices (protein-to-lipid ratio ~1:5), slowing down lateral diffusion by a factor of 5-10 as compared to the dilute case, with anomalous (sub)-diffusion on the μs time scale. The membrane with the less strongly unsaturated palmitoyl-linoleoyl-PC instead of DLiPC, which in the absence of TM α-helices less strongly deviated from ideal mixing, could be brought closer to a miscibility critical point by introducing a high concentration of TM helices. Finally, the 7-TM protein bacteriorhodopsin was found to partition into the l(d) domains irrespective of hydrophobic matching. These results show that it is possible to directly study the lateral reorganization of lipids and proteins in compositionally heterogeneous and crowded model biomembranes with coarse-grained molecular dynamics simulations, a step toward simulations of realistic, compositionally complex cellular membranes. This article is part of a Special Issue entitled: Protein Folding in Membranes.

Holographic tissue dynamics spectroscopy

Tissue dynamics spectroscopy uses digital holography as a coherence gate to extract depth-resolved quasi-elastic dynamic light scattering from inside multicellular tumor spheroids. The temporal speckle contrast provides endogenous dynamical images of proliferating and hypoxic or necrotic tissues. Fluctuation spectroscopy similar to diffusing wave spectroscopy is performed on the dynamic speckle to generate tissue-response spectrograms that track time-resolved changes in intracellular motility in response to environmental perturbations. The spectrograms consist of several frequency bands that range from 0.005 to 5 Hz. The fluctuation spectral density and temporal autocorrelations show the signature of constrained anomalous diffusion, but with large fluctuation amplitudes caused by active processes far from equilibrium. Differences in the tissue-response spectrograms between the proliferating outer shell and the hypoxic inner core differentiate normal from starved conditions. The differential spectrograms provide an initial library of tissue-response signatures to environmental conditions of temperature, osmolarity, pH, and serum growth factors.

The diffusional properties of dendrites depend on the density of dendritic spines

We combined computational modeling and experimental measurements to determine the influence of dendritic structure on the diffusion of intracellular chemical signals in mouse cerebellar Purkinje cells and hippocamal CA1 pyramidal cells. Modeling predicts that molecular trapping by dendritic spines causes diffusion along spiny dendrites to be anomalous and that the value of the anomalous exponent (d(w) ) is proportional to spine density in both cell types. To test these predictions we combined the local photorelease of an inert dye, rhodamine dextran, with two-photon fluorescence imaging to track diffusion along dendrites. Our results show that anomalous diffusion is present in spiny dendrites of both cell types. Further, the anomalous exponent is linearly related to the density of spines in pyramidal cells and d(w) in Purkinje cells is consistent with such a relationship. We conclude that anomalous diffusion occurs in the dendrites of multiple types of neurons. Because spine density is dynamic and depends on neuronal activity, the degree of anomalous diffusion induced by spines can dynamically regulate the movement of molecules along dendrites.

Single macromolecule diffusion in confined environments

We consider the behaviour of single molecules on surfaces and, more generally, in confined environments. These are loosely split into three sections: single molecules in biology, the physics of single molecules on surfaces and controlled (directed) diffusion. With recent advances in single molecule detection techniques, the importance and mechanisms of single molecule processes such as localised enzyme production and intracellular diffusion across membranes has been highlighted, emphasising the extra information that cannot be obtained with techniques that present average behaviour. Progress has also been made in producing artificial systems that can control the rate and direction of diffusion, and because these are still in their infancy (especially in comparison to complex biological systems), we discuss the new physics revealed by these phenomena.

Mobility of BtuB and OmpF in the Escherichia coli outer membrane: implications for dynamic formation of a translocon complex

Diffusion of two Escherichia coli outer membrane proteins-the cobalamin (vitamin B12) receptor (BtuB) and the OmpF porin, which are implicated in the cellular import pathways of colicins and phages-was measured in vivo. The lateral mobility of these proteins is relevant to the mechanism of formation of the translocon for cellular import of colicins such as the rRNase colicin E3. The diffusion coefficient (D) of BtuB, the primary colicin receptor, complexed to fluorescent antibody or colicin, is 0.05±0.01 μm2/s and 0.10±0.02 μm2/s, respectively, over a timescale of 25-150 ms. Mutagenesis of the BtuB TonB box, which eliminates or significantly weakens the interaction between BtuB and the TonB energy-transducing protein that is anchored in the cytoplasmic membrane, resulted in a fivefold larger value of D, 0.27±0.06 μm2/s for antibody-labeled BtuB, indicating a cytoskeletal-like interaction of TonB with BtuB. OmpF has a diffusion coefficient of 0.006±0.002 μm2/s, ∼10-fold smaller than that of BtuB, and is restricted within a domain of diameter 100 nm, showing it to be relatively immobile compared to BtuB. Thus, formation of the outer membrane translocon for cellular import of the nuclease colicins is a demonstrably dynamic process, because it depends on lateral diffusion of BtuB and collisional interaction with relatively immobile OmpF.

Nanometer-scale optical imaging of collagen fibers using gold nanoparticles

We describe 3D single particle tracking of gold nanoparticles (AuNPs) moving along collagen fibers in aqueous environment with two-photon excitation conditions. The photoacoustic effect at the collagen fiber caused by the irradiation with ultrashort, near-infrared laser pulses propels the particles adsorbed to the surface of the collagen fibers. We report the tracking of individual AuNPs in three dimensions with high spatial and temporal resolution, of few nanometers and milliseconds, respectively. Due to the emission signal caused by the interaction between the AuNPs and the weak chromophores in the collagen fiber, the trajectories of individual AuNPs reveal the fiber topography with nanometric resolution. The intensity along the trajectory shows that we are sensitive to the distribution of the weak chromophores on the fiber.

Monte Carlo simulations of plasma membrane corral-induced EGFR clustering

Experimental evidence suggests that the cell membrane is a highly organized structure that is compartmentalized by the underlying membrane cytoskeleton (MSK). The interaction between the cell membrane and the cytoskeleton led to the "picket-fence" model, which was proposed to explain certain aspects of membrane compartmentalization. This model assumes that the MSK hinders and confines the motion of receptors and lipids to compartments in the membrane. However, the impact of the MSK on receptor clustering, aggregation, and downstream signaling remains unclear. For example, some evidence suggests that the MSK enhances dimerization, while other evidence suggests decreased dimerization and signaling. Herein, we use computational Monte Carlo simulations to examine the effects of MSK density and receptor concentration on receptor dimerization and clustering. Preliminary results suggest that the MSK may have the potential to induce receptor clustering, which is a function of both picket-fence density and receptor concentration.

Effects of vibration on differentiation of cultured PC12 cells

Different types of physiological-mechanical stress, such as shear stress in vascular endothelial cells or hydrostatic pressure in chondrocytes are well known as regulators of cell function. In this study, the effects of vibration, a type of non-physiological mechanical stimulation, on differentiation of rat pheochromocytoma (PC12) cells are reported. A nano-vibration system was designed to produce nanometer-scale vibration. The frequency and amplitude of the nano-vibrations were monitored by a capacitance displacement sensor connected to an oscilloscope. When PC12 cells exposed to nerve growth factor were subjected to vibration at 10 kHz, differentiation and elongation of their neurites were promoted earlier in the culture. Vibration promoted differentiation of PC12 cells. This approach could therefore also be promising for determining of the effects of the physical environment on cell differentiation.

Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium

We examine the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient D of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least-squares fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points are used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments.

Quantitative understanding of cell signaling: the importance of membrane organization

Systems biology modeling of signal transduction pathways traditionally employs ordinary differential equations, deterministic models based on the assumptions of spatial homogeneity. However, this can be a poor approximation for certain aspects of signal transduction, especially its initial steps: the cell membrane exhibits significant spatial organization, with diffusion rates approximately two orders of magnitude slower than those in the cytosol. Thus, to unravel the complexities of signaling pathways, quantitative models must consider spatial organization as an important feature of cell signaling. Furthermore, spatial separation limits the number of molecules that can physically interact, requiring stochastic simulation methods that account for individual molecules. Herein, we discuss the need for mathematical models and experiments that appreciate the importance of spatial organization in the membrane.

Snapshot Image Mapping Spectrometer (IMS) with high sampling density for hyperspectral microscopy

A snapshot Image Mapping Spectrometer (IMS) with high sampling density is developed for hyperspectral microscopy, measuring a datacube of dimensions 285 x 285 x 60 (x, y, lambda). The spatial resolution is approximately 0.45 microm with a FOV of 100 x 100 microm(2). The measured spectrum is from 450 nm to 650 nm and is sampled by 60 spectral channels with average sampling interval approximately 3.3 nm. The channel's spectral resolution is approximately 8nm. The spectral imaging results demonstrate the potential of the IMS for real-time cellular fluorescence imaging.

Quantifying biomolecule diffusivity using an optimal Bayesian method

We propose a Bayesian method to extract the diffusivity of biomolecules evolving freely or inside membrane microdomains. This approach assumes a model of motion for the particle considered, namely free Brownian motion or confined diffusion. In each framework, a systematic Bayesian scheme is provided for estimating the diffusivity. We show that this method reaches the best performances theoretically achievable. Its efficiency overcomes that of widely used methods based on the analysis of the mean-square displacement. The approach presented here also gives direct access to the uncertainty on the estimation of the diffusivity and predicts the number of steps of the trajectory necessary to achieve any desired precision. Its robustness with respect to noise on the position of the biomolecule is also investigated.

Adaptive coarse-grained Monte Carlo simulation of reaction and diffusion dynamics in heterogeneous plasma membranes

Background

An adaptive coarse-grained (kinetic) Monte Carlo (ACGMC) simulation framework is applied to reaction and diffusion dynamics in inhomogeneous domains. The presented model is relevant to the diffusion and dimerization dynamics of epidermal growth factor receptor (EGFR) in the presence of plasma membrane heterogeneity and specifically receptor clustering. We perform simulations representing EGFR cluster dissipation in heterogeneous plasma membranes consisting of higher density clusters of receptors surrounded by low population areas using the ACGMC method. We further investigate the effect of key parameters on the cluster lifetime.

Results

Coarse-graining of dimerization, rather than of diffusion, may lead to computational error. It is shown that the ACGMC method is an effective technique to minimize error in diffusion-reaction processes and is superior to the microscopic kinetic Monte Carlo simulation in terms of computational cost while retaining accuracy. The low computational cost enables sensitivity analysis calculations. Sensitivity analysis indicates that it may be possible to retain clusters of receptors over the time scale of minutes under suitable conditions and the cluster lifetime may depend on both receptor density and cluster size.

Conclusions

The ACGMC method is an ideal platform to resolve large length and time scales in heterogeneous biological systems well beyond the plasma membrane and the EGFR system studied here. Our results demonstrate that cluster size must be considered in conjunction with receptor density, as they synergistically affect EGFR cluster lifetime. Further, the cluster lifetime being of the order of several seconds suggests that any mechanisms responsible for EGFR aggregation must operate on shorter timescales (at most a fraction of a second), to overcome dissipation and produce stable clusters observed experimentally.

Direct observation and quantitative analysis of Lck exchange between plasma membrane and cytosol in living T cells

Palmitoylation represents a common motif for anchorage of cytosolic proteins to the plasma membrane. Being reversible, it allows for controlled exchange between cytosolic and plasma membrane-bound subpopulations. In this study, we present a live cell single molecule approach for quantifying the exchange kinetics of plasma membrane and cytosolic populations of fluorescently labeled Lck, the key Src family kinase involved in early T cell signaling. Total internal reflection (TIR) fluorescence microscopy was employed for confining the analysis to membrane-proximal molecules. Upon photobleaching Lck-YFP in TIR configuration, fluorescence recovery proceeds first via the cytosol outside of the evanescent field, so that in the early phase fluorescence signal arises predominantly from membrane-proximal cytosolic Lck. The diffusion constant of each molecule allowed us to distinguish whether the molecule has already associated with the plasma membrane or was still freely diffusing in the cytosol. From the number of molecules that inserted during the recovery time we quantified the insertion kinetics: on average, membrane-proximal molecules within the evanescent field needed approximately 400 ms to be inserted. The average lifetime of Lck in the plasma membrane was estimated at 50 s; together with the mobility of 0.26 microm(2)/s this provides sufficient time to explore the surface of the whole T cell before dissociation into the cytosol. Experiments on palmitoylation-deficient Lck mutants yielded similar on-rates, but substantially increased off-rates. We discuss our findings based on a model for the plasma membrane association and dissociation kinetics of Lck, which accounts for reversible palmitoylation on cysteine 3 and 5.

Spatially distributed cell signalling

Emerging evidence indicates that complex spatial gradients and (micro)domains of signalling activities arise from distinct cellular localization of opposing enzymes, such as a kinase and phosphatase, in signal transduction cascades. Often, an interacting, active form of a target protein has a lower diffusivity than an inactive form, and this leads to spatial gradients of the protein abundance in the cytoplasm. A spatially distributed signalling cascade can create step-like activation profiles, which decay at successive distances from the cell surface, assigning digital positional information to different regions in the cell. Feedback and feedforward network motifs control activity patterns, allowing signalling networks to serve as cellular devices for spatial computations.

A bird's eye view tracking slow nanometer-scale movements of single molecular nano-assemblies

Recent improvements in methods of single-particle fluorescence tracking have permitted detailed studies of molecular motion on the nanometer scale. In a quest to introduce these tools to the burgeoning field of DNA nanotechnology, we have exploited fluorescence imaging with one-nanometer accuracy (FIONA) and single-molecule high-resolution colocalization (SHREC) to monitor the diffusive behavior of synthetic molecular walkers, dubbed "spiders," at the single-molecule level. Here we discuss the imaging methods used, results from tracking individual spiders on pseudo-one-dimensional surfaces, and some of the unique experimental challenges presented by the low velocities (approximately 3 nm/min) of these nanowalkers. These experiments demonstrate the promise of fluorescent particle tracking as a tool for the detailed characterization of synthetic molecular nanosystems at the single-molecule level.

Motion detection for subcellular structure trafficking

A detailed understanding of subcellular structure motility is critical to understanding how cells regulate the delivery of specific proteins from the site of synthesis to the site of action. Diverse modalities have been observed for subcellular dynamics, such as directional movement, random movement, tethered movement, object appearing, and disappearing. Motion modality detection is important for efficient subcelluar structure tracking and population study. In this paper, we present a new technique, called "divergence filter," for detecting subcellular structure motion modalities. The plausibility of the efficient technique was applied to caveolar membrane trafficking sequences obtained using confocal microscopy.

Single-particle tracking methods for the study of membrane receptors dynamics

Single-particle tracking (SPT) applications have been growing rapidly in the field of cell biology, and in particular in neurobiology, as a means of unravelling the involvement of diffusion dynamics of neurotransmitter receptors and other synaptic proteins in the regulation of neuronal activity. Suitable probes and technological improvements make SPT more accessible than it used to be and open up broad applications in cellular biology. In this technical highlight, we give an overview of the experimental approach in SPT. The concepts and results in neurobiology have already been the object of detailed reviews. Here, we focus on a qualitative description of the implementation of SPT, from molecule labelling to acquisition, data treatment and analysis of protein diffusion properties. Constraints, limitations and future developments are discussed.

Time series analysis of particle tracking data for molecular motion on the cell membrane

Biophysicists use single particle tracking (SPT) methods to probe the dynamic behavior of individual proteins and lipids in cell membranes. The mean squared displacement (MSD) has proven to be a powerful tool for analyzing the data and drawing conclusions about membrane organization, including features like lipid rafts, protein islands, and confinement zones defined by cytoskeletal barriers. Here, we implement time series analysis as a new analytic tool to analyze further the motion of membrane proteins. The experimental data track the motion of 40 nm gold particles bound to Class I major histocompatibility complex (MHCI) molecules on the membranes of mouse hepatoma cells. Our first novel result is that the tracks are significantly autocorrelated. Because of this, we developed linear autoregressive models to elucidate the autocorrelations. Estimates of the signal to noise ratio for the models show that the autocorrelated part of the motion is significant. Next, we fit the probability distributions of jump sizes with four different models. The first model is a general Weibull distribution that shows that the motion is characterized by an excess of short jumps as compared to a normal random walk. We also fit the data with a chi distribution which provides a natural estimate of the dimension d of the space in which a random walk is occurring. For the biological data, the estimates satisfy 1 < d < 2, implying that particle motion is not confined to a line, but also does not occur freely in the plane. The dimension gives a quantitative estimate of the amount of nanometer scale obstruction met by a diffusing molecule. We introduce a new distribution and use the generalized extreme value distribution to show that the biological data also have an excess of long jumps as compared to normal diffusion. These fits provide novel estimates of the microscopic diffusion constant. Previous MSD analyses of SPT data have provided evidence for nanometer-scale confinement zones that restrict lateral diffusion, supporting the notion that plasma membrane organization is highly structured. Our demonstration that membrane protein motion is autocorrelated and is characterized by an excess of both short and long jumps reinforces the concept that the membrane environment is heterogeneous and dynamic. Autocorrelation analysis and modeling of the jump distributions are powerful new techniques for the analysis of SPT data and the development of more refined models of membrane organization. The time series analysis also provides several methods of estimating the diffusion constant in addition to the constant provided by the mean squared displacement. The mean squared displacement for most of the biological data shows a power law behavior rather the linear behavior of Brownian motion. In this case, we introduce the notion of an instantaneous diffusion constant. All of the diffusion constants show a strong consistency for most of the biological data.

Coupled stochastic spatial and non-spatial simulations of ErbB1 signaling pathways demonstrate the importance of spatial organization in signal transduction

Background

The ErbB family of receptors activates intracellular signaling pathways that control cellular proliferation, growth, differentiation and apoptosis. Given these central roles, it is not surprising that overexpression of the ErbB receptors is often associated with carcinogenesis. Therefore, extensive laboratory studies have been devoted to understanding the signaling events associated with ErbB activation.

Methodology/Principal Findings

Systems biology has contributed significantly to our current understanding of ErbB signaling networks. However, although computational models have grown in complexity over the years, little work has been done to consider the spatial-temporal dynamics of receptor interactions and to evaluate how spatial organization of membrane receptors influences signaling transduction. Herein, we explore the impact of spatial organization of the epidermal growth factor receptor (ErbB1/EGFR) on the initiation of downstream signaling. We describe the development of an algorithm that couples a spatial stochastic model of membrane receptors with a nonspatial stochastic model of the reactions and interactions in the cytosol. This novel algorithm provides a computationally efficient method to evaluate the effects of spatial heterogeneity on the coupling of receptors to cytosolic signaling partners.

Conclusions/Significance

Mathematical models of signal transduction rarely consider the contributions of spatial organization due to high computational costs. A hybrid stochastic approach simplifies analyses of the spatio-temporal aspects of cell signaling and, as an example, demonstrates that receptor clustering contributes significantly to the efficiency of signal propagation from ligand-engaged growth factor receptors.

Elucidating anomalous protein diffusion in living cells with fluorescence correlation spectroscopy-facts and pitfalls

Anomalous protein diffusion has been frequently observed in intracellular fluids and on membranes of living cells. Indeed, a large variety of specimen, from bacteriae to mammalian cells, and several non-invasive measurement techniques, e.g. fluorescence correlation spectroscopy, have revealed that the mean square displacement (MSD) of proteins in vivo is often characterized by an anomalous power-law increase mean value of tau(t)(2) mean value of ~ t(alpha) with 0.5 < alpha </= 0.8. Here, we review these results with a particular focus on fluorescence correlation spectroscopy, and we report on possible causes of variations of the anomaly degree alpha. Moreover, we highlight generic consequences of anomalous diffusion that are likely to play an important role in the cellular context.

Imaging of the diffusion of single band 3 molecules on normal and mutant erythrocytes

Membrane-spanning proteins may interact with a variety of other integral and peripheral membrane proteins via a diversity of protein-protein interactions. Not surprisingly, defects or mutations in any one of these interacting components can impact the physical and biological properties on the entire complex. Here we use quantum dots to image the diffusion of individual band 3 molecules in the plasma membranes of intact human erythrocytes from healthy volunteers and patients with defects in one of their membrane components, leading to well-known red cell pathologies (hereditary spherocytosis, hereditary elliptocytosis, hereditary hydrocytosis, Southeast Asian ovalocytosis, and hereditary pyropoikilocytosis). After characterizing the motile properties of the major subpopulations of band 3 in intact normal erythrocytes, we demonstrate that the properties of these subpopulations of band 3 change significantly in diseased cells, as evidenced by changes in the microscopic and macroscopic diffusion coefficients of band 3 and in the compartment sizes in which the different band 3 populations can diffuse. Because the above membrane abnormalities largely arise from defects in other membrane components (eg, spectrin, ankyrin), these data suggest that single particle tracking of band 3 might constitute a useful tool for characterizing the general structural integrity of the human erythrocyte membrane.

Particle tracking single protein-functionalized quantum dot diffusion and binding at silica surfaces

We evaluate commercial QD585 and QD605 streptavidin-functionalized quantum dots (QDs) for single-particle tracking microscopy at surfaces using total internal reflectance fluorescence and measure single QD diffusion and nonspecific binding at silica surfaces in static and flow conditions. The QD diffusion coefficient on smooth, near-ideal, highly hydroxylated silica surfaces is near bulk-solution diffusivity, as expected for repulsive surfaces, but many QD trajectories on rougher, less-than-ideal surfaces or regions display transient adsorptions. We attribute the binding to defect sites or adsorbates, possibly in conjunction with protein conformation changes, and estimate binding energies from the transient adsorption lifetimes. We also assess QD parameters relevant to tracking, including hydrodynamic radius, charge state, signal levels, blinking reduction with reducing solutions, and photoinduced blueing and bleaching.

Dynamic partitioning of a glycosyl-phosphatidylinositol-anchored protein in glycosphingolipid-rich microdomains imaged by single-quantum dot tracking

Recent experimental developments have led to a revision of the classical fluid mosaic model proposed by Singer and Nicholson more than 35 years ago. In particular, it is now well established that lipids and proteins diffuse heterogeneously in cell plasma membranes. Their complex motion patterns reflect the dynamic structure and composition of the membrane itself, as well as the presence of the underlying cytoskeleton scaffold and that of the extracellular matrix. How the structural organization of plasma membranes influences the diffusion of individual proteins remains a challenging, yet central, question for cell signaling and its regulation. Here we have developed a raft-associated glycosyl-phosphatidyl-inositol-anchored avidin test probe (Av-GPI), whose diffusion patterns indirectly report on the structure and dynamics of putative raft microdomains in the membrane of HeLa cells. Labeling with quantum dots (qdots) allowed high-resolution and long-term tracking of individual Av-GPI and the classification of their various diffusive behaviors. Using dual-color total internal reflection fluorescence (TIRF) microscopy, we studied the correlation between the diffusion of individual Av-GPI and the location of glycosphingolipid GM1-rich microdomains and caveolae. We show that Av-GPI exhibit a fast and a slow diffusion regime in different membrane regions, and that slowing down of their diffusion is correlated with entry in GM1-rich microdomains located in close proximity to, but distinct, from caveolae. We further show that Av-GPI dynamically partition in and out of these microdomains in a cholesterol-dependent manner. Our results provide direct evidence that cholesterol-/sphingolipid-rich microdomains can compartmentalize the diffusion of GPI-anchored proteins in living cells and that the dynamic partitioning raft model appropriately describes the diffusive behavior of some raft-associated proteins across the plasma membrane.

Diffusion in a fluid membrane with a flexible cortical cytoskeleton

We calculate the influence of a flexible network of long-chain proteins, which is anchored to a fluid membrane, on protein diffusion in this membrane. This is a model for the cortical cytoskeleton and the lipid bilayer of the red blood cell, which we apply to predict the influence of the cytoskeleton on the diffusion coefficient of a mobile band 3 protein. Using the pressure field that the cytoskeleton exerts on the membrane, from the steric repulsion between the diffusing protein and the cytoskeletal filaments, we define a potential landscape for the diffusion within the bilayer. We study the changes to the diffusion coefficient on removal of one type of anchor proteins, e.g., in several hemolytic anemias, as well as for isotropic and anisotropic stretching of the cytoskeleton. We predict an overall increase of the diffusion for a smaller number of anchor proteins and increased diffusion for anisotropic stretching in the direction of the stretch, because of the decrease in the spatial frequency as well as in the height of the potential barriers.

Anomalous diffusion induced by cristae geometry in the inner mitochondrial membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.

Going beyond 2D: Following membrane diffusion and topography in the IgE-Fc[Epsilon]RI system using 3-dimensional tracking microscopy

The ability to follow and observe single molecules as they function in live cells represents a major milestone for molecular-cellular biology. Here we present a tracking microscope that is able to track quantum dots in three dimensions and simultaneously record time-resolved emission statistics from a single dot. This innovative microscopy approach is based on four spatial filters and closed loop feedback to constantly keep a single quantum dot in the focal spot. Using this microscope, we demonstrate the ability to follow quantum dot labeled IgE antibodies bound to FcεRI membrane receptors in live RBL-2H3 cells. The results are consistent with prior studies of two dimensional membrane diffusion (Andrews et al., Nat. Cell Biol., 10, 955, 2008). In addition, the microscope captures motion in the axial (Z) direction, which permits tracking of diffusing receptors relative to the "hills and valleys" of the dynamically changing membrane landscape. This approach is uniquely capable of following single molecule dynamics on live cells with three dimensional spatial resolution.

Dynamics of reaction-diffusion systems in a subdiffusive regime

In this paper, we examine the dynamics of reaction-diffusion systems with fractional time derivatives. It is shown that in these conditions diffusion is anomalous, in the sense that the mean-square displacement r2 approximately tgamma, where gamma<1, a situation known as subdiffusion. We study the conditions for the appearance of a diffusion-driven instability and show that the restrictive conditions for a Turing instability are relaxed. This implies that systems whose kinetics are not of the activator-inhibitor kind can have a Turing instability and a modulated final state. We demonstrate our results with numerical calculations in two dimensions using a generic Turing model.

Inferring maps of forces inside cell membrane microdomains

Mapping of the forces on biomolecules in cell membranes has spurred the development of effective labels, e.g., organic fluorophores and nanoparticles, to track trajectories of single biomolecules. Standard methods use particular statistics, namely the mean square displacement, to analyze the underlying dynamics. Here, we introduce general inference methods to fully exploit information in the experimental trajectories, providing sharp estimates of the forces and the diffusion coefficients in membrane microdomains. Rapid and reliable convergence of the inference scheme is demonstrated on trajectories generated numerically. The method is then applied to infer forces and potentials acting on the receptor of the toxin labeled by lanthanide-ion nanoparticles. Our scheme is applicable to any labeled biomolecule and results show its general relevance for membrane compartmentation.

Reversible binding and rapid diffusion of proteins in complex with inositol lipids serves to coordinate free movement with spatial information

Polyphosphoinositol lipids convey spatial information partly by their interactions with cellular proteins within defined domains. However, these interactions are prevented when the lipids' head groups are masked by the recruitment of cytosolic effector proteins, whereas these effectors must also have sufficient mobility to maximize functional interactions. To investigate quantitatively how these conflicting functional needs are optimized, we used different fluorescence recovery after photobleaching techniques to investigate inositol lipid–effector protein kinetics in terms of the real-time dissociation from, and diffusion within, the plasma membrane. We find that the protein–lipid complexes retain a relatively rapid (∼0.1–1 µm²/s) diffusion coefficient in the membrane, likely dominated by protein–protein interactions, but the limited time scale (seconds) of these complexes, dictated principally by lipid–protein interactions, limits their range of action to a few microns. Moreover, our data reveal that GAP1^IP4BP, a protein that binds PtdIns(4,5)P₂ and PtdIns(3,4,5)P₃ in vitro with similar affinity, is able to “read” PtdIns(3,4,5)P₃ signals in terms of an elongated residence time at the membrane.

Collision coupling, crosstalk, and compartmentalization in G-protein coupled receptor systems: can a single model explain disparate results?

The collision coupling model describes interactions between receptors and G-proteins as first requiring the molecules to find each other by diffusion. A variety of experimental data on G-protein activation have been interpreted as suggesting (or not) the compartmentalization of receptors and/or G-proteins in addition to a collision coupling mechanism. In this work, we use a mathematical model of G-protein activation via collision coupling but without compartmentalization to demonstrate that these disparate observations do not imply the existence of such compartments. In experiments with GTP analogs (commonly GTPgammaS), the extent of G-protein activation is predicted to be a function of both receptor number and the rate of GTP analog hydrolysis. The sensitivity of G-protein activation to receptor number is shown to be dependent upon the assay used, with the sensitivity of phosphate production assays (GTPase) >GTPgammaS-binding assays >cAMP inhibition assays. Finally, the amount of competition or crosstalk between receptor species activating the same type of G-proteins is predicted to depend on receptor and G-protein number, but in some (common) experimental regimes this dependence is expected to be minimal. Taken together, these observations suggest that the collision coupling model, without compartments of receptors and/or G-proteins, is sufficient to explain a variety of observations in literature data.

Design of quantum dot-conjugated lipids for long-term, high-speed tracking experiments on cell surfaces

The current study reports the facile design of quantum dot (QD)-conjugated lipids and their application to high-speed tracking experiments on cell surfaces. CdSe/ZnS core/shell QDs with two types of hydrophilic coatings, 2-(2-aminoethoxy)ethanol (AEE) and a 60:40 molar mixture of 1,2-dipalmitoyl- sn-glycero-3-phosphocholine and 1,2-dipalmitoyl- sn-glycero-3-phosphoethanolamine- N-[methoxy(polyethylene glycol-2000], are conjugated to sulfhydryl lipids via maleimide reactive groups on the QD surface. Prior to lipid conjugation, the colloidal stability of both types of coated QDs in aqueous solution is confirmed using fluorescence correlation spectroscopy. A sensitive assay based on single lipid tracking experiments on a planar solid-supported phospholipid bilayer is presented that establishes conditions of monovalent conjugation of QDs to lipids. The QD-lipids are then employed as single-molecule tracking probes in plasma membranes of several cell types. Initial tracking experiments at a frame rate of 30 frames/s corroborate that QD-lipids diffuse like dye-labeled lipids in the plasma membrane of COS-7, HEK-293, 3T3, and NRK cells, thus confirming monovalent labeling. Finally, QD-lipids are applied for the first time to high-speed single-molecule imaging by tracking their lateral mobility in the plasma membrane of NRK fibroblasts with up to 1000 frames/s. Our high-speed tracking data, which are in excellent agreement with previous tracking experiments that used larger (40 nm) Au labels, not only push the time resolution in long-time, continuous fluorescence-based single-molecule tracking but also show that highly photostable, photoluminescent nanoprobes of 10 nm size can be employed (AEE-coated QDs). These probes are also attractive because, unlike Au nanoparticles, they facilitate complex multicolor experiments.