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

Versatile analysis of single-molecule tracking data by comprehensive testing against Monte Carlo simulations

We propose here an approach for the analysis of single-molecule trajectories which is based on a comprehensive comparison of an experimental data set with multiple Monte Carlo simulations of the diffusion process. It allows quantitative data analysis, particularly whenever analytical treatment of a model is infeasible. Simulations are performed on a discrete parameter space and compared with the experimental results by a nonparametric statistical test. The method provides a matrix of p-values that assess the probability for having observed the experimental data at each setting of the model parameters. We show the testing approach for three typical situations observed in the cellular plasma membrane: i), free Brownian motion of the tracer, ii), hop diffusion of the tracer in a periodic meshwork of squares, and iii), transient binding of the tracer to slowly diffusing structures. By plotting the p-value as a function of the model parameters, one can easily identify the most consistent parameter settings but also recover mutual dependencies and ambiguities which are difficult to determine by standard fitting routines. Finally, we used the test to reanalyze previous data obtained on the diffusion of the glycosylphosphatidylinositol-protein CD59 in the plasma membrane of the human T24 cell line.

Actin restricts FcepsilonRI diffusion and facilitates antigen-induced receptor immobilization

The actin cytoskeleton has been implicated in restricting diffusion of plasma membrane components. Here, simultaneous observations of quantum dot-labelled FcepsilonRI motion and GFP-tagged actin dynamics provide direct evidence that actin filament bundles define micron-sized domains that confine mobile receptors. Dynamic reorganization of actin structures occurs over seconds, making the location and dimensions of actin-defined domains time-dependent. Multiple FcepsilonRI often maintain extended close proximity without detectable correlated motion, suggesting that they are co-confined within membrane domains. FcepsilonRI signalling is activated by crosslinking with multivalent antigen. We show that receptors become immobilized within seconds of crosslinking. Disruption of the actin cytoskeleton results in delayed immobilization kinetics and increased diffusion of crosslinked clusters. These results implicate actin in membrane partitioning that not only restricts diffusion of membrane proteins, but also dynamically influences their long-range mobility, sequestration and response to ligand binding.

Fluorescence recovery after photobleaching: the case of anomalous diffusion

The method of FRAP (fluorescence recovery after photobleaching), which has been broadly used to measure lateral mobility of fluorescent-labeled molecules in cell membranes, is formulated here in terms of continuous time random walks (CTRWs), which offer both analytical expressions and a scheme for numerical simulations. We propose an approach based on the CTRW and the corresponding fractional diffusion equation (FDE) to analyze FRAP results in the presence of anomalous subdiffusion. The FDE generalizes the simple diffusive picture, which has been applied to FRAP when assuming regular diffusion, to account for subdiffusion. We use a subordination relationship between the solutions of the fractional and normal diffusion equations to fit FRAP recovery curves obtained from CTRW simulations, and compare the fits to the commonly used approach based on the simple diffusion equation with a time dependent diffusion coefficient (TDDC). The CTRW and TDDC describe two different dynamical schemes, and although the CTRW formalism appears to be more complicated, it provides a physical description that underlies anomalous lateral diffusion.

Single-molecule observations of surfactant diffusion at the solution-solid interface

Individual fatty acid molecules adsorbed at the interface between hexadecane and fused silica have been tracked using total internal reflection fluorescence microscopy. Two cooperative diffusive mechanisms are observed: continuous small-scale Brownian motion and occasional large "jumps." The continuous diffusion exhibits evidence of confinement. The effective interfacial diffusion coefficients for each mechanism increase systematically with temperature; an Arrhenius analysis gives an activation barrier of approximately 50 kJ/mol for "jumping" and an upper limit of approximately 10 kJ/mol for confined diffusion.

Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises approximately 20% of brain parenchymal volume and contains cell-cell gaps approximately 50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (alpha), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D(o)/D). Experimental D(o)/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D(o)/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D(o)/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D(o)/D using realistic alpha, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D(o)/D for different solute sizes. Also, the modeling showed unanticipated effects on D(o)/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.

Sizing subcellular organelles and nanoparticles confined within aqueous droplets

This article describes two complementary techniques, single-particle tracking and correlation spectroscopy, for accurately sizing nanoparticles confined within picoliter volume aqueous droplets. Single-particle tracking works well with bright particles that can be continuously illuminated and imaged, and we demonstrated this approach for sizing single fluorescent beads. Fluorescence correlation spectroscopy detects small intensity bursts from particles or molecules diffusing through the confocal probe volume, which works well with dim and rapidly diffusing particles or molecules; we demonstrated FCS for sizing synaptic vesicles confined in aqueous droplets. In combination with recent advances in droplet manipulations and analysis, we anticipate this capability to size single nanoparticles and molecules in free solution will complement existing tools for probing cellular systems, subcellular organelles, and nanoparticles.

Molecular motion in cell membranes: analytic study of fence-hindered random walks

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled mu -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

Diffusion-limited reactions in G-protein activation: unexpected consequences of antagonist and agonist competition

In this work, we ask whether the simultaneous movement of agonist and antagonist among surface receptors (i.e. continually associating and dissociating from individual receptors according to specified kinetics) has any unexpected consequences for G-protein activation and receptor desensitization. A Monte Carlo model framework is used to track the diffusion and reaction of individual receptors, allowing the requirement for receptors and G-proteins or receptors and kinases to find each other by diffusion (collision coupling) to be implemented explicitly. We find that at constant agonist occupancy the effect of an antagonist on both G-protein activation and the ratio of G-protein activation to receptor desensitization can be modulated by varying the antagonist dissociation kinetics. The explanation for this effect is that antagonist dissociation kinetics influence the ability of agonists to access particular receptors and thus reach G-proteins and kinases near those receptors. Relevant parameter ranges for observation of these effects are identified. These results are useful for understanding experimental and therapeutic situations when both agonist and antagonist are present, and in addition may offer new insights into insurmountable antagonism.

High-Resolution Models of Motion of Macromolecules in Cell Membranes

The path of a macromolecule on a cell membrane is modeled by a sum of independent identically distributed random variables. Random variables with simple discrete distribution functions capture some important aspects of the jump or hop diffusion reported from single particle tracking experiments that measure the motion of single molecules on a cell membrane. The detail provided by the distribution function for the random variables is critical for accurate simulations of the motion and interactions of macromolecules on the cell membrane. Additionally, the probability distribution for the random variables is easily estimated from single-particle tracking data. The diffusion constant is given by the second moment of the probability distribution, which agrees with the diffusion constant estimated from the mean-square displacement, and thus represents far less information than the distribution function.

Diffusion of nanoparticles in monolayers is modulated by domain size

Langmuir monolayers are often used as simple models for biological membranes. The possibility to change their composition and phase state in a very controlled manner as well as access to a large observation area makes them a versatile tool for the investigation of membrane-related interactions. Inspired by experiments in our group, we investigate the interaction of single, partially charged nanoparticles with lipid microdomains by Monte Carlo simulations. Condensed domains in inhomogeneous Langmuir monolayers exhibit an electric dipole field interacting attractively with the nanoparticle's dipole moment. With increasing domain size, the resulting electric field changes from single dipole to semi-infinite domain characteristics, significantly influencing the motion of the particle. Small immobile domains (R = 1 microm) confine the movement of the tracer to the boundary of the domain whereas for large domains (R > or = 10 microm) its motion is only temporarily hindered. This suggests a powerful mechanism for controlling diffusive transport in lipid membranes.

Line tension and coalescence in heterogeneous membranes

Membrane inhomogeneity gives rise to a perturbation energy that may be manifested as line tension between regions of different compositions. Here we calculate the perturbation energy of a phase-separated fluid membrane composed of domains embedded in a continuous phase and relate it to the line tension in the system. We find that the effective line tension due to the thickness mismatch between the phases varies nonmonotonically as a function of the domain size and spacing when those decrease below about 20 nm. Although we find that the characteristic time scale for domain coalescence increases with domain size, the coalescence time for domains on the order of 25 to 50 nm may be as long as several days. The time scale for domain coalescence is found, quite surprisingly, to be maximal when the bending and area moduli of the domain and continuous phase are similar and to decrease when one phase is stiffer than the other. Domain stability is also found to vary as a function of spacing; as a result, small domains on the order of 5 nm become unstable and tend to coalesce when the domain-phase area fraction increases above 0.5, whereas larger domains on the order of 50 nm become unstable only when the area fraction increases above 0.8.

Microscopic simulation of membrane molecule diffusion on corralled membrane surfaces

The current understanding of how receptors diffuse and cluster in the plasma membrane is limited. Data from single-particle tracking and laser tweezer experiments have suggested that membrane molecule diffusion is affected by the presence of barriers dividing the membrane into corrals. Here, we have developed a stochastic spatial model to simulate the effect of corrals on the diffusion of molecules in the plasma membrane. The results of this simulation confirm that a fence barrier (the ratio of the transition probability for diffusion across a boundary to that within a corral) on the order of 10(3)-10(4) recreates the experimentally measured difference in diffusivity between artificial and natural plasma membranes. An expression for the macroscopic diffusivity of receptors on corralled membranes is derived to analyze the effects of the corral parameters on diffusion rate. We also examine whether the lattice model is an appropriate description of the plasma membrane and look at three different sets of boundary conditions that describe diffusion over the barriers and whether diffusion events on the plasma membrane may occur with a physically relevant length scale. Finally, we show that to observe anomalous (two-timescale) diffusion, one needs high temporal (microsecond) resolution along with sufficiently long (more than milliseconds) trajectories.

Quantitative characterization of changes in dynamical behavior for single-particle tracking studies

Single-particle tracking experiments have been used widely to study the heterogeneity of a sample. Segments with dissimilar diffusive behaviors are associated with different intermediate states, usually by visual inspection of the tracking trace. A likelihood-based, systematic approach is presented to remove this incertitude. Maximum likelihood estimators are derived for the determination of diffusion coefficients. A likelihood ratio test is applied to the localization of the changes in them. Simulations suggest that the proposed procedure is statistically robust and is able to quantitatively recover time-dependent changes in diffusion coefficients even in the presence of large measurement noise.

Nanopipette delivery of individual molecules to cellular compartments for single-molecule fluorescence tracking

We have developed a new method, using a nanopipette, for controlled voltage-driven delivery of individual fluorescently labeled probe molecules to the plasma membrane which we used for single-molecule fluorescence tracking (SMT). The advantages of the method are 1), application of the probe to predefined regions on the membrane; 2), release of only one or a few molecules onto the cell surface; 3), when combined with total internal reflection fluorescence microscopy, very low background due to unbound molecules; and 4), the ability to first optimize the experiment and then repeat it on the same cell. We validated the method by performing an SMT study of the diffusion of individual membrane glycoproteins labeled with Atto 647-wheat germ agglutin in different surface domains of boar spermatozoa. We found little deviation from Brownian diffusion with a mean diffusion coefficient of 0.79 +/- 0.04 microm(2)/s in the acrosomal region and 0.10 +/- 0.02 microm(2)/s in the postacrosomal region; this difference probably reflects different membrane structures. We also showed that we can analyze diffusional properties of different subregions of the cell membrane and probe for the presence of diffusion barriers. It should be straightforward to extend this new method to other probes and cells, and it can be used as a new tool to investigate the cell membrane.

Chemomechanical mapping of ligand-receptor binding kinetics on cells

The binding kinetics between cell surface receptors and extracellular biomolecules is critical to all intracellular and intercellular activity. Modeling and prediction of receptor-mediated cell functions are facilitated by measurement of the binding properties on whole cells, ideally indicating the subcellular locations or cytoskeletal associations that may affect the function of bound receptors. This dual need is particularly acute vis à vis ligand engineering and clinical applications of antibodies to neutralize pathological processes. Here, we map individual receptors and determine whole-cell binding kinetics by means of functionalized force imaging, enabled by scanning probe microscopy and molecular force spectroscopy of intact cells with biomolecule-conjugated mechanical probes. We quantify the number, distribution, and association/dissociation rate constants of vascular endothelial growth factor receptor-2 with respect to a monoclonal antibody on both living and fixed human microvascular endothelial cells. This general approach to direct receptor imaging simultaneously quantifies both the binding kinetics and the nonuniform distribution of these receptors with respect to the underlying cytoskeleton, providing spatiotemporal visualization of cell surface dynamics that regulate receptor-mediated behavior.

Single molecule techniques for the study of membrane proteins

Single molecule techniques promise novel information about the properties and behavior of individual particles, thus enabling access to molecular heterogeneities in biological systems. Their recent developments to accommodate membrane studies have significantly deepened the understanding of membrane proteins. In this short review, we will describe the basics of the three most common single-molecule techniques used on membrane proteins: fluorescence correlation spectroscopy, single particle tracking, and atomic force microscopy. We will discuss the most relevant findings made during the recent years and their contribution to the membrane protein field.

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.

Determination of membrane domain size by fluorescence resonance energy transfer: effects of domain polydispersity and packing

Fluorescence resonance energy transfer (FRET) is sensitive to lateral heterogeneity in multicomponent membranes. Recently, we developed a model that enables the extraction of domain size from time-resolved FRET data, and here we examine the effects of domain polydispersity and spatial ordering on the accuracy of domain size determination. The model is applied to Monte Carlo calculations of membranes containing polydisperse domains, either randomly or hexagonally packed for three probe-partitioning schemes and three domain surface coverages. Statistical analysis of the model fitting results supports the conclusion that time-resolved FRET is a robust and precise technique for determining the size of small membrane domains (</=4 times the Förster distance, approximately 20 nm, of the FRET pair), regardless of domain polydispersity and packing. The confidence estimates, presented here in dimensionless domain diameters (independent of the specific FRET pairs), provide a universal tool for domain size estimation in systems containing membrane-bound fluorophores.

Single particle tracking of complex diffusion in membranes: simulation and detection of barrier, raft, and interaction phenomena

Single particle tracking is being used increasingly to follow the motion of membrane-associated receptors and lipids. Anomalous and complex diffusive behaviors are generally found in cell membranes. We developed computational algorithms to simulate particle trajectories and to detect complex diffusive behaviors in two dimensions, including confined and convective diffusion, intramembrane barrier and raft phenomena, and interparticle interactions. Little useful information regarding barrier, raft, and interaction effects were provided by standard computational procedures for identification of anomalous diffusion, including analysis of mean squared displacement, distributions of diffusion rates and range, and time evolution of particle position. New algorithms were developed and optimized to detect complex diffusive behaviors from simulated single particle trajectories. A barrier detection algorithm was developed on the basis of spatial averaging of particle positions in trajectories. A raft detection algorithm utilized spatially resolved diffusion coefficients and particle density functions. An interaction algorithm utilized interparticle distance distributions. The algorithms developed here are applicable to identify biologically important diffusive phenomena in cell membranes.

(Un)confined diffusion of CD59 in the plasma membrane determined by high-resolution single molecule microscopy

There has been emerging interest whether plasma membrane constituents are moving according to free Brownian motion or hop diffusion. In the latter model, lipids, lipid-anchored proteins, and transmembrane proteins would be transiently confined to periodic corrals in the cell membrane, which are structured by the underlying membrane skeleton. Because this model is based exclusively on results provided by one experimental strategy--high-resolution single particle tracking--we attempted in this study to confirm or amend it using a complementary technique. We developed a novel strategy that employs single molecule fluorescence microscopy to detect confinements to free diffusion of CD59--a GPI-anchored protein--in the plasma membrane of living T24 (ECV) cells. With this method, minimum invasive labeling via fluorescent Fab fragments was sufficient to measure the lateral motion of individual protein molecules on a millisecond timescale, yielding a positional accuracy down to 22 nm. Although no hop diffusion was directly observable, based on a full analytical description our results provide upper boundaries for confinement size and strength.

Cytoskeleton dynamics: fluctuations within the network

Out-of-equilibrium systems, such as the dynamics of a living cytoskeleton (CSK), are inherently noisy with fluctuations arising from the stochastic nature of the underlying biochemical and molecular events. Recently, such fluctuations within the cell were characterized by observing spontaneous nano-scale motions of an RGD-coated microbead bound to the cell surface [Bursac et al., Nat. Mater. 4 (2005) 557-561]. While these reported anomalous bead motions represent a molecular level reorganization (remodeling) of microstructures in contact with the bead, a precise nature of these cytoskeletal constituents and forces that drive their remodeling dynamics are largely unclear. Here, we focused upon spontaneous motions of an RGD-coated bead and, in particular, assessed to what extent these motions are attributable to (i) bulk cell movement (cell crawling), (ii) dynamics of focal adhesions, (iii) dynamics of lipid membrane, and/or (iv) dynamics of the underlying actin CSK driven by myosin motors.

Multiple association states between glycine receptors and gephyrin identified by SPT analysis

The scaffolding protein gephyrin is known to anchor glycine receptors (GlyR) at synapses and to participate in the dynamic equilibrium between synaptic and extrasynaptic GlyR in the neuronal membrane. Here we investigated the properties of this interaction in cells cotransfected with YFP-tagged gephyrin and GlyR subunits possessing an extracellular myc-tag. In HeLa cells and young neurons, single particle tracking was used to follow in real time individual GlyR, labeled with quantum dots, traveling into and out of gephyrin clusters. Analysis of the diffusion properties of two GlyR subunit types--able or unable to bind gephyrin--gave access to the association states of GlyR with its scaffolding protein. Our results indicated that an important portion of GlyR could be linked to a few molecules of gephyrin outside gephyrin clusters. This emphasizes the role of scaffolding proteins in the extrasynaptic membrane and supports the implication of gephyrin-gephyrin interactions in the stabilization of GlyR at synapses. The kinetic parameters controlling the equilibrium between GlyR inside and outside clusters were also characterized. Within clusters, we identified two subpopulations of GlyR with distinct degrees of stabilization between receptors and scaffolding proteins.

Towards a Detailed Understanding of Bacterial Metabolism—Spectroscopic Characterization ofStaphylococcus Epidermidis

Bacteria are a major cause of infection. To fight disease and growing resistance, research interest is focused on understanding bacterial metabolism. For a detailed evaluation of the involved mechanisms, a precise knowledge of the molecular composition of the bacteria is required. In this article, various vibrational spectroscopic techniques are applied to comprehensively characterize, on a molecular level, bacteria of the strain Staphylococcus epidermidis, an opportunistic pathogen which has evolved to become a major cause of nosocomial infections. IR absorption spectroscopy reflects the overall chemical composition of the cells, with major focus on the protein vibrations. Smaller sample volumes-down to a single cell-are sufficient to probe the overall chemical composition by means of micro-Raman spectroscopy. The nucleic-acid and aromatic amino-acid moieties are almost exclusively explored by UV resonance Raman spectroscopy. In combination with statistical evaluation methods [hierarchical cluster analysis (HCA), principal component analysis (PCA), linear discriminant analysis (LDA)], the protein and nucleic-acid components that change during the different bacterial growth phases can be identified from the in vivo vibrational spectra. Furthermore, tip-enhanced Raman spectroscopy (TERS) provides insight into the surface structures and follows the dynamics of the polysaccharide and peptide components on the bacterial cells with a spatial resolution below the diffraction limit. This might open new ways for the elucidation of host-bacteria and drug-bacteria interactions.

Single molecule studies of molecular diffusion in cellular membranes: Determining membrane structure

Since the advent of single particle/molecule microscopies, researchers have applied these techniques to understanding the fluid membranes of cells. By observing diffusion of membrane proteins and lipids in live cell membranes of eukaryotic cells, it has been found that membranes contain a mosaic of fluid compartments. Such structure may be instrumental in understanding key characteristics of the membrane. Recent single molecule observations on prokaryotic cell membranes will also be discussed.

Molecular anatomy of a trafficking organelle

Membrane traffic in eukaryotic cells involves transport of vesicles that bud from a donor compartment and fuse with an acceptor compartment. Common principles of budding and fusion have emerged, and many of the proteins involved in these events are now known. However, a detailed picture of an entire trafficking organelle is not yet available. Using synaptic vesicles as a model, we have now determined the protein and lipid composition; measured vesicle size, density, and mass; calculated the average protein and lipid mass per vesicle; and determined the copy number of more than a dozen major constituents. A model has been constructed that integrates all quantitative data and includes structural models of abundant proteins. Synaptic vesicles are dominated by proteins, possess a surprising diversity of trafficking proteins, and, with the exception of the V-ATPase that is present in only one to two copies, contain numerous copies of proteins essential for membrane traffic and neurotransmitter uptake.

Sources of anomalous diffusion on cell membranes: a Monte Carlo study

A stochastic random walk model of protein molecule diffusion on a cell membrane was used to investigate the fundamental causes of anomalous diffusion in two-dimensional biological media. Three different interactions were considered: collisions with fixed obstacles, picket fence posts, and capture by, or exclusion from, lipid rafts. If motion is impeded by randomly placed, fixed obstacles, we find that diffusion can be highly anomalous, in agreement with previous studies. In contrast, collision with picket fence posts has a negligible effect on the anomalous exponent at realistic picket fence parameters. The effects of lipid rafts are more complex. If proteins partition into lipid rafts there is a small to moderate effect on the anomalous exponent, whereas if proteins are excluded from rafts there is a large effect on the anomalous exponent. In combination, these mechanisms can explain the level of anomaly in experimentally observed membrane diffusion, suggesting that anomalous diffusion is caused by multiple mechanisms whose effects are approximately additive. Finally, we show that the long-range diffusion rate, D(macro), estimated from fluorescence recovery after photobleaching studies, can be much smaller than D(micro), the small-scale diffusion rate, and is highly sensitive to obstacle densities and other impeding structures.

Mitochondrial dynamics in chondrocytes and their connection to the mechanical properties of the cytoplasm

BACKGROUND

The motion and redistribution of intracellular organelles is a fundamental process in cells. Organelle motion is a complex phenomenon that depends on a large number of variables including the shape of the organelle, the type of motors with which the organelles are associated, and the mechanical properties of the cytoplasm. This paper presents a study that characterizes the diffusive motion of mitochondria in chondrocytes seeded in agarose constructs and what this implies about the mechanical properties of the cytoplasm.

METHOD OF APPROACH

Images showing mitochondrial motion in individual cells at 30 s intervals for 15 min were captured with a confocal microscope. Digital image correlation was used to quantify the motion of the mitochondria, and the mean square displacement (MSD) was calculated. Statistical tools for testing whether the characteristic motion of mitochondria varied throughout the cell were developed. Calculations based on statistical mechanics were used to establish connections between the measured MSDs and the mechanical nature of the cytoplasm.

RESULTS

The average MSD of the mitochondria varied with time according to a power law with the power term greater than 1, indicating that mitochondrial motion can be viewed as a combination of diffusion and directional motion. Statistical analysis revealed that the motion of the mitochondria was not uniform throughout the cell, and that the diffusion coefficient may vary by over 50%, indicating intracellular heterogeneity. High correlations were found between movements of mitochondria when they were less than 2 microm apart. The correlation is probably due to viscoelastic properties of the cytoplasm. Theoretical analysis based on statistical mechanics suggests that directed diffusion can only occur in a material that behaves like a fluid on large time scales.

CONCLUSIONS

The study shows that mitochondria in different regions of the cell experience different characteristic motions. This suggests that the cytoplasm is a heterogeneous viscoelastic material. The study provides new insight into the motion of mitochondria in chondrocytes and its connection with the mechanical properties of the cytoplasm.

Particle image correlation spectroscopy (PICS): retrieving nanometer-scale correlations from high-density single-molecule position data

A new data analysis tool that resolves correlations on the nanometer length and millisecond timescale is derived. This tool, adapted from methods of spatiotemporal image correlation spectroscopy, exploits the high positional accuracy of single-particle tracking. While conventional tracking methods break down if multiple particle trajectories intersect, our method works in principle for arbitrarily large molecule densities and diffusion coefficients as long as individual molecules can be identified. The method is computationally cheap and robust and requires no a priori knowledge about the dynamical coefficients, as opposed to other methods. We demonstrate the validity of the method by Monte Carlo simulations and by application to single-molecule tracking data of membrane-anchored proteins in live cells. The results faithfully reproduce those obtained by conventional tracking. Upon activation, a fraction of the small GTPase H-Ras is confined to domains of <200 nm diameter, which further substantiates the prediction that membrane organization is a determinant in cellular signaling.

Single nanoparticle photothermal tracking (SNaPT) of 5-nm gold beads in live cells

Tracking individual nano-objects in live cells during arbitrary long times is a ubiquitous need in modern biology. We present here a method for tracking individual 5-nm gold nanoparticles on live cells. It relies on the photothermal effect and the detection of the Laser Induced Scattering around a NanoAbsorber (LISNA). The key point for recording trajectories at video rate is the use of a triangulation procedure. The effectiveness of the method is tested against single fluorescent molecule tracking in live COS7 cells on subsecond timescales. We further demonstrate recordings for several minutes of AMPA receptors trajectories on the plasma membrane of live neurons. Single Nanoparticle Photothermal Tracking has the unique potential to record arbitrary long trajectory of membrane proteins using nonfluorescent nanometer-sized labels.

Subdiffusion and long-time anticorrelations in a stochastic single file

The subdiffusion of a stochastic single file is interpreted as a jumping process. Contrary to the current continuous time random walk models, its statistics is characterized by finite averages of the jumping times and square displacements. Subdiffusion is then related to a persistent anticorrelation of the jump sequences. In continuous time representation, this corresponds to negative power-law velocity autocorrelations, attributable to the restricted geometry of the file diffusion.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Dynamics and diffusion in photosynthetic membranes from rhodospirillum photometricum

Photosynthetic organisms drive their metabolism by converting light energy into an electrochemical gradient with high efficiency. This conversion depends on the diffusion of quinones within the membrane. In purple photosynthetic bacteria, quinones reduced by the reaction center (RC) diffuse to the cytochrome bc(1) complex and then return once reoxidized to the RC. In Rhodospirillum photometricum the RC-containing core complexes are found in a disordered molecular environment, with fixed light-harvesting complex/core complex ratio but without a fixed architecture, whereas additional light-harvesting complexes synthesized under low-light conditions pack into large paracrystalline antenna domains. Here, we have analyzed, using time-lapse atomic force microscopy, the dynamics of the protein complexes in the different membrane domains and find that the disordered regions are dynamic whereas ordered antennae domains are static. Based on our observations we propose, and analyze using Monte Carlo simulations, a model for quinone diffusion in photosynthetic membranes. We show that the formation of large static antennae domains may represent a strategy for increasing electron transfer rates between distant complexes within the membrane and thus be important for photosynthetic efficiency.

Computational modeling reveals molecular details of epidermal growth factor binding

BACKGROUND

The ErbB family of receptors are dysregulated in a number of cancers, and the signaling pathway of this receptor family is a critical target for several anti-cancer drugs. Therefore a detailed understanding of the mechanisms of receptor activation is critical. However, despite a plethora of biochemical studies and recent single particle tracking experiments, the early molecular mechanisms involving epidermal growth factor (EGF) binding and EGF receptor (EGFR) dimerization are not as well understood. Herein, we describe a spatially distributed Monte Carlo based simulation framework to enable the simulation of in vivo receptor diffusion and dimerization.

RESULTS

Our simulation results are in agreement with the data from single particle tracking and biochemical experiments on EGFR. Furthermore, the simulations reveal that the sequence of receptor-receptor and ligand-receptor reaction events depends on the ligand concentration, receptor density and receptor mobility.

CONCLUSION

Our computer simulations reveal the mechanism of EGF binding on EGFR. Overall, we show that spatial simulation of receptor dynamics can be used to gain a mechanistic understanding of receptor activation which may in turn enable improved cancer treatments in the future.

Quantification and correction of systematic errors due to detector time-averaging in single-molecule tracking experiments

Single-molecule tracking is a powerful way to look at the dynamic organization of plasma membranes. However, there are some limitations to its use. For example, it was recently observed, using numerical simulation, that time-averaging effects inherent to the exposure time of detectors are likely to bias the apparent motion of molecules confined in microdomains. Here, we solve this apparently limiting issue analytically. We explore this phenomenon by calculating its effects on the observed diffusion coefficients and domain sizes. We demonstrate that the real parameters can be easily recovered from the measured apparent ones. Interestingly, we find that single-molecule tracking can be used to explore events occurring at a timescale smaller than the exposure time.

Single-particle tracking of murine polyoma virus-like particles on live cells and artificial membranes

The lateral mobility of individual murine polyoma virus-like particles (VLPs) bound to live cells and artificial lipid bilayers was studied by single fluorescent particle tracking using total internal reflection fluorescence microscopy. The particle trajectories were analyzed in terms of diffusion rates and modes of motion as described by the moment scaling spectrum. Although VLPs bound to their ganglioside receptor in lipid bilayers exhibited only free diffusion, analysis of trajectories on live 3T6 mouse fibroblasts revealed three distinct modes of mobility: rapid random motion, confined movement in small zones (30-60 nm in diameter), and confined movement in zones with a slow drift. After binding to the cell surface, particles typically underwent free diffusion for 5-10 s, and then they were confined in an actin filament-dependent manner without involvement of clathrin-coated pits or caveolae. Depletion of cholesterol dramatically reduced mobility of VLPs independently of actin, whereas inhibition of tyrosine kinases had no effect on confinement. The results suggested that clustering of ganglioside molecules by the multivalent VLPs induced transmembrane coupling that led to confinement of the virus/receptor complex by cortical actin filaments.

Kinetics of the Initial Steps of G Protein-Coupled Receptor-Mediated Cellular Signaling Revealed by Single-Molecule Imaging

We report on an in vivo single-molecule study of the signaling kinetics of G protein-coupled receptors (GPCR) performed using the neurokinin 1 receptor (NK1R) as a representative member. The NK1R signaling cascade is triggered by the specific binding of a fluorescently labeled agonist, substance P (SP). The diffusion of single receptor-ligand complexes in plasma membrane of living HEK 293 cells is imaged using fast single-molecule wide-field fluorescence microscopy at 100 ms time resolution. Diffusion trajectories are obtained which show intra- and intertrace heterogeneity in the diffusion mode. To investigate universal patterns in the diffusion trajectories we take the ligand-binding event as the common starting point. This synchronization allows us to observe changes in the character of the ligand-receptor-complex diffusion. Specifically, we find that the diffusion of ligand-receptor complexes is slowed down significantly and becomes more constrained as a function of time during the first 1000 ms. The decelerated and more constrained diffusion is attributed to an increasing interaction of the GPCR with cellular structures after the ligand-receptor complex is formed.

Three-dimensional characterization of tethered microspheres by total internal reflection fluorescence microscopy

Tethered particle microscopy is a powerful tool to study the dynamics of DNA molecules and DNA-protein complexes in single-molecule experiments. We demonstrate that stroboscopic total internal reflection microscopy can be used to characterize the three-dimensional spatiotemporal motion of DNA-tethered particles. By calculating characteristic measures such as symmetry and time constants of the motion, well-formed tethers can be distinguished from defective ones for which the motion is dominated by aberrant surface effects. This improves the reliability of measurements on tether dynamics. For instance, in observations of protein-mediated DNA looping, loop formation is distinguished from adsorption and other nonspecific events.

Cholesterol dictates the freedom of EGF receptors and HER2 in the plane of the membrane

The flow of information through the epidermal growth factor receptor (EGFR) is shaped by molecular interactions in the plasma membrane. The EGFR is associated with lipid rafts, but their role in modulating receptor mobility and subsequent interactions is unclear. To investigate the role of nanoscale rafts in EGFR dynamics, we used single-molecule fluorescence imaging to track individual receptors and their dimerization partner, human epidermal growth factor receptor 2 (HER2), in the membrane of human mammary epithelial cells. We found that the motion of both receptors was interrupted by dwellings within nanodomains. EGFR was significantly less mobile than HER2. This difference was likely due to F-actin because its depolymerization led to similar diffusion patterns between the EGFR and HER2. Manipulations of membrane cholesterol content dramatically altered the diffusion pattern of both receptors. Cholesterol depletion led to almost complete confinement of the receptors, whereas cholesterol enrichment extended the boundaries of the restricted areas. Interestingly, F-actin depolymerization partially restored receptor mobility in cholesterol-depleted membranes. Our observations suggest that membrane cholesterol provides a dynamic environment that facilitates the free motion of EGFR and HER2, possibly by modulating the dynamic state of F-actin. The association of the receptors with lipid rafts could therefore promote their rapid interactions only upon ligand stimulation.