Anomalous diffusion of major histocompatibility complex class I molecules on HeLa cells determined by single particle tracking

Plant Membrane-On-A-Chip: A Platform for Studying Plant Membrane Proteins and Lipids

The cell plasma membrane is a two-dimensional, fluid mosaic material composed of lipids and proteins that create a semipermeable barrier defining the cell from its environment. Compared with soluble proteins, the methodologies for the structural and functional characterization of membrane proteins are challenging. An emerging tool for studies of membrane proteins in mammalian systems is a "plasma membrane on a chip," also known as a supported lipid bilayer. Here, we create the "plant-membrane-on-a-chip,″ a supported bilayer made from the plant plasma membranes of Arabidopsis thaliana, Nicotiana benthamiana, or Zea mays. Membrane vesicles from protoplasts containing transgenic membrane proteins and their native lipids were incorporated into supported membranes in a defined orientation. Membrane vesicles fuse and orient systematically, where the cytoplasmic side of the membrane proteins faces the chip surface and constituents maintain mobility within the membrane plane. We use plant-membrane-on-a-chip to perform fluorescent imaging to examine protein-protein interactions and determine the protein subunit stoichiometry of FLOTILLINs. We report here that like the mammalian FLOTILLINs, FLOTILLINs expressed in Arabidopsis form a tetrameric complex in the plasma membrane. This plant-membrane-on-a-chip approach opens avenues to studies of membrane properties of plants, transport phenomena, biophysical processes, and protein-protein and protein-lipid interactions in a convenient, cell-free platform.

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

Replisome loading reduces chromatin motion independent of DNA synthesis

Chromatin has been shown to undergo diffusional motion, which is affected during gene transcription by RNA polymerase activity. However, the relationship between chromatin mobility and other genomic processes remains unclear. Hence, we set out to label the DNA directly in a sequence unbiased manner and followed labeled chromatin dynamics in interphase human cells expressing GFP-tagged proliferating cell nuclear antigen (PCNA), a cell cycle marker and core component of the DNA replication machinery. We detected decreased chromatin mobility during the S-phase compared to G1 and G2 phases in tumor as well as normal diploid cells using automated particle tracking. To gain insight into the dynamical organization of the genome during DNA replication, we determined labeled chromatin domain sizes and analyzed their motion in replicating cells. By correlating chromatin mobility proximal to the active sites of DNA synthesis, we showed that chromatin motion was locally constrained at the sites of DNA replication. Furthermore, inhibiting DNA synthesis led to increased loading of DNA polymerases. This was accompanied by accumulation of the single-stranded DNA binding protein on the chromatin and activation of DNA helicases further restricting local chromatin motion. We, therefore, propose that it is the loading of replisomes but not their catalytic activity that reduces the dynamics of replicating chromatin segments in the S-phase as well as their accessibility and probability of interactions with other genomic regions.

A comparative study on the influence of an ivy preparation and an ivy/thyme combination on the β2-adrenergic signal transduction

The β₂-adrenergic receptor (β₂AR) is relevant for surfactant formation in alveolar type 2 cells and reduction of intracellular calcium concentration in bronchial muscle cells and thus for secretolytic and bronchospasmolytic effects. Herbal medicinal products that affect the β₂AR system are used to treat common cold and bronchitis accompanied with mucus covered and narrowed airways. The present work compares the influence of an ivy preparation and an ivy/thyme combination on the β₂-adrenergic signal transduction. For receptor binding studies and characterization of the lateral mobility of β₂AR we have used single molecule detection by fluorescence correlation spectroscopy and single particle tracking. For the determination of both the second messenger cAMP and the internalization of β₂AR we have generated luciferase based reporter cell lines, which produce a cAMP-dependent luciferase in the cytosol and express β₂AR with extracellular luciferase moiety in the plasma membrane. While both preparations increased the β₂AR binding, a significant increase of the cAMP level was observed only for the ivy preparation, which can be explained by the inhibited internalization of HiBiT-tagged β₂AR under stimulating conditions. In contrast, isoprenaline-mediated internalization of HiBiT-tagged β₂AR of ivy/thyme combination pre-treated cells was not inhibited. Cells comparatively pre-treated with a thyme preparation did not show inhibition of ß₂AR internalization either. Furthermore, SNAP-tagged β₂AR of ivy preparation pre-treated cells, which were not internalized after isoprenaline stimulation, showed a redistribution from fast-to-slowly diffusing β₂AR. A corresponding redistribution of these receptors was not observed after pre-treatment with both the ivy/thyme combination and the thyme preparation. Comparable to the ivy/thyme combination, no decrease in the intratrack transitioning probability ratio (p23/p32) for fast and slow diffusing β₂AR was found for the thyme preparation, which, however, significantly decreased for control cells and for pre-treatment with the ivy preparation under stimulating conditions. It can therefore be concluded that the thyme fluid extract fraction in the ivy/thyme combination may have in part a negative effect on the β₂-adrenergic signal transduction.

Dynamic heterogeneity and non-Gaussian statistics for ganglioside GM1s and acetylcholine receptors on live cell membrane

We have carried out a comparative study of the lateral motion of ganglioside GM1, which is a glycosphingolipid residing on the outer leaflet of the plasma membrane, and acetylcholine receptor (AChR), which is a well-characterized ion channel. Both the lipid molecules and the transmembrane proteins reside on the plasma membranes of live Xenopus muscle cells. From a thorough analysis of a large volume of individual molecular trajectories obtained from more than 300 live cells over a wide range of sampling rates and long durations, we find that the GM1s and AChRs share the same dynamic heterogeneity and non-Gaussian statistics. Our measurements with the ATP-depleted cells reveal that the diffusion dynamics of the GM1s and AChRs is uniformly affected by the intracellular ATP level of the living muscle cells, further demonstrating that membrane diffusion is strongly coupled to the dynamics of the underlying cortical actin network, as predicted by the dynamic picket-fence model.

Speeding up Dynamics by Tuning the Noncommensurate Size of Rodlike Particles in a Smectic Phase

Using simulations, we study the diffusion of rodlike guest particles in a smectic environment of rodlike host particles. We find that the dynamics of guest rods across smectic layers changes from a fast nematiclike diffusion to a slow hopping-type dynamics via an intermediate switching regime by varying the length of the guest rods with respect to the smectic layer spacing. We determine the optimal rod length that yields the fastest and the slowest diffusion in a lamellar environment. We show that this behavior can be rationalized by a complex 1D effective periodic potential exhibiting two energy barriers, resulting in a varying preferred mean position of the guest particle in the smectic layer. The interplay of these two barriers controls the dynamics of the guest particles yielding a slow, an intermediate, and a fast diffusion regime depending on the particle length.

A novel computational framework for D(t) from Fluorescence Recovery after Photobleaching data reveals various anomalous diffusion types in live cell membranes

Diffusion of proteins and lipids in lipid membranes plays a pivotal role in almost all aspects of cellular biology, including motility, exo-/endocytosis and signal transduction. For this reason, gaining a detailed understanding of membrane structure and function has long been a major area of cell biology research. To better elucidate this structure-function relationship, various tools have been developed for diffusion measurements, including Fluorescence Recovery After Photobleaching (FRAP). Because of the complexity of cellular microenvironments, biological diffusion is often correlated over time and described by a time-dependent diffusion coefficient, D(t), although the underlying mechanisms are not fully understood. Since D(t) provides important information regarding cellular structures, such as the existence of subresolution barriers to diffusion, many efforts have been made to quantify D(t) by FRAP assuming a single power law, D(t) = Γt ^α - 1 where Γ and α are transport coefficient and anomalous exponent. However, straightforward approaches to quantify a general form of D(t) are lacking. In this study, we develop a novel mathematical and computational framework to compute the mean square displacement of diffusing molecules and diffusion coefficient D(t) from each individual time point of confocal FRAP data without the single power law assumption. Additionally, we developed an auxiliary equation for D(t) which can readily distinguish normal diffusion or single power law anomalous diffusion from other types of anomalous diffusion directly from FRAP data. Importantly, by applying this approach to FRAP data from a variety of membrane markers, we demonstrate the single power law anomalous diffusion assumption is not sufficient to describe various types of D(t) of membrane proteins. Lastly, we discuss how our new approaches can be applied to other fluorescence microscopy tools such as Fluorescence Correlation Spectroscopy (FCS) and Single Particle Tracking (SPT).

Controlling Anomalous Diffusion in Lipid Membranes

Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.

Numerical Simulation and FRAP Experiments Show That the Plasma Membrane Binding Protein PH-EFA6 Does Not Exhibit Anomalous Subdiffusion in Cells

The fluorescence recovery after photobleaching (FRAP) technique has been used for decades to measure movements of molecules in two-dimension (2D). Data obtained by FRAP experiments in cell plasma membranes are assumed to be described through a means of two parameters, a diffusion coefficient, D (as defined in a pure Brownian model) and a mobile fraction, M. Nevertheless, it has also been shown that recoveries can be nicely fit using anomalous subdiffusion. Fluorescence recovery after photobleaching (FRAP) at variable radii has been developed using the Brownian diffusion model to access geometrical characteristics of the surrounding landscape of the molecule. Here, we performed numerical simulations of continuous time random walk (CTRW) anomalous subdiffusion and interpreted them in the context of variable radii FRAP. These simulations were compared to experimental data obtained at variable radii on living cells using the pleckstrin homology (PH) domain of the membrane binding protein EFA6 (exchange factor for ARF6, a small G protein). This protein domain is an excellent candidate to explore the structure of the interface between cytosol and plasma membrane in cells. By direct comparison of our numerical simulations to the experiments, we show that this protein does not exhibit anomalous diffusion in baby hamster kidney (BHK) cells. The non Brownian PH-EFA6 dynamics observed here are more related to spatial heterogeneities such as cytoskeleton fence effects.

Biologically Complex Planar Cell Plasma Membranes Supported on Polyelectrolyte Cushions Enhance Transmembrane Protein Mobility and Retain Native Orientation

Reconstituted supported lipid bilayers (SLB) are widely used as in vitro cell-surface models because they are compatible with a variety of surface-based analytical techniques. However, one of the challenges of using SLBs as a model of the cell surface is the limited complexity in membrane composition, including the incorporation of transmembrane proteins and lipid diversity that may impact the activity of those proteins. Additionally, it is challenging to preserve the transmembrane protein native orientation, function, and mobility in SLBs. Here, we leverage the interaction between cell plasma membrane vesicles and polyelectrolyte brushes to create planar bilayers from cell plasma membrane vesicles that have budded from the cell surface. This approach promotes the direct incorporation of membrane proteins and other species into the planar bilayer without using detergent or reconstitution and preserves membrane constituents. Furthermore, the structure of the polyelectrolyte brush serves as a cushion between the planar bilayer and rigid supporting surface, limiting the interaction of the cytosolic domains of membrane proteins with this surface. Single particle tracking was used to analyze the motion of GPI-linked yellow fluorescent proteins (GPI-YFP) and neon-green fused transmembrane P2X2 receptors (P2X2-neon) and shows that this platform retains over 75% mobility of multipass transmembrane proteins in its native membrane environment. An enzyme accessibility assay confirmed that the protein orientation is preserved and results in the extracellular domain facing toward the bulk phase and the cytosolic side facing the support. Because the platform presented here retains the complexity of the cell plasma membrane and preserves protein orientation and mobility, it is a better representative mimic of native cell surfaces, which may find many applications in biological assays aimed at understanding cell membrane phenomena.

Supported Planar Mammalian Membranes as Models of in Vivo Cell Surface Architectures

Emerging technologies use cell plasma membrane vesicles or "blebs" as an intermediate to form molecularly complete, planar cell surface mimetics that are compatible with a variety of characterization tools and microscopy methods. This approach enables direct incorporation of membrane proteins into supported lipid bilayers without using detergents and reconstitution and preserves native lipids and membrane species. Such a system can be advantageous as in vitro models of in vivo cell surfaces for study of the roles of membrane proteins as drug targets in drug delivery, host-pathogen interactions, tissue engineering, and many other bioanalytical and sensing applications. However, the impact of methods used to induce cell blebbing (vesiculation) on protein and membrane properties is still unknown. This study focuses on characterization of cell blebs created under various bleb-inducing conditions and the result on protein properties (orientation, mobility, activity, etc.) and lipid scrambling in this platform. The orientation of proteins in the cell blebs and planar bilayers is revealed using a protease cleavage assay. Lipid scrambling in both cell blebs and planar bilayers is indicated through an annexin V binding assay. To quantify protein confinement, immobility, etc., incorporation of GPI-linked yellow fluorescent protein (GPI-YFP) was used in conjunction with single-molecule tracking (SMT) microscopy. Finally, to investigate the impact of the bleb induction method on protein activity and expression level, cell blebs expressing human aminopeptidase N (hAPN) were analyzed by an enzyme activity assay and immunoblotting. This work enriches our understanding of cell plasma membrane bleb bilayers as a biomimetic platform, reveals conditions under which specific properties are met, and represents one of the few ways to make molecularly complete supported bilayers directly from cell plasma membranes.

Colloidal diffusion over a quenched two-dimensional random potential

A two-layer colloidal system is developed for the study of diffusion over a quenched two-dimensional random potential. A mixture of bidisperse silica spheres is used to form a randomly packed colloidal monolayer on the bottom substrate. The corrugated surface of the bottom colloidal monolayer provides a gravitational potential field for the dilute diffusing particles in the top layer. The population probability histogram P(x,y) of the diffusing particles is obtained to fully characterize the random potential landscape U(x,y) via the Boltzmann distribution. The dynamical properties of the top diffusing particles, such as their mean square displacement (MSD), histogram of the escape time, and long-time self-diffusion coefficient, are simultaneously measured from the particle trajectories. A quantitative relationship between the long-time diffusion coefficient and the random potential is obtained, which is in good agreement with the theoretical prediction. The measured MSD reveals a wide region of subdiffusion resulting from the structural disorders. The crossover from subdiffusion to normal diffusion is explained by the Lorentz model for tracer diffusion through a heterogeneous space filled with a set of randomly distributed obstacles.

Single-point single-molecule FRAP distinguishes inner and outer nuclear membrane protein distribution

The normal distribution of nuclear envelope transmembrane proteins (NETs) is disrupted in several human diseases. NETs are synthesized on the endoplasmic reticulum and then transported from the outer nuclear membrane (ONM) to the inner nuclear membrane (INM). Quantitative determination of the distribution of NETs on the ONM and INM is limited in available approaches, which moreover provide no information about translocation rates in the two membranes. Here we demonstrate a single-point single-molecule FRAP microscopy technique that enables determination of distribution and translocation rates for NETs in vivo.

Fisher information theory for parameter estimation in single molecule microscopy: tutorial

Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based super-resolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramér-Rao lower bound. The Cramér-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramér-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation and, more generally, to demonstrate the flexibility of the mathematical framework.

Dynamic heterogeneity and non-Gaussian statistics for acetylcholine receptors on live cell membrane

The Brownian motion of molecules at thermal equilibrium usually has a finite correlation time and will eventually be randomized after a long delay time, so that their displacement follows the Gaussian statistics. This is true even when the molecules have experienced a complex environment with a finite correlation time. Here, we report that the lateral motion of the acetylcholine receptors on live muscle cell membranes does not follow the Gaussian statistics for normal Brownian diffusion. From a careful analysis of a large volume of the protein trajectories obtained over a wide range of sampling rates and long durations, we find that the normalized histogram of the protein displacements shows an exponential tail, which is robust and universal for cells under different conditions. The experiment indicates that the observed non-Gaussian statistics and dynamic heterogeneity are inherently linked to the slow-active remodelling of the underlying cortical actin network.

Membrane Protein Mobility and Orientation Preserved in Supported Bilayers Created Directly from Cell Plasma Membrane Blebs

Membrane protein interactions with lipids are crucial for their native biological behavior, yet traditional characterization methods are often carried out on purified protein in the absence of lipids. We present a simple method to transfer membrane proteins expressed in mammalian cells to an assay-friendly, cushioned, supported lipid bilayer platform using cell blebs as an intermediate. Cell blebs, expressing either GPI-linked yellow fluorescent proteins or neon-green fused transmembrane P2X2 receptors, were induced to rupture on glass surfaces using PEGylated lipid vesicles, which resulted in planar supported membranes with over 50% mobility for multipass transmembrane proteins and over 90% for GPI-linked proteins. Fluorescent proteins were tracked, and their diffusion in supported bilayers characterized, using single molecule tracking and moment scaling spectrum (MSS) analysis. Diffusion was characterized for individual proteins as either free or confined, revealing details of the local lipid membrane heterogeneity surrounding the protein. A particularly useful result of our bilayer formation process is the protein orientation in the supported planar bilayer. For both the GPI-linked and transmembrane proteins used here, an enzymatic assay revealed that protein orientation in the planar bilayer results in the extracellular domains facing toward the bulk, and that the dominant mode of bleb rupture is via the "parachute" mechanism. Mobility, orientation, and preservation of the native lipid environment of the proteins using cell blebs offers advantages over proteoliposome reconstitution or disrupted cell membrane preparations, which necessarily result in significant scrambling of protein orientation and typically immobilized membrane proteins in SLBs. The bleb-based bilayer platform presented here is an important step toward integrating membrane proteomic studies on chip, especially for future studies aimed at understanding fundamental effects of lipid interactions on protein activity and the roles of membrane proteins in disease pathways.

Direct observation of mobility state transitions in RNA trajectories by sensitive single molecule feedback tracking

Observation and tracking of fluorescently labeled molecules and particles in living cells reveals detailed information about intracellular processes on the molecular level. Whereas light microscopic particle observation is usually limited to two-dimensional projections of short trajectory segments, we report here image-based real-time three-dimensional single particle tracking in an active feedback loop with single molecule sensitivity. We tracked particles carrying only 1-3 fluorophores deep inside living tissue with high spatio-temporal resolution. Using this approach, we succeeded to acquire trajectories containing several hundred localizations. We present statistical methods to find significant deviations from random Brownian motion in such trajectories. The analysis allowed us to directly observe transitions in the mobility of ribosomal (r)RNA and Balbiani ring (BR) messenger (m)RNA particles in living Chironomus tentans salivary gland cell nuclei. We found that BR mRNA particles displayed phases of reduced mobility, while rRNA particles showed distinct binding events in and near nucleoli.

Spatial distributions at equilibrium under heterogeneous transient subdiffusion

Experimental measurements of the mobility of macromolecules, especially proteins, in cells and their membranes consistently report transient subdiffusion with possibly position-dependent—non-homogeneous—properties. However, the spatiotemporal dynamics of protein mobility when transient subdiffusion is restricted to a subregion of space is still unclear. Here, we investigated the spatial distribution at equilibrium of proteins undergoing transient subdiffusion due to continuous-time random walks (CTRW) in a restricted subregion of a two-dimensional space. Our Monte-Carlo simulations suggest that this process leads to a non-homogeneous spatial distribution of the proteins at equilibrium, where proteins increasingly accumulate in the CTRW subregion as its anomalous properties are increasingly marked. In the case of transient CTRW, we show that this accumulation is dictated by the asymptotic Brownian regime and not by the initial anomalous transient dynamics. Moreover, our results also show that this dominance of the asymptotic Brownian regime cannot be simply generalized to other scenarios of transient subdiffusion. In particular, non-homogeneous transient subdiffusion due to hindrance by randomly-located immobile obstacles does not lead to such a strong local accumulation. These results suggest that, even though they exhibit the same time-dependence of the mean-squared displacement, the different scenarios proposed to account for subdiffusion in the cell lead to different protein distribution in space, even at equilibrium and without coupling with reaction.

Actin cytoskeleton reorganization by Syk regulates Fcγ receptor responsiveness by increasing its lateral mobility and clustering

Clustering of immunoreceptors upon association with multivalent ligands triggers important responses including phagocytosis, secretion of cytokines, and production of immunoglobulins. We applied single-molecule detection and tracking methods to study the factors that control the mobility and clustering of phagocytic Fcγ receptors (FcγR). While the receptors exist as monomers in resting macrophages, two distinct populations were discernible based on their mobility: some diffuse by apparent free motion, while others are confined within submicron boundaries that reduce the frequency of spontaneous collisions. Src-family and Syk kinases determine the structure of the actin cytoskeleton, which is fenestrated, accounting for the heterogeneous diffusion of the FcγR. Stimulation of these kinases during phagocytosis induces reorganization of the cytoskeleton both locally and distally in a manner that alters receptor mobility and clustering, generating a feedback loop that facilitates engagement of FcγR at the tip of pseudopods, directing the progression of phagocytosis.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.

Anomalous diffusion due to hindering by mobile obstacles undergoing Brownian motion or Orstein-Ulhenbeck processes

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent α<1 (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.

Quantified colocalization reveals heterotypic histocompatibility class I antigen associations on trophoblast cell membranes: relevance for human pregnancy

Human placental syncytiotrophoblasts lack expression of most types of human leukocyte antigen (HLA) class I and class II molecules; this is thought to contribute to a successful pregnancy. However, the HLA class Ib antigens HLA-G, -E, and -F and the HLA class Ia antigen HLA-C are selectively expressed on extravillous trophoblast cells, and they are thought to play a major role in controlling feto-maternal tolerance. We have hypothesized that selective expression, coupled with the preferential physical association of pairs of HLA molecules, contribute to the function of HLA at the feto-maternal interface and the maternal recognition of the fetus. We have developed a unique analytical model that allows detection and quantification of the heterotypic physical associations of HLA class I molecules expressed on the membrane of human trophoblast choriocarcinoma cells, ACH-3P and JEG-3. Automated image analysis was used to estimate the degree of overlap of HLA molecules labeled with different fluorochromes. This approach yields an accurate measurement of the degree of colocalization. In both JEG-3 and ACH-3P cells, HLA-C, -E, and -G were detected on the cell membrane, while the expression of HLA-F was restricted to the cytoplasm. Progesterone treatment alone induced a significant increase in the expression level of the HLA-G/HLA-E association, suggesting that this heterotypic association is modulated by this hormone. Our data shows that the cell-surface HLA class I molecules HLA-G, -E, and -C colocalize with each other and have the potential to form preferential heterotypic associations.

Single-molecule observations for determining the orientation and diffusivity of dye molecules in lipid bilayers

The molecular orientation and diffusion of dye molecules in artificial lipid bilayers were observed using total internal reflection fluorescence microscopy. An artificial lipid bilayer composed of a ternary lipid mixture of 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC), and cholesterol was used. The molecular orientation, which was obtained through defocused imaging, clarified the microscopic features, including cholesterol-induced changes in the local packing structure. Diffusion analysis gave insights into the macroscopic aspects of phase distribution in the heterogeneous bilayer system. Combining these two independent investigations, we revealed the effect of cholesterol addition on microscopic local packing and macroscopic phase structures. Our observations showed a transition from a DLPC-network-like structure to a DPPC-network-like structure upon the addition of cholesterol, which was not evident from previous domain shape observations. The present single-molecule observations yielded the actual phase structure that controls the motion of molecules in the membrane. The results imply that the orientation and diffusivity of molecules offer useful information regarding the phase distribution, which may be hindered by the apparent phase structure in a heterogeneous lipid bilayer that contains cholesterol.

Time-resolved fluorescence anisotropy and fluctuation correlation analysis of major histocompatibility complex class I proteins in fibroblast cells

Major histocompatibility complex class I proteins, MHC(I), are expressed in almost all nucleated cells and synthesized in the endoplasmic reticulum (ER). The orientation and mobility of these complexes are crucial in their biological function in the immune system, i.e., the cytosolic pathogen peptides loading and their presentation to T-cell receptors at the plasma membrane, where cell destruction is triggered. Here, we investigate the structural flexibility and associations of GFP-encoded MHC(I) alleles (H2L(d)), namely H2L(d)GFPin and H2L(d)GFPout, in cultured mouse fibroblast cells. Time-resolved fluorescence anisotropy of H2L(d)GFPin in the ER indicates a dominant overall tumbling motion of 56±7 ns (ER), with a fast conformational flexibility, as compared with a restricted rotation of H2L(d)GFPout. At the single-molecule level, the diffusion coefficient of H2L(d)GFPin and H2L(d)GFPout in the ER is (1.8±0.5)×10(-9) and (2.1±0.6)×10(-9) cm(2)/s, respectively, as revealed by fluorescence correlation spectroscopy. A complementary immunoblotting of H2L(d)GFP constructs, isolated from mouse fibroblast cells, reveals band at 75 kDa as compared with 29 kDa of the free EGFP. These real-time dynamics provide new insights into the structural flexibility and intracellular associations of GFP-labeled MHC(I) alleles (H2L(d)) in living cells.

Anomalous transport in the crowded world of biological cells

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

Anomalous diffusion and multifractional Brownian motion: simulating molecular crowding and physical obstacles in systems biology

There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our sample data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.

Crowding effects in vehicular traffic

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from a negatively-skewed normal to an exponential distribution. Moreover, crowding broadens the distribution of cars’ trap times and cluster sizes. At steady state, the subdiffusive state persists only when there is a large variability in car speeds. We further relate our work to prior findings from random walk models of transport in cellular systems.

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

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

Interaction of HLA-DR and CD74 at the cell surface of antigen-presenting cells by single particle image analysis

Major histocompatibility complex (MHC) class II-associated antigen presentation involves an array of interacting molecules. CD74, the cell surface isoform of the MHC class II-associated invariant chain, is one such molecule; its role remains poorly defined. To address this, we have employed a high-resolution single-particle imaging method for quantifying the colocalization of CD74 with human leukocyte antigen (HLA)-DR molecules on human fibroblast cells known for their capacity to function as antigen-presenting cells. We have also examined whether the colocalization induces internalization of HLA-DR using HA(307-319), a "universal" peptide that binds specifically to the peptide-binding groove of all HLA-DR molecules, irrespective of their alleles. We have determined that 25 ± 1.3% of CD74 and 17 ± 0.3% of HLA-DR are colocalized, and the association of CD74 with HLA-DR and the internalization of HLA-DR are both inhibited by HA(307-319). A similar inhibition of HLA-DR internalization was observed in freshly isolated monocyte-derived dendritic cells. A key role of CD74 is to translocate HLA-DR molecules to early endosomes for reloading with peptides prior to recycling to the cell surface. We conclude that CD74 regulates the balance of peptide-occupied and peptide-free forms of MHC class II at the cell surface.

Obstructed diffusion propagator analysis for single-particle tracking

We describe a method for the analysis of the distribution of displacements, i.e., the propagators, of single-particle tracking measurements for the case of obstructed subdiffusion in two-dimensional membranes. The propagator for the percolation cluster is compared with a two-component mobility model against Monte Carlo simulations. To account for diffusion in the presence of obstacle concentrations below the percolation threshold, a propagator that includes the transient motion in finite percolation clusters and hopping between obstacle-induced compartments is derived. Finally, these models are shown to be effective in the analysis of Kv2.1 channel diffusive measurements in the membrane of living mammalian cells.

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.

Terbutaline causes immobilization of single β2-adrenergic receptor-ligand complexes in the plasma membrane of living A549 cells as revealed by single-molecule microscopy

G-protein-coupled receptors are important targets for various drugs. After signal transduction, regulatory processes, such as receptor desensitization and internalization, change the lateral receptor mobility. In order to study the lateral diffusion of β(2)-adrenergic receptors (β(2)AR) complexed with fluorescently labeled noradrenaline (Alexa-NA) in plasma membranes of A549 cells, trajectories of single receptor-ligand complexes were monitored using single-particle tracking. We found that a fraction of 18% of all β(2)ARs are constitutively immobile. About 2/3 of the β(2)ARs moved with a diffusion constant of D(2) = 0.03 ± 0.001 μm(2)/s and about 17% were diffusing five-fold faster (D(3) = 0.15 ± 0.02 μm(2)/s). The mobile receptors moved within restricted domains and also showed a discontinuous diffusion behavior. Analysis of the trajectory lengths revealed two different binding durations with τ(1) = 77 ± 1 ms and τ(2) = 388 ± 11 ms. Agonistic stimulation of the β(2)AR-Alexa-NA complexes with 1 μM terbutaline caused immobilization of almost 50% of the receptors within 35 min. Simultaneously, the mean area covered by the mobile receptors decreased significantly. Thus, we demonstrated that agonistic stimulation followed by cell regulatory processes results in a change in β(2)AR mobility suggesting that different receptor dynamics characterize different receptor states.

Limit of the Accuracy of Parameter Estimation for Moving Single Molecules Imaged by Fluorescence Microscopy

In this paper, we consider the problem of the accuracy of estimating the location and other attributes of a moving single molecule whose trajectory is imaged by fluorescence microscopy. As accuracy in parameter estimation is closely related to the Fisher information matrix, we first give a general expression of the Fisher information matrix for the estimated parameters for a single object moving in three-dimensional (3D) space. Explicit Cramér-Rao lower bound (CRLB) expressions are then obtained from the Fisher information matrix for a single object moving in the two-dimensional (2D) focus plane with the object trajectory being either linear or circular. We also investigate how extraneous noise sources, pixelation, parameters of the detection system and parameters of the trajectory affect the limit of the accuracy. The results obtained in this paper provide insights that enable the experimentalists to optimize their experimental setups for tracking single molecules in order to achieve the best possible accuracy. They are also applicable to the general problem of tracking an object using quantum limited detectors.

HIV-1 Nef binds a subpopulation of MHC-I throughout its trafficking itinerary and down-regulates MHC-I by perturbing both anterograde and retrograde trafficking

The HIV protein Nef is thought to mediate immune evasion and promote viral persistence in part by down-regulating major histocompatibility complex class I protein (MHC-I or HLA-I) from the cell surface. Two different models have been proposed to explain this phenomenon as follows: 1) stimulation of MHC-I retrograde trafficking from and aberrant recycling to the plasma membrane, and 2) inhibition of anterograde trafficking of newly synthesized HLA-I from the endoplasmic reticulum to the plasma membrane. We show here that Nef simultaneously uses both mechanisms to down-regulate HLA-I in peripheral blood mononuclear cells or HeLa cells. Consistent with this, we found by using fluorescence correlation spectroscopy that a third of diffusing HLA-I at the endoplasmic reticulum, Golgi/trans-Golgi network, and the plasma membrane (PM) was associated with Nef. The binding of Nef was similarly avid for native HLA-I and recombinant HLA-I A2 at the PM. Nef binding to HLA-I at the PM was sensitive to specific inhibition of endocytosis. It was also attenuated by cyclodextrin disruption of PM lipid micro-domain architecture, a change that also retarded lateral diffusion and induced large clusters of HLA-I. In all, our data support a model for Nef down-regulation of HLA-I that involves both major trafficking itineraries and persistent protein-protein interactions throughout the cell.

Spatio-temporal modeling of signaling protein recruitment to EGFR

Background

A stochastic simulator was implemented to study EGFR signal initiation in 3D with single molecule detail. The model considers previously unexplored contributions to receptor-adaptor coupling, such as receptor clustering and diffusive properties of both receptors and binding partners. The agent-based and rule-based approach permits consideration of combinatorial complexity, a problem associated with multiple phosphorylation sites and the potential for simultaneous binding of adaptors.

Results

The model was used to simulate recruitment of four different signaling molecules (Grb2, PLCγ1, Stat5, Shc) to the phosphorylated EGFR tail, with rules based on coarse-grained prediction of spatial constraints. Parameters were derived in part from quantitative immunoblotting, immunoprecipitation and electron microscopy data. Results demonstrate that receptor clustering increases the efficiency of individual adaptor retainment on activated EGFR, an effect that is overridden if crowding is imposed by receptor overexpression. Simultaneous docking of multiple proteins is highly dependent on receptor-adaptor stability and independent of clustering.

Conclusions

Overall, we propose that receptor density, reaction kinetics and membrane spatial organization all contribute to signaling efficiency and influence the carcinogenesis process.

Fractional chemotaxis diffusion equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

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.

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.

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.

Stochastic simulations of ErbB homo and heterodimerisation: potential impacts of receptor conformational state and spatial segregation

ErbB overexpression is linked to carcinogenesis. It is hypothesised that this is due to increased receptor density and receptor clustering, leading to increased receptor dimerisation and activation. Herein, spatial stochastic simulations have been performed to shed light receptor dimerisation processes. First, ligand-independent homodimerisation, is considered, based upon constitutive oligomerisation estimates (14%) in A431 cells that overexpress epidermal growth factor receptor (EGFR). When autocrine stimulation is blocked, ligand-independent EGFR activation is demonstrated by persistent, low levels of phosphorylation. The possibility that ligand-independent signalling is due to the fluctuation of EGFR conformation is considered. The agent-based model predicts the frequency (expressed as a probability) that uniformly distributed receptors would need to flux to the open conformation to reach 14% EGFR dimers at high receptor density. Simulations suggest that ligand-independent EGFR homodimerisation is highly density dependent, since collisions between 'open', dimerisation-competent receptors are a rare event at low receptor levels. Simulations that incorporate receptor clustering lower the threshold for homodimerisation of unoccupied receptors as well as the estimate of the probability for fluxing to the dimer-competent conformation. The impact of ErbB receptor clustering patterns on hetero and homodimerisation rates is also considered, using immunoelectron microscopy data derived from SKBR3 breast cancer cells that express ErbB2>>EGFR>ErbB3. Partial spatial segregation of ErbB receptors has a profound effect on simulated heterodimerisation rates. Despite the general assumption that ErbB2 is a preferred heterodimerising partner for other ErbBs, it is predicted that most ErbB2 will form homodimers. Overall, it is proposed that both receptor density and membrane spatial organisation contribute to the carcinogenesis process.

High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells

Single particle tracking in three dimensions in a live cell environment holds the promise of revealing important new biological insights. However, conventional microscopy-based imaging techniques are not well suited for fast three-dimensional (3D) tracking of single particles in cells. Previously we developed an imaging modality multifocal plane microscopy (MUM) to image fast intracellular dynamics in three dimensions in live cells. Here, we introduce an algorithm, the MUM localization algorithm (MUMLA), to determine the 3D position of a point source that is imaged using MUM. We validate MUMLA through simulated and experimental data and show that the 3D position of quantum dots can be determined over a wide spatial range. We demonstrate that MUMLA indeed provides the best possible accuracy with which the 3D position can be determined. Our analysis shows that MUM overcomes the poor depth discrimination of the conventional microscope, and thereby paves the way for high accuracy tracking of nanoparticles in a live cell environment. Here, using MUM and MUMLA we report for the first time the full 3D trajectories of QD-labeled antibody molecules undergoing endocytosis in live cells from the plasma membrane to the sorting endosome deep inside the cell.