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

Tracking Low-Copy Transcription Factors in Living Bacteria: The Case of the lac Repressor

Transcription factors control the expression of genes by binding to specific sites in DNA and repressing or activating transcription in response to stimuli. The lac repressor (LacI) is a well characterized transcription factor that regulates the ability of bacterial cells to uptake and metabolize lactose. Here, we study the intracellular mobility and spatial distribution of LacI in live bacteria using photoactivated localization microscopy combined with single-particle tracking. Since we track single LacI molecules in live cells by stochastically photoactivating and observing fluorescent proteins individually, there are no limitations on the copy number of the protein under study; as a result, we were able to study the behavior of LacI in bacterial strains containing the natural copy numbers (∼40 monomers), as well as in strains with much higher copy numbers due to LacI overexpression. Our results allowed us to determine the relative abundance of specific, near-specific, and non-specific DNA binding modes of LacI in vivo, showing that all these modes are operational inside living cells. Further, we examined the spatial distribution of LacI in live cells, confirming its specific binding to lac operator regions on the chromosome; we also showed that mobile LacI molecules explore the bacterial nucleoid in a way similar to exploration by other DNA-binding proteins. Our work also provides an example of applying tracking photoactivated localization microscopy to studies of low-copy-number proteins in living bacteria.

Accuracy of the detection of binding events using 3D single particle tracking

BACKGROUND

Nanoparticles can be used as markers to track the position of biomolecules, such as single proteins, inside living cells. The activity of a protein can sometimes be inferred from changes in the mobility of the attached particle. Mean Square Displacement analysis is the most common method to obtain mobility information from trajectories of tracked particles, such as the diffusion coefficient D. However, the precision of D sets a limit to discriminate changes in mobility caused by biological events from changes that reflect the stochasticity inherent to diffusion. This issue is of particular importance in an experiment aiming to quantify dynamic processes.

RESULTS

Here, we present simulations and 3D tracking experiments with Gold Nanorods freely diffusing in glycerol solution to establish the best analysis parameters to extract the diffusion coefficient. We applied this knowledge to the detection of a temporary change in diffusion, as it can occur due to the transient binding of a particle to an immobile structure within the cell, and tested its dependence on the magnitude of the change in diffusion and duration of this event.

CONCLUSIONS

The simulations show that the spatial accuracy of particle tracking generally does not limit the detection of short binding events. Careful analysis of the magnitude of the change in diffusion and the number of frames per binding event is required for accurate quantification of such events.

Application of Noncanonical Amino Acids for Protein Labeling in a Genomically Recoded Escherichia coli

Small synthetic fluorophores are in many ways superior to fluorescent proteins as labels for imaging. A major challenge is to use them for a protein-specific labeling in living cells. Here, we report on our use of noncanonical amino acids that are genetically encoded via the pyrrolysyl-tRNA/pyrrolysyl-RNA synthetase pair at artificially introduced TAG codons in a recoded E. coli strain. The strain is lacking endogenous TAG codons and the TAG-specific release factor RF1. The amino acids contain bioorthogonal groups that can be clicked to externally supplied dyes, thus enabling protein-specific labeling in live cells. We find that the noncanonical amino acid incorporation into the target protein is robust for diverse amino acids and that the usefulness of the recoded E. coli strain mainly derives from the absence of release factor RF1. However, the membrane permeable dyes display high nonspecific binding in intracellular environment and the electroporation of hydrophilic nonmembrane permeable dyes severely impairs growth of the recoded strain. In contrast, proteins exposed on the outer membrane of E. coli can be labeled with hydrophilic dyes with a high specificity as demonstrated by labeling of the osmoporin OmpC. Here, labeling can be made sufficiently specific to enable single molecule studies as exemplified by OmpC single particle tracking.

Convergence of lateral dynamic measurements in the plasma membrane of live cells from single particle tracking and STED-FCS

Fluorescence correlation spectroscopy (FCS) in combination with the super-resolution imaging method STED (STED-FCS), and single-particle tracking (SPT) are able to directly probe the lateral dynamics of lipids and proteins in the plasma membrane of live cells at spatial scales much below the diffraction limit of conventional microscopy. However, a major disparity in interpretation of data from SPT and STED-FCS remains, namely the proposed existence of a very fast (unhindered) lateral diffusion coefficient, ⩾5 µm2 s-1, in the plasma membrane of live cells at very short length scales, ≈⩽ 100 nm, and time scales, ≈1-10 ms. This fast diffusion coefficient has been advocated in several high-speed SPT studies, for lipids and membrane proteins alike, but the equivalent has not been detected in STED-FCS measurements. Resolving this ambiguity is important because the assessment of membrane dynamics currently relies heavily on SPT for the determination of heterogeneous diffusion. A possible systematic error in this approach would thus have vast implications in this field. To address this, we have re-visited the analysis procedure for SPT data with an emphasis on the measurement errors and the effect that these errors have on the measurement outputs. We subsequently demonstrate that STED-FCS and SPT data, following careful consideration of the experimental errors of the SPT data, converge to a common interpretation which for the case of a diffusing phospholipid analogue in the plasma membrane of live mouse embryo fibroblasts results in an unhindered, intra-compartment, diffusion coefficient of  ≈0.7-1.0 µm2 s-1, and a compartment size of about 100-150 nm.

Ultrasensitive Label-Free Nanosensing and High-Speed Tracking of Single Proteins

Label-free detection, analysis, and rapid tracking of nanoparticles is crucial for future ultrasensitive sensing applications, ranging from understanding of biological interactions to the study of size-dependent classical-quantum transitions. Yet optical techniques to distinguish nanoparticles directly among their background remain challenging. Here we present amplified interferometric scattering microscopy (a-iSCAT) as a new all-optical method capable of detecting individual nanoparticles as small as 15 kDa proteins that is equivalent to half a GFP. By balancing scattering and reflection amplitudes the interference contrast of the nanoparticle signal is amplified 1 to 2 orders of magnitude. Beyond high sensitivity, a-iSCAT allows high-speed image acquisition exceeding several hundreds of frames-per-second. We showcase the performance of our approach by detecting single Streptavidin binding events and by tracking single Ferritin proteins at 400 frames-per-second with 12 nm localization precision over seconds. Moreover, due to its extremely simple experimental realization, this advancement finally enables a cheap and routine implementation of label-free all-optical single nanoparticle detection platforms with sensitivity operating at the single protein level.

Visible/near-infrared subdiffraction imaging reveals the stochastic nature of DNA walkers

DNA walkers are designed with the structural specificity and functional diversity of oligonucleotides to actively convert chemical energy into mechanical translocation. Compared to natural protein motors, DNA walkers' small translocation distance (mostly <100 nm) and slow reaction rate (<0.1 nm s^-1) make single-molecule characterization of their kinetics elusive. An important indication of single-walker kinetics is the rate-limiting reactions that a particular walker design bears. We introduce an integrated super-resolved fluorescence microscopy approach that is capable of long-term imaging to investigate the stochastic behavior of DNA walkers. Subdiffraction tracking and imaging in the visible and second near-infrared spectra resolve walker structure and reaction rates. The distributions of walker kinetics are analyzed using a stochastic model to reveal reaction randomness and the rate-limiting biochemical reaction steps.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Confined Mobility of TonB and FepA in Escherichia coli Membranes

The important process of nutrient uptake in Escherichia coli, in many cases, involves transit of the nutrient through a class of beta-barrel proteins in the outer membrane known as TonB-dependent transporters (TBDTs) and requires interaction with the inner membrane protein TonB. Here we have imaged the mobility of the ferric enterobactin transporter FepA and TonB by tracking them in the membranes of live E. coli with single-molecule resolution at time-scales ranging from milliseconds to seconds. We employed simple simulations to model/analyze the lateral diffusion in the membranes of E.coli, to take into account both the highly curved geometry of the cell and artifactual effects expected due to finite exposure time imaging. We find that both molecules perform confined lateral diffusion in their respective membranes in the absence of ligand with FepA confined to a region 0.180−0.007+0.006 μm in radius in the outer membrane and TonB confined to a region 0.266−0.009+0.007 μm in radius in the inner membrane. The diffusion coefficient of these molecules on millisecond time-scales was estimated to be 21−5+9 μm²/s and 5.4−0.8+1.5 μm²/s for FepA and TonB, respectively, implying that each molecule is free to diffuse within its domain. Disruption of the inner membrane potential, deletion of ExbB/D from the inner membrane, presence of ligand or antibody to FepA and disruption of the MreB cytoskeleton was all found to further restrict the mobility of both molecules. Results are analyzed in terms of changes in confinement size and interactions between the two proteins.

There Is No Simple Model of the Plasma Membrane Organization

Ever since technologies enabled the characterization of eukaryotic plasma membranes, heterogeneities in the distributions of its constituents were observed. Over the years this led to the proposal of various models describing the plasma membrane organization such as lipid shells, picket-and-fences, lipid rafts, or protein islands, as addressed in numerous publications and reviews. Instead of emphasizing on one model we in this review give a brief overview over current models and highlight how current experimental work in one or the other way do not support the existence of a single overarching model. Instead, we highlight the vast variety of membrane properties and components, their influences and impacts. We believe that highlighting such controversial discoveries will stimulate unbiased research on plasma membrane organization and functionality, leading to a better understanding of this essential cellular structure.

Single Molecule Studies of the Diffusion of Band 3 in Sickle Cell Erythrocytes

Sickle cell disease (SCD) is caused by an inherited mutation in hemoglobin that leads to sickle hemoglobin (HbS) polymerization and premature HbS denaturation. Previous publications have shown that HbS denaturation is followed by binding of denatured HbS (a.k.a. hemichromes) to band 3, the consequent clustering of band 3 in the plane of the erythrocyte membrane that in turn promotes binding of autologous antibodies to the clustered band 3, and removal of the antibody-coated erythrocytes from circulation. Although each step of the above process has been individually demonstrated, the fraction of band 3 that is altered by association with denatured HbS has never been determined. For this purpose, we evaluated the lateral diffusion of band 3 in normal cells, reversibly sickled cells (RSC), irreversibly sickled cells (ISC), and hemoglobin SC erythrocytes (HbSC) in order to estimate the fraction of band 3 that was diffusing more slowly due to hemichrome-induced clustering. We labeled fewer than ten band 3 molecules per intact erythrocyte with a quantum dot to avoid perturbing membrane structure and we then monitored band 3 lateral diffusion by single particle tracking. We report here that the size of the slowly diffusing population of band 3 increases in the sequence: normal cells<HbSC<RSC<ISC. We also demonstrate that the size of the compartment in which band 3 is free to diffuse decreases roughly in the same order, with band 3 diffusing in two compartments of sizes 35 and 71 nm in normal cells, but only a single compartment in HbSC cells (58 nm), RSC (45 nm) and ISC (36 nm). These data suggest that the mobility of band 3 is increasingly constrained during SCD progression, suggesting a global impact of the mutated hemoglobin on erythrocyte membrane properties.

Monte Carlo simulations of protein micropatterning in biomembranes: effects of immobile sticky obstacles

Single molecule trajectories of lipids and proteins can yield valuable information about the nanoscopic organization of the plasma membrane itself. The interpretation of such trajectories, however, is complicated, as the mobility of molecules can be affected by the presence of immobile obstacles, and the transient binding of the tracers to these obstacles. We have previously developed a micropatterning approach that allows for immobilizing a plasma membrane protein and probing the diffusional behavior of a putative interaction partner in living cells. Here, we provide guidelines on how this micropatterning approach can be extended to quantify interaction parameters between plasma membrane constituents in their natural environment. We simulated a patterned membrane system and evaluated the effect of different surface densities of patterned immobile obstacles on the relative mobility as well as the surface density of diffusing tracers. In the case of inert obstacles, the size of the obstacle can be assessed from its surface density at the percolation threshold, which in turn can be extracted from the diffusion behavior of the tracer. For sticky obstacles, two-dimensional dissociation constants can be determined from the tracer diffusion or surface density.

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.

Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane

We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer. By comparing the diffusion coefficients measured in horizontal vs. vertical defects, we conclude that band-3 mobility is primarily controlled by the horizontal connectivity.

Glasslike Membrane Protein Diffusion in a Crowded Membrane

Many functions of the plasma membrane depend critically on its structure and dynamics. Observation of anomalous diffusion in vivo and in vitro using fluorescence microscopy and single particle tracking has advanced our concept of the membrane from a homogeneous fluid bilayer with freely diffusing proteins to a highly organized crowded and clustered mosaic of lipids and proteins. Unfortunately, anomalous diffusion could not be related to local molecular details given the lack of direct and unlabeled molecular observation capabilities. Here, we use high-speed atomic force microscopy and a novel analysis methodology to analyze the pore forming protein lysenin in a highly crowded environment and document coexistence of several diffusion regimes within one membrane. We show the formation of local glassy phases, where proteins are trapped in neighbor-formed cages for time scales up to 10 s, which had not been previously experimentally reported for biological membranes. Furthermore, around solid-like patches and immobile molecules a slower glass phase is detected leading to protein trapping and creating a perimeter of decreased membrane diffusion.

Non-Brownian diffusion in lipid membranes: Experiments and simulations

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Current approaches to studying membrane organization

The local structure and composition of the outer membrane of an animal cell are important factors in the control of many membrane processes and mechanisms. These include signaling, sorting, and exo- and endocytic processes that are occurring all the time in a living cell. Paradoxically, not only are the local structure and composition of the membrane matters of much debate and discussion, the mechanisms that govern its genesis remain highly controversial. Here, we discuss a swathe of new technological advances that may be applied to understand the local structure and composition of the membrane of a living cell from the molecular scale to the scale of the whole membrane.

Extracting Diffusive States of Rho GTPase in Live Cells: Towards In Vivo Biochemistry

Resolving distinct biochemical interaction states when analyzing the trajectories of diffusing proteins in live cells on an individual basis remains challenging because of the limited statistics provided by the relatively short trajectories available experimentally. Here, we introduce a novel, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and demonstrate that pEM is capable of uncovering the proper number of underlying diffusive states with an accurate characterization of their diffusion properties. We then apply pEM to experimental protein trajectories of Rho GTPases, an integral regulator of cytoskeletal dynamics and cellular homeostasis, in vivo via single particle tracking photo-activated localization microcopy. Remarkably, pEM uncovers 6 distinct diffusive states conserved across various Rho GTPase family members. The variability across family members in the propensities for each diffusive state reveals non-redundant roles in the activation states of RhoA and RhoC. In a resting cell, our results support a model where RhoA is constantly cycling between activation states, with an imbalance of rates favoring an inactive state. RhoC, on the other hand, remains predominantly inactive.

Single particle tracking is a powerful tool that captures the diffusive dynamics of proteins as they undergo various interactions in living cells. Uncovering different biochemical interactions by analyzing the diffusive behaviors of individual protein trajectories, however, is challenging due to the limited statistics provided by short trajectories and experimental noise sources which are intimately coupled into each protein’s localization. Here, we introduce a novel, unsupervised, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and in vivo on the biological system of Rho GTPase, a signal transduction protein responsible for regulating cytoskeletal dynamics. We envision that the presented methodology will be applicable to a wide range of single protein tracking data where different biochemical interactions result in distinct diffusive behaviors. More generally, this study brings us an important step closer to the possibility of monitoring the endogenous biochemistry of diffusing proteins within live cells with single molecule resolution.

Probing molecular dynamics at the nanoscale via an individual paramagnetic centre

We demonstrate a protocol using individual nitrogen-vacancy centres in diamond to observe the time evolution of proton spins from organic molecules located a few nanometres from the diamond surface. The protocol records temporal correlations among the interacting protons, and thus is sensitive to the local dynamics via its impact on the nuclear spin relaxation and interaction with the nitrogen vacancy. We gather information on the nanoscale rotational and translational diffusion dynamics by analysing the time dependence of the nuclear magnetic resonance signal. Applying this technique to liquid and solid samples, we find evidence that liquid samples form a semi-solid layer of 1.5-nm thickness on the surface of diamond, where translational diffusion is suppressed while rotational diffusion remains present. Extensions of the present technique could be exploited to highlight the chemical composition of molecules tethered to the diamond surface or to investigate thermally or chemically activated dynamical processes such as molecular folding.

Nitrogen vacancy centres in diamond form spin-1 defects which may be exploited as sensitive probes of nanoscale magnetic phenomena. Here, the authors use individual nitrogen vacancies to perform nuclear magnetic resonance measurements of the ¹H spins of adsorbed organic molecules.

Fluorescence recovery after photobleaching in material and life sciences: putting theory into practice

Fluorescence recovery after photobleaching (FRAP) is a versatile tool for determining diffusion and interaction/binding properties in biological and material sciences. An understanding of the mechanisms controlling the diffusion requires a deep understanding of structure-interaction-diffusion relationships. In cell biology, for instance, this applies to the movement of proteins and lipids in the plasma membrane, cytoplasm and nucleus. In industrial applications related to pharmaceutics, foods, textiles, hygiene products and cosmetics, the diffusion of solutes and solvent molecules contributes strongly to the properties and functionality of the final product. All these systems are heterogeneous, and accurate quantification of the mass transport processes at the local level is therefore essential to the understanding of the properties of soft (bio)materials. FRAP is a commonly used fluorescence microscopy-based technique to determine local molecular transport at the micrometer scale. A brief high-intensity laser pulse is locally applied to the sample, causing substantial photobleaching of the fluorescent molecules within the illuminated area. This causes a local concentration gradient of fluorescent molecules, leading to diffusional influx of intact fluorophores from the local surroundings into the bleached area. Quantitative information on the molecular transport can be extracted from the time evolution of the fluorescence recovery in the bleached area using a suitable model. A multitude of FRAP models has been developed over the years, each based on specific assumptions. This makes it challenging for the non-specialist to decide which model is best suited for a particular application. Furthermore, there are many subtleties in performing accurate FRAP experiments. For these reasons, this review aims to provide an extensive tutorial covering the essential theoretical and practical aspects so as to enable accurate quantitative FRAP experiments for molecular transport measurements in soft (bio)materials.

Tracking single-particle rotation during macrophage uptake

We investigated the rotational dynamics of single microparticles during their internalization by macrophage cells. The microparticles used were triblock patchy particles that display two fluorescent patches on their two poles. The optical anisotropy made it possible to directly visualize and quantify the orientation and rotation of the particles. We show that particles exhibit a mixture of fast and slow rotation as they are uptaken by macrophages and transiently undergo directional rotation during their entry into the cell. The size of the particles and the surface presentation of ligands exerted a negligible influence on this heterogeneity of particle rotation.

Chromosomal locus tracking with proper accounting of static and dynamic errors

The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object's motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics ("static error") and motion blur due to finite exposure time ("dynamic error") on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors.

Photothermal raster image correlation spectroscopy of gold nanoparticles in solution and on live cells

Raster image correlation spectroscopy (RICS) measures the diffusion of fluorescently labelled molecules from stacks of confocal microscopy images by analysing correlations within the image. RICS enables the observation of a greater and, thus, more representative area of a biological system as compared to other single molecule approaches. Photothermal microscopy of gold nanoparticles allows long-term imaging of the same labelled molecules without photobleaching. Here, we implement RICS analysis on a photothermal microscope. The imaging of single gold nanoparticles at pixel dwell times short enough for RICS (60 μs) with a piezo-driven photothermal heterodyne microscope is demonstrated (photothermal raster image correlation spectroscopy, PhRICS). As a proof of principle, PhRICS is used to measure the diffusion coefficient of gold nanoparticles in glycerol : water solutions. The diffusion coefficients of the nanoparticles measured by PhRICS are consistent with their size, determined by transmission electron microscopy. PhRICS was then used to probe the diffusion speed of gold nanoparticle-labelled fibroblast growth factor 2 (FGF2) bound to heparan sulfate in the pericellular matrix of live fibroblast cells. The data are consistent with previous single nanoparticle tracking studies of the diffusion of FGF2 on these cells. Importantly, the data reveal faster FGF2 movement, previously inaccessible by photothermal tracking, and suggest that inhomogeneity in the distribution of bound FGF2 is dynamic.

Subdiffusion in an external potential: Anomalous effects hiding behind normal behavior

We propose a model of subdiffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the dramatic change of particles behavior compared to the standard continuous time random walk model in the long time limit. Constant force leads to the transition from non-ergodic subdiffusion to ergodic diffusive behavior. However, we show this behavior remains anomalous in a sense that the diffusion coefficient depends on the external force and on the anomalous exponent. For quadratic potential we find that the system remains non-ergodic. The anomalous exponent in this case defines not only the speed of convergence but also the stationary distribution which is different from standard Boltzmann equilibrium.

Extracting physics of life at the molecular level: A review of single-molecule data analyses

Studying individual biomolecules at the single-molecule level has proved very insightful recently. Single-molecule experiments allow us to probe both the equilibrium and nonequilibrium properties as well as make quantitative connections with ensemble experiments and equilibrium thermodynamics. However, it is important to be careful about the analysis of single-molecule data because of the noise present and the lack of theoretical framework for processes far away from equilibrium. Biomolecular motion, whether it is free in solution, on a substrate, or under force, involves thermal fluctuations in varying degrees, which makes the motion noisy. In addition, the noise from the experimental setup makes it even more complex. The details of biologically relevant interactions, conformational dynamics, and activities are hidden in the noisy single-molecule data. As such, extracting biological insights from noisy data is still an active area of research. In this review, we will focus on analyzing both fluorescence-based and force-based single-molecule experiments and gaining biological insights at the single-molecule level. Inherently nonequilibrium nature of biological processes will be highlighted. Simulated trajectories of biomolecular diffusion will be used to compare and validate various analysis techniques.

Introduction: membrane properties (good) for life

Membranes protect cells from the surrounding environment but also provide a means for the optimization of processes such as metabolism, signalling, or mitogenesis. Membrane structure and function is determined by its molecular composition. How lipid species define membrane properties is discussed in this introductory chapter.

In situ single molecule imaging of cell membranes: linking basic nanotechniques to cell biology, immunology and medicine

The cell membrane, which consists of a viscous phospholipid bilayer, different kinds of proteins and various nano/micrometer-sized domains, plays a very important role in ensuring the stability of the intracellular environment and the order of cellular signal transductions. Exploring the precise cell membrane structure and detailed functions of the biomolecules in a cell membrane would be helpful to understand the underlying mechanisms involved in cell membrane signal transductions, which could further benefit research into cell biology, immunology and medicine. The detection of membrane biomolecules at the single molecule level can provide some subtle information about the molecular structure and the functions of the cell membrane. In particular, information obtained about the molecular mechanisms and other information at the single molecule level are significantly different from that detected from a large amount of biomolecules at the large-scale through traditional techniques, and can thus provide a novel perspective for the study of cell membrane structures and functions. However, the precise investigations of membrane biomolecules prompts researchers to explore cell membranes at the single molecule level by the use of in situ imaging methods, as the exact conformation and functions of biomolecules are highly controlled by the native cellular environment. Recently, the in situ single molecule imaging of cell membranes has attracted increasing attention from cell biologists and immunologists. The size of biomolecules and their clusters on the cell surface are set at the nanoscale, which makes it mandatory to use high- and super-resolution imaging techniques to realize the in situ single molecule imaging of cell membranes. In the past few decades, some amazing imaging techniques and instruments with super resolution have been widely developed for molecule imaging, which can also be further employed for the in situ single molecule imaging of cell membranes. In this review, we attempt to summarize the characteristics of these advanced techniques for use in the in situ single molecule imaging of cell membranes. We believe that this work will help to promote the technological and methodological developments of super-resolution techniques for the single molecule imaging of cell membranes and help researchers better understand which technique is most suitable for their future exploring of membrane biomolecules; ultimately promoting further developments in cell biology, immunology and medicine.

Dark-field-based observation of single-nanoparticle dynamics on a supported lipid bilayer for in situ analysis of interacting molecules and nanoparticles

Observation of single plasmonic nanoparticles in reconstituted biological systems allows us to obtain snapshots of dynamic processes between molecules and nanoparticles with unprecedented spatiotemporal resolution and single-molecule/single-particle-level data acquisition. This Concept is intended to introduce nanoparticle-tethered supported lipid bilayer platforms that allow for the dynamic confinement of nanoparticles on a two-dimensional fluidic surface. The dark-field-based long-term, stable, real-time observation of freely diffusing plasmonic nanoparticles on a lipid bilayer enables one to extract a broad range of information about interparticle and molecular interactions throughout the entire reaction period. Herein, we highlight important developments in this context to provide ideas on how molecular interactions can be interpreted by monitoring dynamic behaviors and optical signals of laterally mobile nanoparticles.

From fast fluorescence imaging to molecular diffusion law on live cell membranes in a commercial microscope

It has become increasingly evident that the spatial distribution and the motion of membrane components like lipids and proteins are key factors in the regulation of many cellular functions. However, due to the fast dynamics and the tiny structures involved, a very high spatio-temporal resolution is required to catch the real behavior of molecules. Here we present the experimental protocol for studying the dynamics of fluorescently-labeled plasma-membrane proteins and lipids in live cells with high spatiotemporal resolution. Notably, this approach doesn't need to track each molecule, but it calculates population behavior using all molecules in a given region of the membrane. The starting point is a fast imaging of a given region on the membrane. Afterwards, a complete spatio-temporal autocorrelation function is calculated correlating acquired images at increasing time delays, for example each 2, 3, n repetitions. It is possible to demonstrate that the width of the peak of the spatial autocorrelation function increases at increasing time delay as a function of particle movement due to diffusion. Therefore, fitting of the series of autocorrelation functions enables to extract the actual protein mean square displacement from imaging (iMSD), here presented in the form of apparent diffusivity vs average displacement. This yields a quantitative view of the average dynamics of single molecules with nanometer accuracy. By using a GFP-tagged variant of the Transferrin Receptor (TfR) and an ATTO488 labeled 1-palmitoyl-2-hydroxy-sn-glycero-3-phosphoethanolamine (PPE) it is possible to observe the spatiotemporal regulation of protein and lipid diffusion on µm-sized membrane regions in the micro-to-milli-second time range.

Dynamics of the serine chemoreceptor in the Escherichia coli inner membrane: a high-speed single-molecule tracking study

We investigated the mobility of the polar localized serine chemoreceptor, Tsr, labeled by the fluorescent protein Venus in the inner membrane of live Escherichia coli cells at observation rates up to 1000 Hz. A fraction (7%) of all Tsr molecules shows free diffusion over the entire cell surface with an average diffusion coefficient of 0.40 ± 0.01 μm(2) s(-1). The remaining molecules were found to be ultimately confined in compartments of size 290 ± 15 nm and showed restricted diffusion at an inner barrier found at 170 ± 10 nm. At the shortest length-scales (<170 nm), all Tsr molecules diffuse equally. Disruption of the cytoskeleton and rounding of the cells resulted in an increase in the mobile fraction of Tsr molecules and a fragmenting of the previously polar cluster of Tsr consistent with a curvature-based mechanism of Tsr cluster maintenance.

Single-molecule analysis of diffusion and trapping of STIM1 and Orai1 at endoplasmic reticulum-plasma membrane junctions

STIM1 and Orai1 move to endoplasmic reticulum–plasma membrane (ER-PM) junctions to trigger store-operated Ca²⁺ entry. Single-molecule tracking reveals pure diffusion of STIM1 in the ER, subdiffusion of Orai1 in the PM, and trapping at junctions via STIM-Orai binding. STIM-Orai binding is loose, generating free proteins that can exchange freely with extrajunctional pools.

Following endoplasmic reticulum (ER) Ca²⁺ depletion, STIM1 and Orai1 complexes assemble autonomously at ER–plasma membrane (PM) junctions to trigger store-operated Ca²⁺ influx. One hypothesis to explain this process is a diffusion trap in which activated STIM1 diffusing in the ER becomes trapped at junctions through interactions with the PM, and STIM1 then traps Orai1 in the PM through binding of its calcium release-activated calcium activation domain. We tested this model by analyzing STIM1 and Orai1 diffusion using single-particle tracking, photoactivation of protein ensembles, and Monte Carlo simulations. In resting cells, STIM1 diffusion is Brownian, while Orai1 is slightly subdiffusive. After store depletion, both proteins slow to the same speeds, consistent with complex formation, and are confined to a corral similar in size to ER–PM junctions. While the escape probability at high STIM:Orai expression ratios is <1%, it is significantly increased by reducing the affinity of STIM1 for Orai1 or by expressing the two proteins at comparable levels. Our results provide direct evidence that STIM-Orai complexes are trapped by their physical connections across the junctional gap, but also reveal that the complexes are surprisingly dynamic, suggesting that readily reversible binding reactions generate free STIM1 and Orai1, which engage in constant diffusional exchange with extrajunctional pools.

Generalized similarity, renormalization groups, and nonlinear clocks for multiscaling

Fixed points of the renormalization group operator Rp,rX(t)≡X(rt)/rp are said to be p-self-similar. Here X(t) is an arbitrary stochastic process. The concept of a p-self-similar process is generalized via the renormalization group operator RF,GX(t)=F[X(G(t))], where F and G are bijections on (-∞,∞) and [0,∞), respectively. If X(t) is a fixed point of RF,G, then X(t) is said to be (F,G)-self-similar. We say Y(t) is (F,G)-X(t)-similar if RF,GX(t)=Y(t) in distribution. Exit time distributions and finite-size Lyapunov exponents were obtained for these latter processes. A power law multiscaling process is defined with a multipower-law clock. This process is employed to statistically represent diffusion in a nanopore, a monolayer fluid confined between atomically structured surfaces. The tools presented provide a straightforward method to statistically represent any multiscaling process in time.

Molecular probes to visualize the location, organization and dynamics of lipids

Cellular lipids play crucial roles in the cell, including in energy storage, the formation of cellular membranes, and in signaling and vesicular trafficking. To understand the functions and characteristics of lipids within cells, various methods to image lipids have been established. In this Commentary, we discuss the four main types of molecular probes that have significantly contributed to our understanding of the cell biology of lipids. In particular, genetically encoded biosensors and antibodies will be discussed, and how they have been used extensively with traditional light and electron microscopy to determine the subcellular localization of lipids and their spatial and temporal regulation. We highlight some of the recent studies that have investigated the distribution of lipids and their ability to cluster using super-resolution and electron microscopy. We also examine methods for analyzing the movement and dynamics of lipids, including single-particle tracking (SPT), fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS). Although the combination of these lipid probes and the various microscopic techniques is very powerful, we also point out several potential caveats and limitations. Finally, we discuss the need for new probes for a variety of phospholipids and cholesterol.

Bayesian decision tree for the classification of the mode of motion in single-molecule trajectories

Membrane proteins move in heterogeneous environments with spatially (sometimes temporally) varying friction and with biochemical interactions with various partners. It is important to reliably distinguish different modes of motion to improve our knowledge of the membrane architecture and to understand the nature of interactions between membrane proteins and their environments. Here, we present an analysis technique for single molecule tracking (SMT) trajectories that can determine the preferred model of motion that best matches observed trajectories. The method is based on Bayesian inference to calculate the posteriori probability of an observed trajectory according to a certain model. Information theory criteria, such as the Bayesian information criterion (BIC), the Akaike information criterion (AIC), and modified AIC (AICc), are used to select the preferred model. The considered group of models includes free Brownian motion, and confined motion in 2nd or 4th order potentials. We determine the best information criteria for classifying trajectories. We tested its limits through simulations matching large sets of experimental conditions and we built a decision tree. This decision tree first uses the BIC to distinguish between free Brownian motion and confined motion. In a second step, it classifies the confining potential further using the AIC. We apply the method to experimental Clostridium Perfingens [Formula: see text]-toxin (CP[Formula: see text]T) receptor trajectories to show that these receptors are confined by a spring-like potential. An adaptation of this technique was applied on a sliding window in the temporal dimension along the trajectory. We applied this adaptation to experimental CP[Formula: see text]T trajectories that lose confinement due to disaggregation of confining domains. This new technique adds another dimension to the discussion of SMT data. The mode of motion of a receptor might hold more biologically relevant information than the diffusion coefficient or domain size and may be a better tool to classify and compare different SMT experiments.

Tracking of single receptor molecule mobility in neuronal membranes: a quick theoretical and practical guide

Single-molecule detection enables us to visualise the real-time dynamics of individual molecules in live cells. We review the recent advancements in single-molecule fluorescence tracking of receptor protein mobility in the neuronal membrane. First, we discuss the practical consideration of single-molecule tracking in neurones, including the choice of cells and possible fluorescent labelling, as well as the appropriate optical set-up and imaging technology. We then describe the analysis of the single-molecule imaging data, including its theoretical and practical aspects of and relevant estimations of the biophysical parameters. Finally, we provide an example of a single-molecule tracking study in neuroendocrinology and highlight the next frontiers of single-molecule detection technologies.

Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes

Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concentration of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is observed to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent associated with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations associated with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically observed in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the physical limits of protein motion. Our results suggest that protein concentration is anything but constant in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.

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.

A Bright Light to Reveal Mobility: Single Quantum Dot Tracking Reveals Membrane Dynamics and Cellular Mechanisms

This perspective describes recent progress in single quantum dot techniques, with an emphasis on their applications in exploring membrane dynamics and cellular mechanisms. In these cases, conventional population measurements, such as fluorescence recovery after photobleaching, yield only a mean value on an ensemble or bulk collection of molecules, where the behavior of individual proteins and vehicles is missing. In recent years, the single quantum dot imaging approach has been introduced as a sub-category of single molecule fluorescent techniques to reveal single protein/vehicle dynamics in real-time. One of the major advantages of using single quantum dots is the high signal-to-noise ratio originating from their unique photophysical properties such as extraordinarily high molar extinction coefficients and large effective Stokes shifts. In addition to a brief overview on the principle of single quantum dot imaging techniques, we highlight recent discoveries and discuss future directions in the field.

Superdiffusive transport by multivalent molecular walkers moving under load

We introduce a model for translational molecular motors to demonstrate that a multivalent catalytic walker with flexible, uncoordinated legs can transform the free energy of surface-bound substrate sites into mechanical work and undergo biased, superdiffusive motion, even in opposition to an external load force. The walker in the model lacks any inherent orientation of body or track, and its legs have no chemomechanical coupling other than the passive constraint imposed by their connection to a common body. Yet, under appropriate kinetic conditions, the walker's motion is biased in the direction of unvisited sites, which allows the walker to move nearly ballistically away from the origin as long as a local supply of unmodified substrate sites is available. The multivalent random walker model is mathematically formulated as a continuous-time Markov process and is studied numerically. We use Monte Carlo simulations to generate ensemble estimates of the mean squared displacement and mean work done for this nonergodic system. Our results show that a residence time bias between visited and unvisited sites leads to superdiffusive motion over significant times and distances. This mechanism can be used to adapt any enzyme-substrate system with appropriate kinetics for use as a functional chemical implementation of a molecular motor, without the need for structural anisotropy or conformationally mediated chemomechanical coordination.

Single-molecule tracking of mRNA in living cells

Some mRNAs localize to specific regions within eukaryotic cells to express their functions. The movement and localization of mRNA molecules provides valuable information about how they concentrate to particular regions. Recent technical advances in optical microscopy and image analysis algorithms enable real-time tracking of single mRNA molecules in living cells. This chapter presents the methods to visualize and track single β-actin mRNA molecules that localize at the leading edge of chicken embryo fibroblasts. Furthermore, this chapter presents an analysis approach for single-molecule tracking data to extract quantitative information about the microenvironments of the mRNA molecules.

A critical survey of methods to detect plasma membrane rafts

The plasma membrane is still one of the enigmatic cellular structures. Although the microscopic structure is getting clearer, not much is known about the organization at the nanometre level. Experimental difficulties have precluded unambiguous approaches, making the current picture rather fuzzy. In consequence, a variety of different membrane models has been proposed over the years, on the basis of different experimental strategies. Recent data obtained via high-resolution single-molecule microscopy shed new light on the existing hypotheses. We thus think it is a good time for reviewing the consistency of the existing models with the new data. In this paper, we summarize the available models in ten propositions, each of which is discussed critically with respect to the applied technologies and the strengths and weaknesses of the approaches. Our aim is to provide the reader with a sound basis for his own assessment. We close this chapter by exposing our picture of the membrane organization at the nanoscale.

Single-molecule imaging in live bacteria cells

Bacteria, such as Escherichia coli and Caulobacter crescentus, are the most studied and perhaps best-understood organisms in biology. The advances in understanding of living systems gained from these organisms are immense. Application of single-molecule techniques in bacteria have presented unique difficulties owing to their small size and highly curved form. The aim of this review is to show advances made in single-molecule imaging in bacteria over the past 10 years, and to look to the future where the combination of implementing such high-precision techniques in well-characterized and controllable model systems such as E. coli could lead to a greater understanding of fundamental biological questions inaccessible through classic ensemble methods.

Anomalous dynamics in 2D polymer melts

The dynamics in polymer monolayers where chains are strongly confined and adopt 2D conformations are drastically different to those in the bulk. It is shown that viscoelastic hydrodynamic interactions play a major role defining the anomalous chain diffusion properties in such systems where chains cannot cross each other. We developed a quantitative analytical theory of polymer subdiffusion in 2D systems revealing a complex behavior controlled by a delicate interplay of inertial, viscoelastic hydrodynamic interactions, finite-box-size and frictional effects. The theory is fully supported by extensive momentum-conserving and Langevin molecular-dynamics simulation data explaining the highly cooperative character of 2D polymer motions.

Membrane cholesterol strongly influences confined diffusion of prestin

Prestin is the membrane motor protein that drives outer hair cell (OHC) electromotility, a process that is essential for mammalian hearing. Prestin function is sensitive to membrane cholesterol levels, and numerous studies have suggested that prestin localizes in cholesterol-rich membrane microdomains. Previously, fluorescence recovery after photobleaching experiments were performed in HEK cells expressing prestin-GFP after cholesterol manipulations, and revealed evidence of transient confinement. To further characterize this apparent confined diffusion of prestin, we conjugated prestin to a photostable fluorophore (tetramethylrhodamine) and performed single-molecule fluorescence microscopy. Using single-particle tracking, we determined the microscopic diffusion coefficient from the full time course of the mean-squared deviation. Our results indicate that prestin undergoes diffusion in confinement regions, and that depletion of membrane cholesterol increases confinement size and decreases confinement strength. By interpreting the data in terms of a mathematical model of hop-diffusion, we quantified these cholesterol-induced changes in membrane organization. A complementary analysis of the distribution of squared displacements confirmed that cholesterol depletion reduces prestin confinement. These findings support the hypothesis that prestin function is intimately linked to membrane organization, and further promote a regulatory role for cholesterol in OHC and auditory function.

Investigative and clinical applications of synthetic immune synapses

The immune synapse (IS) has emerged as a compelling model of cell-cell communication. This interface between a T cell and antigen-presenting cell (APC) serves as a key point in coordinating the immune response. A distinguishing feature of this interface is that juxtacrine signaling molecules form complex patterns that are defined at micrometer and submicrometer scales. Moreover, these patterns are highly dynamic. While cellular and molecular approaches have provided insight into the influence of these patterns on cell-cell signaling, replacing the APC with a synthetic, micro/nanoengineered surface promises a new level of sophistication to these studies. Micropatterning of multiple ligands onto a surface, for example, allowed the direct demonstration that T cells can sense and respond to microscale geometry of the IS. Supported lipid bilayers have captured the lateral mobility of natural ligands, allowing insight into this complex property of the cell-cell interface in model systems. Finally, engineered surfaces have allowed the study of forces and mechanosensing in T cell activation, an emerging area of immune cell research. In addition to providing new insight into biophysical principles, investigations into IS function may allow control over ex vivo T cell expansion. Bioreactors based on these concepts may find immediate application in enhancing cellular-based immunotherapy.

Single-molecule study of molecular mobility in the cytoplasm of Escherichia coli

The cytoplasm of bacterial cells is filled with individual molecules and molecular complexes that rely on diffusion to bring them together for interaction. The mobility of molecules in the cytoplasm has been characterized by several techniques mainly using fluorescent probes and ensemble methods. In order to probe the microenvrionment inside the cytoplasm as viewed by an individual molecule, we have studied single green fluorescent proteins (GFPs) diffusing in the cytoplasm of Escherichia coli cells at observation at rates ranging from 60 to 1000 Hz. Over long times the diffusion shows confinement due to the geometry of the cells themselves. A simulation in model cells using the actual distribution of cell sizes found in the experiments describes accurately the experimental results as well as reveals a short time diffusion coefficient that agrees well with that determined by ensemble methods. Higher short time diffusion coefficients can be obtained by filling the simulated cell with small spheres modeling cytoplasmic molecules and, depending on the density of particles included in the modeled cytoplasm, can approach the diffusion coefficient of GFPs found in water. Thus, single-molecule tracking combined with analysis using simple simulation of Brownian motion is able to reveal the main contributors to the GFP mobility in the cytoplasm of E. coli.

Tracing Molecular Propagation in Dextran Solutions by Pulsed Field Gradient NMR

We have exploited the pulsed field gradient (PFG) technique of NMR to measure molecular diffusion in aqueous solutions of a mixture of dextran molecules. From detailed studies by fluorescence correlation spectroscopy (FCS), the lighter component of such mixtures is known to undergo subdiffusion, up to diffusion path lengths on the order of 0.5 μm. Our studies provide clear evidence of a crossover to normal diffusion for diffusion path lengths from this range up to about 1 μm.