STED nanoscopy reveals molecular details of cholesterol- and cytoskeleton-modulated lipid interactions in living cells

Details about molecular membrane dynamics in living cells, such as lipid-protein interactions, are often hidden from the observer because of the limited spatial resolution of conventional far-field optical microscopy. The superior spatial resolution of stimulated emission depletion (STED) nanoscopy can provide new insights into this process. The application of fluorescence correlation spectroscopy (FCS) in focal spots continuously tuned down to 30 nm in diameter distinguishes between free and anomalous molecular diffusion due to, for example, transient binding of lipids to other membrane constituents, such as lipids and proteins. We compared STED-FCS data recorded on various fluorescent lipid analogs in the plasma membrane of living mammalian cells. Our results demonstrate details about the observed transient formation of molecular complexes. The diffusion characteristics of phosphoglycerolipids without hydroxyl-containing headgroups revealed weak interactions. The strongest interactions were observed with sphingolipid analogs, which showed cholesterol-assisted and cytoskeleton-dependent binding. The hydroxyl-containing headgroup of gangliosides, galactosylceramide, and phosphoinositol assisted binding, but in a much less cholesterol- and cytoskeleton-dependent manner. The observed anomalous diffusion indicates lipid-specific transient hydrogen bonding to other membrane molecules, such as proteins, and points to a distinct connectivity of the various lipids to other membrane constituents. This strong interaction is different from that responsible for forming cholesterol-dependent, liquid-ordered domains in model membranes.     

Dynamics of Small Molecules in a Dense Polymer Matrix: Molecular Dynamics Studies

Abstract

The anomalous diffusion regime appearing in the self-diffusion of small molecules in bulk amorphous polymers has been extensively studied by molecular dynamics simulations. A rather long simulation of duration ～ 10 ^?8 s is performed on a polyethylene-like simple polymer model containing either oxygen molecules or helium atoms as a diffusant. Dynamic properties evaluated for these diffusants are the mean-square displacement, the van Hove self correlation function, and the self part of the density autocorrelation. It is first confirmed that the anomalous diffusion regime appears in a few hundred picoseconds for oxygen molecule, while the Einstein relation adopted beyond this regime results in the self-diffusion coefficient of the order of ～ 10^?5 cm²/s. This anomaly is still observed for helium that diffuses much faster than oxygen. In the anomalous diffusion regime, it is found that the correlation functions for the two diffusants show characteristic features and become essentially the same as time is scaled appropriately. These features allow the estimation of the two characteristic spatial scales which are probably dominated by the microstructure of the polymer matrix, namely, the cage size and the distance between adjacent cages. The time dependence of the mean-square displacements of the two diffusants can be well interpreted by these characteristic spatial scales as time is scaled with the self-diffusion coefficients. It is shown that the anomalous diffusion regime arises from the inhomogeneous microstructure of the polymer matrix.     

Nanoscale organization and dynamics of the siglec CD22 cooperate with the cytoskeleton in restraining BCR signalling

Receptor organization and dynamics at the cell membrane are important factors of signal transduction regulation. Using super‐resolution microscopy and single‐particle tracking, we show how the negative coreceptor CD22 works with the cortical cytoskeleton in restraining BCR signalling. In naïve B cells, we found endogenous CD22 to be highly mobile and organized into nanodomains. The landscape of CD22 and its lateral diffusion were perturbed either in the absence of CD45 or when the CD22 lectin domain was mutated. To understand how a relatively low number of CD22 molecules can keep BCR signalling in check, we generated Brownian dynamic simulations and supported them with ex vivo experiments. This combined approach suggests that the inhibitory function of CD22 is influenced by its nanoscale organization and is ensured by its fast diffusion enabling a “global BCR surveillance” at the plasma membrane.     

Spatial Structure and Diffusive Dynamics from Single-Particle Trajectories Using Spline Analysis

Single-particle tracking of biomolecular probes has provided a wealth of information about intracellular trafficking and the dynamics of proteins and lipids in the cell membrane. Conventional mean-square displacement (MSD) analysis of single-particle trajectories often assumes that probes are moving in a uniform environment. However, the observed two-dimensional motion of probe particles is influenced by the local three-dimensional geometry of the cell membrane and intracellular structures, which are rarely flat at the submicron scale. This complex geometry can lead to spatially confined trajectories that are difficult to analyze and interpret using conventional two-dimensional MSD analysis. Here we present two methods to analyze spatially confined trajectories: spline-curve dynamics analysis, which extends conventional MSD analysis to measure diffusive motion in confined trajectories; and spline-curve spatial analysis, which measures spatial structures smaller than the limits of optical resolution. We show, using simulated random walks and experimental trajectories of quantum dot probes, that differences in measured two-dimensional diffusion coefficients do not always reflect differences in underlying diffusive dynamics, but can instead be due to differences in confinement geometries of cellular structures.     

Development of time-integrated multipoint moment analysis for spatially resolved fluctuation spectroscopy with high time resolution

Spatial gradients in the behaviors of soluble proteins are thought to underlie many phenomena in cell and developmental biology, but the nature and even the existence of these gradients are often unclear because few techniques can adequately characterize them. Methods with sufficient temporal resolution to study the dynamics of diffusing molecules can only sample relatively small regions, whereas methods that are capable of imaging larger areas cannot probe fast timescales. To overcome these limitations, we developed and implemented time-integrated multipoint moment analysis (TIMMA), a form of fluorescence fluctuation spectroscopy that is capable of probing timescales down to 20 μs at hundreds of different locations simultaneously in a sample. We show that TIMMA can be used to measure the diffusion of small-molecule dyes and fluorescent colloids, and that it can create spatial maps of the behavior of soluble fluorescent proteins throughout mammalian tissue culture cells. We also demonstrate that TIMMA can characterize internal gradients in the diffusion of freely moving proteins in single cells.     

Diffusion, Transport, and Cell Membrane Organization Investigated by Imaging Fluorescence Cross-Correlation Spectroscopy

Cell membrane organization is dynamic and is assumed to have different characteristic length scales. These length scales, which are influenced by lipid and protein composition as well as by the cytoskeleton, can range from below the optical resolution limit (as with rafts or microdomains) to far above the resolution limit (as with capping phenomena or the formation of lipid “platforms”). The measurement of these membrane features poses a significant problem because membrane dynamics are on the millisecond timescale and are thus beyond the time resolution of conventional imaging approaches. Fluorescence correlation spectroscopy (FCS), a widely used spectroscopic technique to measure membrane dynamics, has the required time resolution but lacks imaging capabilities. A promising solution is the recently introduced method known as imaging total internal reflection (ITIR)-FCS, which can probe diffusion phenomena in lipid membranes with good temporal and spatial resolution. In this work, we extend ITIR-FCS to perform ITIR fluorescence cross-correlation spectroscopy (ITIR-FCCS) between pixel areas of arbitrary shape and derive a generalized expression that is applicable to active transport and diffusion. ITIR-FCCS is applied to model systems exhibiting diffusion, active transport, or a combination of the two. To demonstrate its applicability to live cells, we observe the diffusion of a marker, the sphingolipid-binding domain (SBD) derived from the amyloid peptide Aβ, on live neuroblastoma cells. We investigate the organization and dynamics of SBD-bound lipid microdomains under the conditions of cholesterol removal and cytoskeleton disruption.     

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Cell membranes display a range of receptors that bind ligands and activate signaling pathways. Signaling is characterized by dramatic changes in membrane molecular topography, including the co-clustering of receptors with signaling molecules and the segregation of other signaling molecules away from receptors. Electron microscopy of immunogold-labeled membranes is a critical technique to generate topographical information at the 5–10 nm resolution needed to understand how signaling complexes assemble and function. However, due to experimental limitations, only two molecular species can usually be labeled at a time. A formidable challenge is to integrate experimental data across multiple experiments where there are from 10 to 100 different proteins and lipids of interest and only the positions of two species can be observed simultaneously. As a solution, we propose the use of Markov random field (MRF) modeling to reconstruct the distribution of multiple cell membrane constituents from pair-wise data sets. MRFs are a powerful mathematical formalism for modeling correlations between states associated with neighboring sites in spatial lattices. The presence or absence of a protein of a specific type at a point on the cell membrane is a state. Since only two protein types can be observed, i.e., those bound to particles, and the rest cannot be observed, the problem is one of deducing the conditional distribution of a MRF with unobservable (hidden) states. Here, we develop a multiscale MRF model and use mathematical programming techniques to infer the conditional distribution of a MRF for proteins of three types from observations showing the spatial relationships between only two types. Application to synthesized data shows that the spatial distributions of three proteins can be reliably estimated. Application to experimental data provides the first maps of the spatial relationship between groups of three different signaling molecules. The work is an important step toward a more complete understanding of membrane spatial organization and dynamics during signaling.     

Single-molecule anisotropy imaging

A novel method, single-molecule anisotropy imaging, has been employed to simultaneously study lateral and rotational diffusion of fluorescence-labeled lipids on supported phospholipid membranes. In a fluid membrane composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, in which the rotational diffusion time is on the order of the excited-state lifetime of the fluorophore rhodamine, a rotational diffusion constant, D(rot) = 7 x 10(7) rad(2)/s, was determined. The lateral diffusion constant, measured by direct analysis of single-molecule trajectories, was D(lat) = 3.5 x 10(-8) cm(2)/s. As predicted from the free-volume model for diffusion, the results exhibit a significantly enhanced mobility on the nanosecond time scale. For membranes of DPPC lipids in the L(beta) gel phase, the slow rotational mobility permitted the direct observation of the rotation of individual molecules characterized by D(rot) = 1.2 rad(2)/s. The latter data were evaluated by a mean square angular displacement analysis. The technique developed here should prove itself profitable for imaging of conformational motions of individual proteins on the time scale of milliseconds to seconds.     

Computing the self-diffusion coefficient for TIP4P water

A molecular dynamics study was made for the TIP4P model of liquid water. Thermal dependences of water density and radial distribution functions were calculated for model verification. Different methods were used to calculate the self-diffusion coefficient, and assessed for sensitivity to molecular system size and trajectory length. The Green-Kubo formula deriving the diffusion coefficient from the velocity autocorrelation function is preferable in short MD simulations with a high sampling rate, whereas the Einstein equation for diffusion is the method of choice in long simulations. The latter approach yields more stable and reliable results, especially at very short times and for a small number of molecules, if the diffusion coefficient is estimated not from the limit ratio of mean squared displacement to time, but from the slope of the time plot of mean squared displacement.     

Variable-angle epifluorescence microscopy: a new way to look at protein dynamics in the plant cell cortex

Live-cell microscopy imaging of fluorescent-tagged fusion proteins is an essential tool for cell biologists. Total internal reflection fluorescence microscopy (TIRFM) has joined confocal microscopy as a complementary system for the imaging of cell surface protein dynamics in mammalian and yeast systems because of its high temporal and spatial resolution. Here we present an alternative to TIRFM, termed variable-angle epifluorescence microscopy (VAEM), for the visualization of protein dynamics at or near the plasma membrane of plant epidermal cells and root hairs in whole, intact seedlings that provides high-signal, low-background and near real-time imaging. VAEM uses highly oblique subcritical incident angles to decrease background fluorophore excitation. We discuss the utilities and advantages of VAEM for imaging of fluorescent fusion-tagged marker proteins in studying cortical cytoskeletal and membrane proteins. We believe that the application of VAEM will be an invaluable imaging tool for plant cell biologists.     

Superresolution imaging reveals structural features of EB1 in microtubule plus-end tracking

Visualization of specific molecules and their interactions in real time and space is essential to delineate how cellular dynamics and the signaling circuit are orchestrated. Spatial regulation of conformational dynamics and structural plasticity of protein interactions is required to rewire signaling circuitry in response to extracellular cues. We introduce a method for optically imaging intracellular protein interactions at nanometer spatial resolution in live cells, using photoactivatable complementary fluorescent (PACF) proteins. Subsets of complementary fluorescent protein molecules were activated, localized, and then bleached; this was followed by the assembly of superresolution images from aggregate position of sum interactive molecules. Using PACF, we obtained precise localization of dynamic microtubule plus-end hub protein EB1 dimers and their distinct distributions at the leading edges and in the cell bodies of migrating cells. We further delineated the structure–function relationship of EB1 by generating EB1-PACF dimers (EB1^wt:EB1^wt, EB1^wt:EB1^mt, and EB1^mt:EB1^mt) and imaging their precise localizations in culture cells. Surprisingly, our analyses revealed critical role of a previously uncharacterized EB1 linker region in tracking microtubule plus ends in live cells. Thus PACF provides a unique approach to delineating spatial dynamics of homo- or heterodimerized proteins at the nanometer scale and establishes a platform to report the precise regulation of protein interactions in space and time in live cells.     

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.     

Spatial-temporal studies of membrane dynamics: scanning fluorescence correlation spectroscopy (SFCS)

Giant unilamellar vesicles (GUVs) have been widely used as a model membrane system to study membrane organization, dynamics, and protein-membrane interactions. Most recent studies have relied on imaging methods, which require good contrast for image resolution. Multiple sequential image processing only detects slow components of membrane dynamics. We have developed a new fluorescence correlation spectroscopy (FCS) technique, termed scanning FCS (i.e., SFCS), which performs multiple FCS measurements simultaneously by rapidly directing the excitation laser beam in a uniform (circular) scan across the bilayer of the GUVs in a repetitive fashion. The scan rate is fast compared to the diffusion of the membrane proteins and even small molecules in the GUVs. Scanning FCS outputs a "carpet" of timed fluorescence intensity fluctuations at specific points along the scan. In this study, GUVs were assembled from rat kidney brush border membranes, which included the integral membrane proteins. Scanning FCS measurements on GUVs allowed for a straightforward detection of spatial-temporal interactions between the protein and the membrane based on the diffusion rate of the protein. To test for protein incorporation into the bilayers of the GUVs, antibodies against one specific membrane protein (NaPi II cotransporter) were labeled with ALEXA-488. Fluorescence images of the GUVs in the presence of the labeled antibody showed marginal fluorescence enhancement on the GUV membrane bilayers (poor image contrast and resolution). With the application of scanning FCS, the binding of the antibody to the GUVs was detected directly from the analysis of diffusion rates of the fluorescent antibody. The diffusion coefficient of the antibody bound to NaPi II in the GUVs was approximately 200-fold smaller than that in solution. Scanning FCS provided a simple, quantitative, yet highly sensitive method to study protein-membrane interactions.     

Fluorescence correlation spectroscopy in living cells

Fluorescence correlation spectroscopy (FCS) is an ideal analytical tool for studying concentrations, propagation, interactions and internal dynamics of molecules at nanomolar concentrations in living cells. FCS analyzes minute fluorescence-intensity fluctuations about the equilibrium of a small ensemble (<10(3)) of molecules. These fluctuations act like a 'fingerprint' of a molecular species detected when entering and leaving a femtoliter-sized optically defined observation volume created by a focused laser beam. In FCS the fluorescence fluctuations are recorded as a function of time and then statistically analyzed by autocorrelation analysis. The resulting autocorrelation curve yields a measure of self-similarity of the system after a certain time delay, and its amplitude describes the normalized variance of the fluorescence fluctuations. By fitting the curves to an appropriate physical model, this method provides precise information about a multitude of measurement parameters, including diffusion coefficients, local concentration, states of aggregation and molecular interactions. FCS operates in real time with diffraction-limited spatial and sub-microsecond temporal resolution. Assessing diverse molecular dynamics within the living cell is a challenge well met by FCS because of its single-molecule sensitivity and high dynamic resolution. For these same reasons, however, intracellular FCS measurements also harbor the large risk of collecting artifacts and thus producing erroneous data. Here we provide a step-by-step guide to the application of FCS to cellular systems, including methods for minimizing artifacts, optimizing measurement conditions and obtaining parameter values in the face of diverse and complex conditions of the living cell. A discussion of advantages and disadvantages of one-photon versus two-photon excitation for FCS is available in Supplementary Methods online.     

Membrane lateral mobility obstructed by polymer-tethered lipids studied at the single molecule level

Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single molecule fluorescence microscopy. The obstacles are well-controlled concentrations of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer molecules is well described by a percolating system with different percolation thresholds for lipids and proteins. Data analysis using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calculations reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concentrations. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the analysis of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concentrations of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few molecules.     

Membrane order and molecular dynamics associated with IgE receptor cross-linking in mast cells

Cholesterol-rich microdomains (or "lipid rafts") within the plasma membrane have been hypothesized to exist in a liquid-ordered phase and play functionally important roles in cell signaling; however, these microdomains defy detection using conventional imaging. To visualize domains and relate their nanostructure and dynamics to mast cell signaling, we use two-photon (760 nm and 960 nm) fluorescence lifetime imaging microscopy and fluorescence polarization anisotropy imaging, with comparative one-photon anisotropy imaging and single-point lifetime and anisotropy decay measurements. The inherent sensitivity of ultrafast excited-state dynamics and rotational diffusion to the immediate surroundings of a fluorophore allows for real-time monitoring of membrane structure and organization. When the high affinity receptor for IgE (FcepsilonRI) is extensively cross-linked with anti-IgE, molecules associated with cholesterol-rich microdomains (e.g., saturated lipids (the lipid analog diI-C(18) or glycosphingolipids)) and lipid-anchored proteins coredistribute with cross-linked IgE-FcepsilonRI. We find an enhancement in fluorescence lifetime and anisotropy of diI-C(18) and Alexa 488-labeled IgE-FcepsilonRI in the domains where these molecules colocalize. Our results suggest that fluorescence lifetime and, particularly, anisotropy permit us to correlate the recruitment of lipid molecules into more ordered domains that serve as platforms for IgE-mediated signaling.     

Mathematical Model for Spatial Segregation of the Rho-Family GTPases Based on Inhibitory Crosstalk

Cdc42, Rac, and Rho are small GTPases known to play a central role in signal transduction to the actin cytoskeleton. These proteins regulate cell motility, by affecting nucleation, uncapping, and depolymerization of actin filaments, and acto-myosin contractility. Studies of crosstalk and mutual feedbacks in these three proteins have led to a number of proposals for their interaction. At the same time, observations of the spatio-temporal dynamics of Rho-family proteins give evidence of spatial polarization and mutual exclusion between Cdc42/Rac and Rho. In this paper, we formulate a mathematical model to account for such observations, based on the known underlying biology of these proteins. We first investigate which of the crosstalk schemes proposed in the literature is consistent with observed dynamics, and then derive a simple model that can correctly describe these dynamics (assuming crosstalk is mediated via Rho GEFs). We show that cooperativity is an essential ingredient in the interactions of the proteins. The co-occurrence of a stable rest state with the possibility of fast spatial segregation can be related to bistability in a set of underlying ODEs in which the inactive forms of these proteins are fixed at a constant level. We show that the fast diffusion of the inactive forms is essential for stabilizing the transition fronts in the PDE formulation of the model, leading to robust spatial polarization, rather than traveling waves.     

Spatio-Temporal Dynamics of Hypoxia during Radiotherapy

Tumour hypoxia plays a pivotal role in cancer therapy for most therapeutic approaches from radiotherapy to immunotherapy. The detailed and accurate knowledge of the oxygen distribution in a tumour is necessary in order to determine the right treatment strategy. Still, due to the limited spatial and temporal resolution of imaging methods as well as lacking fundamental understanding of internal oxygenation dynamics in tumours, the precise oxygen distribution map is rarely available for treatment planing. We employ an agent-based in silico tumour spheroid model in order to study the complex, localized and fast oxygen dynamics in tumour micro-regions which are induced by radiotherapy. A lattice-free, 3D, agent-based approach for cell representation is coupled with a high-resolution diffusion solver that includes a tissue density-dependent diffusion coefficient. This allows us to assess the space- and time-resolved reoxygenation response of a small subvolume of tumour tissue in response to radiotherapy. In response to irradiation the tumour nodule exhibits characteristic reoxygenation and re-depletion dynamics which we resolve with high spatio-temporal resolution. The reoxygenation follows specific timings, which should be respected in treatment in order to maximise the use of the oxygen enhancement effects. Oxygen dynamics within the tumour create windows of opportunity for the use of adjuvant chemotherapeutica and hypoxia-activated drugs. Overall, we show that by using modelling it is possible to follow the oxygenation dynamics beyond common resolution limits and predict beneficial strategies for therapy and in vitro verification. Models of cell cycle and oxygen dynamics in tumours should in the future be combined with imaging techniques, to allow for a systematic experimental study of possible improved schedules and to ultimately extend the reach of oxygenation monitoring available in clinical treatment.     

The cell-type specificity of mitochondrial dynamics

Recent advances in mitochondrial imaging have revealed that in many cells mitochondria can be highly dynamic. They can undergo fission/fusion processes modulated by various mitochondria-associated proteins and also by conformational transitions in the inner mitochondrial membrane. Moreover, precise mitochondrial distribution can be achieved by their movement along the cytoskeleton, recruiting various connector and motor proteins. Such movement is evident in various cell types ranging from yeast to mammalian cells and serves to direct mitochondria to cellular regions of high ATP demand or to transport mitochondria destined for elimination. Existing data also demonstrate that many aspects of mitochondrial dynamics, morphology, regulation and intracellular organization can be cell type-/tissue-specific. In many cells like neurons, pancreatic cells, HL-1 cells, etc., complex dynamics of mitochondria include fission, fusion, small oscillatory movements of mitochondria, larger movements like filament extension, retraction, fast branching in the mitochondrial network and rapid long-distance intracellular translocation of single mitochondria. Alternatively, mitochondria can be rather fixed in other cells and tissues like adult cardiomyocytes or skeletal muscles with a very regular organelle organization between myofibrils, providing the bioenergetic basis for contraction. Adult cardiac cells show no displacement of mitochondria with only very small-amplitude rapid vibrations, demonstrating remarkable, cell type-dependent differences in the dynamics and spatial arrangement of mitochondria. These variations and the cell-type specificity of mitochondrial dynamics could be related to specific cellular functions and demands, also indicating a significant role of integrations of mitochondria with other intracellular systems like the cytoskeleton, nucleus and endoplasmic reticulum (ER).     

Statistical Analysis of Lateral Diffusion and Multistate Kinetics in Single-Molecule Imaging

Single-molecule trajectories of molecules on the membrane of living cells have indicated the possibility that the lateral mobility of individual molecules is variable with time. Such temporal variation in mobility may indicate intrinsic kinetics of multiple molecular states. To clarify the mechanisms of signal processing on the membrane, quantitative characterizations of such temporal variations are necessary. Here we propose a method to analyze and characterize the multiple states in lateral mobility and their transition kinetics from single-molecule trajectories based on a displacement probability density function and an autocorrelation function of squared displacements. We performed our method for three cases: a molecule with a single diffusion coefficient (D), a mixture of molecules in two states with different D-values, and a molecule switching between two states with different D-values. Our analysis of numerically generated trajectories successfully distinguished the three cases and estimated the characteristic parameters for mobility and the kinetics of state transitions. This method is applicable to single-molecule tracking analysis of molecules in multiple functional states with different lateral mobility on the membrane of living cells.