Classification of Dynamical Diffusion States in Single Molecule Tracking Microscopy

Single molecule tracking of membrane proteins by fluorescence microscopy is a promising method to investigate dynamic processes in live cells. Translating the trajectories of proteins to biological implications, such as protein interactions, requires the classification of protein motion within the trajectories. Spatial information of protein motion may reveal where the protein interacts with cellular structures, because binding of proteins to such structures often alters their diffusion speed. For dynamic diffusion systems, we provide an analytical framework to determine in which diffusion state a molecule is residing during the course of its trajectory. We compare different methods for the quantification of motion to utilize this framework for the classification of two diffusion states (two populations with different diffusion speed). We found that a gyration quantification method and a Bayesian statistics-based method are the most accurate in diffusion-state classification for realistic experimentally obtained datasets, of which the gyration method is much less computationally demanding. After classification of the diffusion, the lifetime of the states can be determined, and images of the diffusion states can be reconstructed at high resolution. Simulations validate these applications. We apply the classification and its applications to experimental data to demonstrate the potential of this approach to obtain further insights into the dynamics of cell membrane proteins.     

Transient directed motions of GABA(A) receptors in growth cones detected by a speed correlation index

Single-molecule tracking of membrane proteins has become an important tool for investigating dynamic processes in live cells, such as cell signaling, membrane compartmentation or trafficking. The extraction of relevant parameters, such as interaction times between molecular partners or confinement-zone sizes, from the trajectories of single molecules requires appropriate statistical methods. Here we report a new tool, the speed correlation index, designed to detect transient periods of directed motion within trajectories of diffusing molecules. The ability to detect such events in a wide range of biologically relevant parameter values (speed, diffusion coefficient, and durations of the directed period) was first established on simulated data. The method was next applied to analyze the trajectories of quantum-dot-labeled GABA(A) receptors in nerve growth cones. The use of the speed correlation index revealed that the receptors had a "conveyor belt" type of motion due to temporary interactions ( approximately 4.0 s) between the receptors and the microtubules, leading to an average directed motion (velocity approximately 0.3 mum s(-1)) in the growth-cone membrane. Our observations point to the possibility of a cytoskeleton-dependent redistribution of the sensing molecules in the membrane, which could play a role in the modulation of the cell response to external signals.     

Translational diffusion of individual class II MHC membrane proteins in cells

Single-molecule epifluorescence microscopy was used to observe the translational motion of GPI-linked and native I-E(k) class II MHC membrane proteins in the plasma membrane of CHO cells. The purpose of the study was to look for deviations from Brownian diffusion that might arise from barriers to this motion. Detergent extraction had suggested that these proteins may be confined to lipid microdomains in the plasma membrane. The individual I-E(k) proteins were visualized with a Cy5-labeled peptide that binds to a specific extracytoplasmic site common to both proteins. Single-molecule trajectories were used to compute a radial distribution of displacements, yielding average diffusion coefficients equal to 0.22 (GPI-linked I-E(k)) and 0.18 microm(2)/s (native I-E(k)). The relative diffusion of pairs of proteins was also studied for intermolecular separations in the range 0.3-1.0 microm, to distinguish between free diffusion of a protein molecule and diffusion of proteins restricted to a rapidly diffusing small domain. Both analyses show that motion is predominantly Brownian. This study finds no strong evidence for significant confinement of either GPI-linked or native I-E(k) in the plasma membrane of CHO cells.     

Detection of temporary lateral confinement of membrane proteins using single-particle tracking analysis.

Techniques such as single-particle tracking allow the characterization of the movements of single or very few molecules. Features of the molecular trajectories, such as confined diffusion or directed transport, can reveal interesting biological interactions, but they can also arise from simple Brownian motion. Careful analysis of the data, therefore, is necessary to identify interesting effects from pure random movements. A method was developed to detect temporary confinement in the trajectories of membrane proteins that cannot be accounted for by Brownian motion. This analysis was applied to trajectories of two lipid-linked members of the immunoglobulin superfamily, Thy-1 and a neural cell adhesion molecule (NCAM 125), and the results were compared with those for simulated random walks. Approximately 28% of the trajectories for both proteins exhibited periods of transient confinement, which were < 0.07% likely to arise from random movements. In contrast to these results, only 1.5% of the simulated trajectories showed confined periods. Transient confinement for both proteins lasted on average 8 s in regions that were approximately 280 nm in diameter.     

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.     

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 -toxin (CPT) 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 CPT 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.     

How do biomolecular systems speed up and regulate rates?

The viability of a biological system depends upon careful regulation of the rates of various processes. These rates have limits imposed by intrinsic chemical or physical steps (e.g., diffusion). These limits can be expanded by interactions and dynamics of the biomolecules. For example, (a) a chemical reaction is catalyzed when its transition state is preferentially bound to an enzyme; (b) the folding of a protein molecule is speeded up by specific interactions within the transition-state ensemble and may be assisted by molecular chaperones; (c) the rate of specific binding of a protein molecule to a cellular target can be enhanced by mechanisms such as long-range electrostatic interactions, nonspecific binding and folding upon binding; (d) directional movement of motor proteins is generated by capturing favorable Brownian motion through intermolecular binding energy; and (e) conduction and selectivity of ions through membrane channels are controlled by interactions and the dynamics of channel proteins. Simple physical models are presented here to illustrate these processes and provide a unifying framework for understanding speed attainment and regulation in biomolecular systems.     

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.     

Observing membrane protein diffusion at subnanometer resolution

Single sodium-driven rotors from a bacterial ATP synthase were embedded into a lipid membrane and observed in buffer solution at subnanometer resolution using atomic force microscopy (AFM). Time-lapse AFM topographs show the movement of single proteins within the membrane. Subsequent analysis of their individual trajectories, in consideration of the environment surrounding the moving protein, allow principal modes of the protein motion to be distinguished. Within one trajectory, individual proteins can undergo movements assigned to free as well as to obstacled diffusion. The diffusion constants of these two modes of motion are considerably different. Without the structural information about the membrane environment restricting the moving proteins, it would not be possible to reveal insight into these mechanisms. The high-resolution AFM topographs suggest that, in future studies, such data revealed under various physiological conditions will provide novel insights into molecular mechanisms that drive membrane protein assembly and supply excellent boundary conditions to model protein-protein arrangements.     

Fluorescence imaging of two-photon linear dichroism: cholesterol depletion disrupts molecular orientation in cell membranes

The plasma membrane of cells is an ordered environment, giving rise to anisotropic orientation and restricted motion of molecules and proteins residing in the membrane. At the same time as being an organized matrix of defined structure, the cell membrane is heterogeneous and dynamic. Here we present a method where we use fluorescence imaging of linear dichroism to measure the orientation of molecules relative to the cell membrane. By detecting linear dichroism as well as fluorescence anisotropy, the orientation parameters are separated from dynamic properties such as rotational diffusion and homo energy transfer (energy migration). The sensitivity of the technique is enhanced by using two-photon excitation for higher photo-selection compared to single photon excitation. We show here that we can accurately image lipid organization in whole cell membranes and in delicate structures such as membrane nanotubes connecting two cells. The speed of our wide-field imaging system makes it possible to image changes in orientation and anisotropy occurring on a subsecond timescale. This is demonstrated by time-lapse studies showing that cholesterol depletion rapidly disrupts the orientation of a fluorophore located within the hydrophobic region of the cell membrane but not of a surface bound probe. This is consistent with cholesterol having an important role in stabilizing and ordering the lipid tails within the plasma membrane.     

Dynamic Superresolution Imaging of Endogenous Proteins on Living Cells at Ultra-High Density

Versatile superresolution imaging methods, able to give dynamic information of endogenous molecules at high density, are still lacking in biological science. Here, superresolved images and diffusion maps of membrane proteins are obtained on living cells. The method consists of recording thousands of single-molecule trajectories that appear sequentially on a cell surface upon continuously labeling molecules of interest. It allows studying any molecules that can be labeled with fluorescent ligands including endogenous membrane proteins on living cells. This approach, named universal PAINT (uPAINT), generalizes the previously developed point-accumulation-for-imaging-in-nanoscale-topography (PAINT) method for dynamic imaging of arbitrary membrane biomolecules. We show here that the unprecedented large statistics obtained by uPAINT on single cells reveal local diffusion properties of specific proteins, either in distinct membrane compartments of adherent cells or in neuronal synapses.     

Tracking single proteins within cells

We present experiments in which single proteins were imaged and tracked within mammalian cells. Single proteins of R-phycoerythrin (RPE) were imaged by epifluorescence microscopy in the nucleoplasm and cytoplasm at 71 frames/s. We acquired two-dimensional trajectories of proteins (corresponding to the projection of three-dimensional trajectories onto the plane of focus) for an average of 17 frames in the cytoplasm and 16 frames in the nucleus. Diffusion constants were determined from linear fits to the mean square displacement and from the mean displacement squared per frame. We find that the distribution of diffusion constants for RPE within cells is broader than the distributions obtained from RPE in a glycerol solution, from a Monte Carlo simulation, and from the theoretical distribution for simple diffusion. This suggests that on the time scales of our measurements, the motion of single RPE proteins in the cytoplasm and nucleoplasm cannot be modeled by simple diffusion with a unique diffusion constant. Our results demonstrate that it is possible to follow the motion of single proteins within cells and that the technique of single molecule tracking can be used to probe the dynamics of intracellular macromolecules.     

Structure-Based Derivation of Protein Folding Intermediates and Energies from Optical Tweezers

Optical tweezers (OTs) measure the force-dependent time-resolved extension of a single macromolecule tethered between two trapped beads. From this measurement, it is possible to determine the folding intermediates, energies, and kinetics of the macromolecule. Previous data analysis generally has used the extension as a reaction coordinate to characterize the observed folding transitions. Despite its convenience, the extension poorly describes folding in the absence of force. Here, we chose the contour length of the unfolded polypeptide as a reaction coordinate and modeled the extensions of protein structures along their predicted folding pathways based on high-resolution structures of the proteins in their native states. We included the extension in our model to calculate the total extensions, energies, and transition rates of the proteins as a function of force. We fit these calculations to the corresponding experimental measurements and obtained the best-fit conformations and energies of proteins in different folding states. We applied our method to analyze single-molecule trajectories of two representative protein complexes responsible for membrane fusion, the HIV-1 glycoprotein 41 and the synaptic SNARE proteins, which involved transitions between two and five states, respectively. Nonlinear fitting of the model to the experimental data revealed the structures of folding intermediates and transition states and their associated energies. Our results demonstrate that the contour length is a useful reaction coordinate to characterize protein folding and that intrinsic extensions of protein structures should be taken into account to properly derive the conformations and energies of protein folding intermediates from single-molecule manipulation experiments.     

Analysis and Interpretation of Superresolution Single-Particle Trajectories

A large number (tens of thousands) of single molecular trajectories on a cell membrane can now be collected by superresolution methods. The data contains information about the diffusive motion of molecule, proteins, or receptors and here we review methods for its recovery by statistical analysis of the data. The information includes the forces, organization of the membrane, the diffusion tensor, the long-time behavior of the trajectories, and more. To recover the long-time behavior and statistics of long trajectories, a stochastic model of their nonequilibrium motion is required. Modeling and data analysis serve extracting novel biophysical features at an unprecedented spatiotemporal resolution. The review presents data analysis, modeling, and stochastic simulations applied in particular on surface receptors evolving in neuronal cells.     

Quantitative Microscopy: Protein Dynamics and Membrane Organisation

The mobility of membrane proteins is a critical determinant of their interaction capabilities and protein functions. The heterogeneity of cell membranes imparts different types of motion onto proteins; immobility, random Brownian motion, anomalous sub-diffusion, 'hop' or confined diffusion, or directed flow. Quantifying the motion of proteins therefore enables insights into the lateral organisation of cell membranes, particularly membrane microdomains with high viscosity such as lipid rafts. In this review, we examine the hypotheses and findings of three main techniques for analysing protein dynamics: fluorescence recovery after photobleaching, single particle tracking and fluorescence correlation spectroscopy. These techniques, and the physical models employed in data analysis, have become increasingly sophisticated and provide unprecedented details of the biophysical properties of protein dynamics and membrane domains in cell membranes. Yet despite these advances, there remain significant unknowns in the relationships between cholesterol-dependent lipid microdomains, protein-protein interactions, and the effect of the underlying cytoskeleton. New multi-dimensional microscopy approaches may afford greater temporal and spatial resolution resulting in more accurate quantification of protein and membrane dynamics in live cells.     

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.     

NMR studies on fully hydrated membrane proteins, with emphasis on bacteriorhodopsin as a typical and prototype membrane protein

The 3D structures or dynamic feature of fully hydrated membrane proteins are very important at ambient temperature, in relation to understanding their biological activities, although their data, especially from the flexible portions such as surface regions, are unavailable from X-ray diffraction or cryoelectron microscope at low temperature. In contrast, high-resolution solid-state NMR spectroscopy has proved to be a very convenient alternative means to be able to reveal their dynamic structures. To clarify this problem, we describe here how we are able to reveal such structures and dynamic features, based on intrinsic probes from high-resolution solid-state NMR studies on bacteriorhodopsin (bR) as a typical membrane protein in 2D crystal, regenerated preparation in lipid bilayer and detergents. It turned out that their dynamic features are substantially altered upon their environments where bR is present. We further review NMR applications to study structure and dynamics of a variety of membrane proteins, including sensory rhodopsin, rhodopsin, photoreaction centers, diacylglycerol kinases, etc.     

NMR studies on fully hydrated membrane proteins, with emphasis on bacteriorhodopsin as a typical and prototype membrane protein

The 3D structures or dynamic feature of fully hydrated membrane proteins are very important at ambient temperature, in relation to understanding their biological activities, although their data, especially from the flexible portions such as surface regions, are unavailable from X-ray diffraction or cryoelectron microscope at low temperature. In contrast, high-resolution solid-state NMR spectroscopy has proved to be a very convenient alternative means to be able to reveal their dynamic structures. To clarify this problem, we describe here how we are able to reveal such structures and dynamic features, based on intrinsic probes from high-resolution solid-state NMR studies on bacteriorhodopsin (bR) as a typical membrane protein in 2D crystal, regenerated preparation in lipid bilayer and detergents. It turned out that their dynamic features are substantially altered upon their environments where bR is present. We further review NMR applications to study structure and dynamics of a variety of membrane proteins, including sensory rhodopsin, rhodopsin, photoreaction centers, diacylglycerol kinases, etc.     

The Fluid—Mosaic Model of Membrane Structure: Still relevant to understanding the structure,function and dynamics of biological membranes after more than 40 years

In 1972 the Fluid—Mosaic Membrane Model of membrane structure was proposed based on thermodynamic principals of organization of membrane lipids and proteins and available evidence of asymmetry and lateral mobility within the membrane matrix [S. J. Singer and G. L. Nicolson, Science 175 (1972) 720–731]. After over 40 years, this basic model of the cell membrane remains relevant for describing the basic nano-structures of a variety of intracellular and cellular membranes of plant and animal cells and lower forms of life. In the intervening years, however, new information has documented the importance and roles of specialized membrane domains, such as lipid rafts and protein/glycoprotein complexes, in describing the macrostructure, dynamics and functions of cellular membranes as well as the roles of membrane-associated cytoskeletal fences and extracellular matrix structures in limiting the lateral diffusion and range of motion of membrane components. These newer data build on the foundation of the original model and add new layers of complexity and hierarchy, but the concepts described in the original model are still applicable today. In updated versions of the model more emphasis has been placed on the mosaic nature of the macrostructure of cellular membranes where many protein and lipid components are limited in their rotational and lateral motilities in the membrane plane, especially in their natural states where lipid–lipid, protein–protein and lipid–protein interactions as well as cell–matrix, cell–cell and intracellular membrane-associated protein and cytoskeletal interactions are important in restraining the lateral motility and range of motion of particular membrane components. The formation of specialized membrane domains and the presence of tightly packed integral membrane protein complexes due to membrane-associated fences, fenceposts and other structures are considered very important in describing membrane dynamics and architecture. These structures along with membrane-associated cytoskeletal and extracellular structures maintain the long-range, non-random mosaic macro-organization of membranes, while smaller membrane nano- and submicro-sized domains, such as lipid rafts and protein complexes, are important in maintaining specialized membrane structures that are in cooperative dynamic flux in a crowded membrane plane. This Article is Part of a Special Issue Entitled: Membrane Structure and Function: Relevance in the Cell's Physiology, Pathology and Therapy.