Detection of Diffusion Heterogeneity in Single Particle Tracking Trajectories Using a Hidden Markov Model with Measurement Noise Propagation

We develop a Bayesian analysis framework to detect heterogeneity in the diffusive behaviour of single particle trajectories on cells, implementing model selection to classify trajectories as either consistent with Brownian motion or with a two-state (diffusion coefficient) switching model. The incorporation of localisation accuracy is essential, as otherwise false detection of switching within a trajectory was observed and diffusion coefficient estimates were inflated. Since our analysis is on a single trajectory basis, we are able to examine heterogeneity between trajectories in a quantitative manner. Applying our method to the lymphocyte function-associated antigen 1 (LFA-1) receptor tagged with latex beads (4 s trajectories at 1000 frames s⁻¹), both intra- and inter-trajectory heterogeneity were detected; 12–26% of trajectories display clear switching between diffusive states dependent on condition, whilst the inter-trajectory variability is highly structured with the diffusion coefficients being related by D ₁ = 0.68D ₀ − 1.5 × 10⁴ nm² s⁻¹, suggestive that on these time scales we are detecting switching due to a single process. Further, the inter-trajectory variability of the diffusion coefficient estimates (1.6 × 10² − 2.6 × 10⁵ nm² s⁻¹) is very much larger than the measurement uncertainty within trajectories, suggesting that LFA-1 aggregation and cytoskeletal interactions are significantly affecting mobility, whilst the timescales of these processes are distinctly different giving rise to inter- and intra-trajectory variability. There is also an ‘immobile’ state (defined as D < 3.0 × 10³ nm² s⁻¹) that is rarely involved in switching, immobility occurring with the highest frequency (47%) under T cell activation (phorbol-12-myristate-13-acetate (PMA) treatment) with enhanced cytoskeletal attachment (calpain inhibition). Such ‘immobile’ states frequently display slow linear drift, potentially reflecting binding to a dynamic actin cortex. Our methods allow significantly more information to be extracted from individual trajectories (ultimately limited by time resolution and time-series length), and allow statistical comparisons between trajectories thereby quantifying inter-trajectory heterogeneity. Such methods will be highly informative for the construction and fitting of molecule mobility models within membranes incorporating aggregation, binding to the cytoskeleton, or traversing membrane microdomains.     

Tracking Single Serotonin Transporter Molecules at the Endoplasmic Reticulum and Plasma Membrane

Transmembrane proteins are synthesized and folded in the endoplasmic reticulum (ER), an interconnected network of flattened sacs or tubes. Up to now, this organelle has eluded a detailed analysis of the dynamics of its constituents, mainly due to the complex three-dimensional morphology within the cellular cytosol, which precluded high-resolution, single-molecule microscopy approaches. Recent evidences, however, pointed out that there are multiple interaction sites between ER and the plasma membrane, rendering total internal reflection microscopy of plasma membrane proximal ER regions feasible. Here we used single-molecule fluorescence microscopy to study the diffusion of the human serotonin transporter at the ER and the plasma membrane. We exploited the single-molecule trajectories to map out the structure of the ER close to the plasma membrane at subdiffractive resolution. Furthermore, our study provides a comparative picture of the diffusional behavior in both environments. Under unperturbed conditions, the majority of proteins showed similar mobility in the two compartments; at the ER, however, we found an additional 15% fraction of molecules moving with 25-fold faster mobility. Upon degradation of the actin skeleton, the diffusional behavior in the plasma membrane was strongly influenced, whereas it remained unchanged in the ER.Live-cell microscopy and three-dimensional electron tomography has boosted our understanding of endoplasmic reticulum (ER) dynamics and morphology. Proteins have been identified which regulate the formation of cisternae versus tubelike membranes, and the contacts between ER and the various cellular organelles have been studied in detail (1). Little information, however, is available when it comes to protein dynamics and organization within the ER membrane. Its complex three-dimensional topology hampers standard diffraction-limited fluorescence microscopy approaches: in fluorescence recovery after photobleaching, for example, the obtained diffusion coefficients can be several-folds off, if the ER morphology is not correctly taken into account (2). A method is therefore needed which allows for resolving molecular movements on length scales below the typical dimensions of the ER structures.In principle, single-molecule tracking would provide the required spatial resolution due to the high precision in localizing the moving point emitters: localization errors of <40 nm can be easily achieved (3). This technique has given rise to multiple studies, in which the paths of the diffusing objects were used to make conclusions on the properties of the environment; particularly, the plasma membrane has become a favorite target for such investigations, yielding precise determinations of the diffusion coefficients of a variety of membrane proteins or lipids (4).Here, we report what is, to our knowledge, the first application of single-molecule tracking for a comparative study of the diffusion dynamics of a membrane protein at the ER versus the plasma membrane. As the protein of interest, we chose the human serotonin transporter (SERT): it is a polytopic membrane protein containing 12 transmembrane domains, with both C- and N-termini residing in the cytoplasm. Stable SERT oligomers of various degrees were observed to coexist in the plasma membrane (5). Functionally, SERT (6) is a pivotal element in shaping serotonergic neurotransmission: SERT-mediated high-affinity uptake of released serotonin clears the synaptic cleft and supports refilling of vesicular stores (7). Wild-type SERT (SERT-wt) is efficiently targeted to the presynaptic plasma membrane, whereas the truncation of its C-terminus (SERT-ΔC30) retains the mutant protein in the ER (8). The N-terminal mGFP- and eYFP-fusion constructs of the two versions of SERT thus allowed us to specifically address SERT located at the ER (eYFP-SERT-ΔC30) or at the plasma membrane (mGFP-SERT-wt (7)).Our experiments were performed at 37°C on proteins heterologously expressed in CHO cells. Total internal reflection (TIR) illumination afforded a reduction in background fluorescence and allowed for selective imaging of single mGFP-SERT-wt molecules at the cells’ plasma membrane or single eYFP-SERT-ΔC30 molecules at plasma membrane-proximal ER (Fig. 1 and see the Supporting Material). TIR was particularly crucial for single-molecule imaging of the ER-retained mutant, where out-of-focus background would surpass the weak single-molecule signals in epi-illumination.Open in a separate windowFigure 1Schematics of the plasma membrane (PM) and a part of the ER containing mGFP-SERT-wt or the ER-retained eYFP-SERT-ΔC30 mutant, respectively. Both can be excited by total internal reflection fluorescence (TIRF) excitation. Experiments were carried out either on cells expressing mGFP-SERT-wt or eYFP-SERT-ΔC30.For both mutants, the majority of molecules were mobile: in fluorescence-recovery-after-photobleaching experiments we observed a mobile fraction of 82 ± 8% for mGFP-SERT-wt and 91 ± 4% for eYFP-SERT-ΔC30. For single-molecule tracking, the high surface density of signals was reduced by completely photobleaching a rectangular part of the cell in epi-illumination; after a brief recovery period, a few single-molecule signals had entered the bleached area and could be monitored and tracked at high signal/noise using TIR excitation. Samples were illuminated stroboscopically for t_ill = 2 ms, and movies of 500 frames were recorded with a delay of t_del = 6 ms; the short delay times ensured that even rapidly diffusing molecules hardly reached the borders of the ER tubes between two consecutive frames. This illumination protocol was run for 20 times per cell, yielding ∼2500 trajectories per cell.The single-molecule localizations were first used to map those areas that are accessible to the diffusing proteins. eYFP-SERT-ΔC30 showed distinct hotspots, representing plasma membrane-proximal ER, excitable by the evanescent field (Fig. 2 A). These hotspots hardly moved within the timescale of an experiment (tens of minutes, see Fig. S1 in the Supporting Material); indeed, remarkable ER stability was previously observed using superresolution microscopy (9). In contrast, a rather homogeneous distribution was observed for mGFP-SERT-wt in the plasma membrane (Fig. 2 B).Open in a separate windowFigure 2Superresolution and tracking data at the ER and the plasma membrane. Superresolution images are shown for the ER-retained SERT mutant eYFP-SERT-ΔC30 (A) and for mGFP-SERT-wt in the plasma membrane (B). (C and D) Diffusion coefficients of eYFP-SERT-ΔC30 (C) and mGFP-SERT-wt (D) are shown as normalized histograms before (blue) and after (red) Cytochalasin D treatment. Data were fitted by Gaussian mobility distributions (see Table S1 in the Supporting Material for the fit results).Next, we compared the mobility of the observed proteins. Single-molecule localizations were linked to trajectories as described in Gao and Kilfoil (10), and the apparent diffusion coefficient, D, of each molecule was estimated from the first two points of the mean-square displacement membrane. The distribution of log₁₀ D showed a pronounced single peak (Fig. 2 D). It could be well fitted by a linear combination of two Gaussian functions, with the major fraction (85%) characterized by D_wt = 0.30 μm²/s; a broad shoulder to the left indicates the presence of proteins that are immobilized during the observation period. In contrast, the mobility of the ER-retained mutant showed a substantially different distribution, containing two clearly visible peaks (Fig. 2 C). We fitted the data with a three-component Gaussian model: the main fraction (82%) behaved similar to SERT at the plasma membrane, with D_ΔC30 = 0.32 μm²/s. In addition, a large fraction (15%) with high mobility of D_ΔC30 = 7.8 μm²/s and a minor fraction (3%) with low mobility was observed. The proteins responded as expected to degradation of the actin membrane skeleton (red bars in Fig. 2, C and D): at the plasma membrane, the mobility of mGFP-SERT-wt increased 4.6-fold (mean values), whereas at the ER membrane there was only a minor change for eYFP-SERT-ΔC30 mobility (1.06-fold increase; note that the ER is not connected to actin filaments (11)).The observation of a high mobility subfraction at the ER membrane is surprising. In general, the presence of obstacles—irrespective of whether randomly distributed or clustered, mobile or immobile—reduces the diffusivity of mobile tracers in a membrane (12). It is generally assumed that the high protein density in cell membranes is responsible for the rather low fluidity when compared to synthetic membranes (compare, e.g., Saxton and Jacobson (13) with Weiss et al. (14)). Interestingly, the observed diffusion constant of 7.8 μm²/s is of similar order as the mobility determined for various proteins in synthetic lipid membranes (14). It is thus tempting to hypothesize the presence of extended protein-depleted regions of higher fluidity within the ER membrane; such membrane domains were indeed observed already at the plasma membrane (15). We were also concerned, however, that protein degradation fragments could have contributed to our data: the three-dimensional mobility of an 85-kDa protein is ∼10 μm²/s (16), similar to the high mobility diffusion constant of eYFP-SERT-ΔC30.We tested the two explanations by analyzing the spatial distribution of fast (D_ΔC30 > 1 μm²/s) versus slow trajectories (D_ΔC30 < 1 μm²/s) of eYFP-SERT-ΔC30 (Fig. 3). Both types of trajectories clustered in the same regions, and no segregation into ER subdomains was observable at the resolved length scales. This finding—on the one hand—disfavors freely diffusing protein fragments as the origin of the high mobility fraction. On the other hand, it calls for further experiments to identify the origin of the fast and the slow mobility subfraction. Interestingly, when analyzing all eYFP-SERT-ΔC30 trajectories we found that 80% of the molecules showed diffusion confined to domains of 230-nm radius (see Fig. S2). This size is clearly smaller than the lateral extensions of the visible ER regions observed in Fig. 3. The finding indicates domain formation at the ER membrane; domains are averaged out in Fig. 3 due to the long recording times. Note that free diffusion was observed for mGFP-SERT-wt at the plasma membrane (5).Open in a separate windowFigure 3Ripley’s K function analysis of the different mobility fractions in the ER. For the cell presented in Fig. 2, the first position of every slow (D < 1 μm²/s; red) and fast (D > 1 μm²/s; blue) trajectory was plotted in panel A. Contour lines indicate regions of ER attachment to the plasma membrane. In panel B, the point-correlation function L(r)−r is plotted for the slow (red) and fast (blue) fraction. Furthermore, the correlation between fast versus slow is plotted (green). All three curves show a peak at ∼450 nm, which agrees with the extensions of the ER attachment zones.In conclusion, we have shown that single-molecule tracking is feasible for constituents of the ER membrane. We found a surprising diffusion behavior of SERT resulting in the following:

• 1.A slow fraction showing mobility reminiscent of protein diffusion in the plasma membrane, likely reflecting SERT diffusing in protein-crowded regions of the ER membrane; and
• 2.A fast fraction showing 25-fold faster diffusion kinetics.

This likely represents diffusion in altered ER membrane environments, possibly of different lipid or protein composition. Given the fact that synthesis of virtually all membrane proteins and most lipids proceeds at the ER membrane, ER heterogeneity at the nanoscale due to the continuous synthesis activity and selection for correct folding appears highly plausible.     

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

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

Asymmetric PTEN Distribution Regulated by Spatial Heterogeneity in Membrane-Binding State Transitions

The molecular mechanisms that underlie asymmetric PTEN distribution at the posterior of polarized motile cells and regulate anterior pseudopod formation were addressed by novel single-molecule tracking analysis. Heterogeneity in the lateral mobility of PTEN on a membrane indicated the existence of three membrane-binding states with different diffusion coefficients and membrane-binding lifetimes. The stochastic state transition kinetics of PTEN among these three states were suggested to be regulated spatially along the cell polarity such that only the stable binding state is selectively suppressed at the anterior membrane to cause local PTEN depletion. By incorporating experimentally observed kinetic parameters into a simple mathematical model, the asymmetric PTEN distribution can be explained quantitatively to illustrate the regulatory mechanisms for cellular asymmetry based on an essential causal link between individual stochastic reactions and stable localizations of the ensemble.     

Tracking Single Serotonin Transporter Molecules at the Endoplasmic Reticulum and Plasma Membrane

Transmembrane proteins are synthesized and folded in the endoplasmic reticulum (ER), an interconnected network of flattened sacs or tubes. Up to now, this organelle has eluded a detailed analysis of the dynamics of its constituents, mainly due to the complex three-dimensional morphology within the cellular cytosol, which precluded high-resolution, single-molecule microscopy approaches. Recent evidences, however, pointed out that there are multiple interaction sites between ER and the plasma membrane, rendering total internal reflection microscopy of plasma membrane proximal ER regions feasible. Here we used single-molecule fluorescence microscopy to study the diffusion of the human serotonin transporter at the ER and the plasma membrane. We exploited the single-molecule trajectories to map out the structure of the ER close to the plasma membrane at subdiffractive resolution. Furthermore, our study provides a comparative picture of the diffusional behavior in both environments. Under unperturbed conditions, the majority of proteins showed similar mobility in the two compartments; at the ER, however, we found an additional 15% fraction of molecules moving with 25-fold faster mobility. Upon degradation of the actin skeleton, the diffusional behavior in the plasma membrane was strongly influenced, whereas it remained unchanged in the ER.     

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

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

Single-molecule visualization in cell biology

Recent progress in single-molecule detection techniques has allowed us to visualize the dynamic behaviour and reaction kinetics of individual biological molecules inside living cells. Single-molecule visualization provides a direct way to quantify, with a high spatial and temporal resolution, biological events inside cells at the single-molecule level. In this article, we discuss how single-molecule visualization can be used in cell biology.     

Single-molecule analysis of CD9 dynamics and partitioning reveals multiple modes of interaction in the tetraspanin web

Tetraspanins regulate cell migration, sperm–egg fusion, and viral infection. Through interactions with one another and other cell surface proteins, tetraspanins form a network of molecular interactions called the tetraspanin web. In this study, we use single-molecule fluorescence microscopy to dissect dynamics and partitioning of the tetraspanin CD9. We show that lateral mobility of CD9 in the plasma membrane is regulated by at least two modes of interaction that each exhibit specific dynamics. The majority of CD9 molecules display Brownian behavior but can be transiently confined to an interaction platform that is in permanent exchange with the rest of the membrane. These platforms, which are enriched in CD9 and its binding partners, are constant in shape and localization. Two CD9 molecules undergoing Brownian trajectories can also codiffuse, revealing extra platform interactions. CD9 mobility and partitioning are both dependent on its palmitoylation and plasma membrane cholesterol. Our data show the high dynamic of interactions in the tetraspanin web and further indicate that the tetraspanin web is distinct from raft microdomains.     

TRH-receptor mobility and function in intact and cholesterol-depleted plasma membrane of HEK293 cells stably expressing TRH-R-eGFP

Here we investigated the effect of disruption of plasma membrane integrity by cholesterol depletion on thyrotropin-releasing hormone receptor (TRH-R) surface mobility in HEK293 cells stably expressing TRH-R-eGFP fusion protein (VTGP cells). Detailed analysis by fluorescence recovery after photobleaching (FRAP) in bleached spots of different sizes indicated that cholesterol depletion did not result in statistically significant alteration of mobile fraction of receptor molecules (M_f). The apparent diffusion coefficient (D_app) was decreased, but this decrease was detectable only under the special conditions of screening and calculation of FRAP data. Analysis of mobility of receptor molecules by raster image correlation spectroscopy (RICS) did not indicate any significant difference between control and cholesterol-depleted cells. Results of our FRAP and RICS experiments may be collectively interpreted in terms of a “membrane fence” model which regards the plasma membrane of living cells as compartmentalized plane where lateral diffusion of membrane proteins is limited to restricted areas by cytoskeleton constraints. Hydrophobic interior of plasma membrane, studied by steady-state and time-resolved fluorescence anisotropy of hydrophobic membrane probe DPH, became substantially more “fluid” and chaotically organized in cholesterol-depleted cells. Decrease of cholesterol level impaired the functional coupling between the receptor and the cognate G proteins of G_q/G₁₁ family.In conclusion: the presence of an unaltered level of cholesterol in the plasma membrane represents an obligatory condition for an optimum functioning of TRH-R signaling cascade. The decreased order and increased fluidity of hydrophobic membrane interior suggest an important role of this membrane area in TRH-R–G_q/G₁₁α protein coupling.     

Automatic detection of single fluorophores in live cells

Recent developments in light microscopy enable individual fluorophores to be observed in aqueous conditions. Biological molecules, labeled with a single fluorophore, can be localized as isolated spots of light when viewed by optical microscopy. Total internal reflection fluorescence microscopy greatly reduces background fluorescence and allows single fluorophores to be observed inside living cells. This advance in live-cell imaging means that the spatial and temporal dynamics of individual molecules can be measured directly. Because of the stochastic nature of single molecule behavior a statistically meaningful number of individual molecules must be detected and their separate trajectories in space and time stored and analyzed. Here, we describe digital image processing methods that we have devised for automatic detection and tracking of hundreds of molecules, observed simultaneously, in vitro and within living cells. Using this technique we have measured the diffusive behavior of pleckstrin homology domains bound to phosphoinositide phospholipids at the plasma membrane of live cultured mammalian cells. We found that mobility of these membrane-bound protein domains is dominated by mobility of the lipid molecule to which they are attached and is highly temperature dependent. Movement of PH domains isolated from the tail region of myosin-10 is consistent with a simple random walk, whereas, diffusion of intact PLC-delta1 shows behavior inconsistent with a simple random walk. Movement is rapid over short timescales but much slower at longer timescales. This anomalous behavior can be explained by movement being restricted to membrane regions of 0.7 microm diameter.     

The effect of hydration on the mobility of phospholipids in the gel state. A proton nuclear magnetic resonance spin echo study

Proton nuclear magnetic resonance (NMR) dipolar echo studies are presented for the gel state of dipalmitoylglycerophosphocholine (dipalmitoyl-GPC) — heavy water dispersions. The mobility and the mean order of the chains and the head group of dipalmitoyl-GPC were determined for different water concentrations and temperatures. For smaller than 5 mol D₂O per mol dipalmitoyl-GPC the molecule undergoes temperature- and hydration-dependent restricted rotational oscillations about the long axis of the molecule. For hydration numbers equal or larger than 5 mol D₂O per mol dipalmitoyl-GPC the molecules rotate effectively about their long axes and intermolecular dipolar interactions between proton groups of neighbour molecules are averaged. The onset of the lateral diffusion of dipalmitoyl-GPC is observed which averages out all intermolecular dipolar interactions. Deviations of the individual segments of the chains from the all-trans state have to be considered. The widely accepted model that the dipalmitoyl-GPC molecules rotate about their long axes with stiff all-trans chains should be modified. The polar head groups of dipalmitoyl-GPC effectively rotate about the bilayer-normal and restricted rotations about single bonds in the head group are allowed. An order parameter of about 0.6 for the head group was obtained for fully hydrated dipalmitoyl-GPC molecules at ambient temperature.     

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.     

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.     

High-density mapping of single-molecule trajectories with photoactivated localization microscopy

We combined photoactivated localization microscopy (PALM) with live-cell single-particle tracking to create a new method termed sptPALM. We created spatially resolved maps of single-molecule motions by imaging the membrane proteins Gag and VSVG, and obtained several orders of magnitude more trajectories per cell than traditional single-particle tracking enables. By probing distinct subsets of molecules, sptPALM can provide insight into the origins of spatial and temporal heterogeneities in membranes.     

Characterization of Horizontal Lipid Bilayers as a Model System to Study Lipid Phase Separation

Artificial lipid membranes are widely used as a model system to study single ion channel activity using electrophysiological techniques. In this study, we characterize the properties of the artificial bilayer system with respect to its dynamics of lipid phase separation using single-molecule fluorescence fluctuation and electrophysiological techniques. We determined the rotational motions of fluorescently labeled lipids on the nanosecond timescale using confocal time-resolved anisotropy to probe the microscopic viscosity of the membrane. Simultaneously, long-range mobility was investigated by the lateral diffusion of the lipids using fluorescence correlation spectroscopy. Depending on the solvent used for membrane preparation, lateral diffusion coefficients in the range D_lat = 10-25 μm²/s and rotational diffusion coefficients ranging from D_rot = 2.8 − 1.4 × 10⁷ s⁻¹ were measured in pure liquid-disordered (L_d) membranes. In ternary mixtures containing saturated and unsaturated phospholipids and cholesterol, liquid-ordered (L_o) domains segregated from the L_d phase at 23°C. The lateral mobility of lipids in L_o domains was around eightfold lower compared to those in the L_d phase, whereas the rotational mobility decreased by a factor of 1.5. Burst-integrated steady-state anisotropy histograms, as well as anisotropy imaging, were used to visualize the rotational mobility of lipid probes in phase-separated bilayers. These experiments and fluorescence correlation spectroscopy measurements at different focal diameters indicated a heterogeneous microenvironment in the L_o phase. Finally, we demonstrate the potential of the optoelectro setup to study the influence of lipid domains on the electrophysiological properties of ion channels. We found that the electrophysiological activity of gramicidin A (gA), a well-characterized ion-channel-forming peptide, was related to lipid-domain partitioning. During liquid-liquid phase separation, gA was largely excluded from L_o domains. Simultaneously, the number of electrically active gA dimers increased due to the increased surface density of gA in the L_d phase.     

Empirical Bayes Methods Enable Advanced Population-Level Analyses of Single-Molecule FRET Experiments

Many single-molecule experiments aim to characterize biomolecular processes in terms of kinetic models that specify the rates of transition between conformational states of the biomolecule. Estimation of these rates often requires analysis of a population of molecules, in which the conformational trajectory of each molecule is represented by a noisy, time-dependent signal trajectory. Although hidden Markov models (HMMs) may be used to infer the conformational trajectories of individual molecules, estimating a consensus kinetic model from the population of inferred conformational trajectories remains a statistically difficult task, as inferred parameters vary widely within a population. Here, we demonstrate how a recently developed empirical Bayesian method for HMMs can be extended to enable a more automated and statistically principled approach to two widely occurring tasks in the analysis of single-molecule fluorescence resonance energy transfer (smFRET) experiments: 1), the characterization of changes in rates across a series of experiments performed under variable conditions; and 2), the detection of degenerate states that exhibit the same FRET efficiency but differ in their rates of transition. We apply this newly developed methodology to two studies of the bacterial ribosome, each exemplary of one of these two analysis tasks. We conclude with a discussion of model-selection techniques for determination of the appropriate number of conformational states. The code used to perform this analysis and a basic graphical user interface front end are available as open source software.     

Empirical Bayes Methods Enable Advanced Population-Level Analyses of Single-Molecule FRET Experiments

Many single-molecule experiments aim to characterize biomolecular processes in terms of kinetic models that specify the rates of transition between conformational states of the biomolecule. Estimation of these rates often requires analysis of a population of molecules, in which the conformational trajectory of each molecule is represented by a noisy, time-dependent signal trajectory. Although hidden Markov models (HMMs) may be used to infer the conformational trajectories of individual molecules, estimating a consensus kinetic model from the population of inferred conformational trajectories remains a statistically difficult task, as inferred parameters vary widely within a population. Here, we demonstrate how a recently developed empirical Bayesian method for HMMs can be extended to enable a more automated and statistically principled approach to two widely occurring tasks in the analysis of single-molecule fluorescence resonance energy transfer (smFRET) experiments: 1), the characterization of changes in rates across a series of experiments performed under variable conditions; and 2), the detection of degenerate states that exhibit the same FRET efficiency but differ in their rates of transition. We apply this newly developed methodology to two studies of the bacterial ribosome, each exemplary of one of these two analysis tasks. We conclude with a discussion of model-selection techniques for determination of the appropriate number of conformational states. The code used to perform this analysis and a basic graphical user interface front end are available as open source software.     

Investigating intracellular dynamics of FtsZ cytoskeleton with photoactivation single-molecule tracking

Using photoactivatable fluorescent protein as an intracellular protein label for single-molecule tracking offers several advantages over the traditional methods. Here we demonstrate the technique of photoactivation single-molecule tracking by investigating the mobility dynamics of intracellular FtsZ protein molecules in live Escherichia coli cells. FtsZ is a prokaryotic cytoskeleton protein (a homolog of tubulin) and plays important roles in cytokinesis. We demonstrate two heterogeneous subpopulations of FtsZ molecules with distinct diffusional dynamics. The FtsZ molecules forming the Z-rings near the center of the cell were mostly stationary, consistent with the assumption that they are within polymeric filamentous structures. The rest of the FtsZ molecules, on the other hand, undergo Brownian motion spanning the whole cell length. Surprisingly, the diffusion of FtsZ is spatially restricted to helical-shaped regions, implying an energy barrier for free diffusion. Consistently, the measured mean-square displacements of FtsZ showed anomalous diffusion characteristics. These results demonstrated the feasibility and advantages of photoactivation single-molecule tracking, and suggested new levels of complexity in the prokaryotic membrane organization.