TrackArt: the user friendly interface for single molecule tracking data analysis and simulation applied to complex diffusion in mica supported lipid bilayers

Background

Studies on membrane dynamics using lipid- or protein-based probes specific for different membrane regions or local environments, such as domains of ordered lipids enriched in cholesterol and sphingolipids, provide deep insight into the organization of both plasma membranes and artificial lipid bilayers [1–8].

Ensemble averaging methods such as FCS or FRAP are effective for accurately determining diffusion over large data sets consisting of mobile particles. Although multiple component diffusion can be quantified using these methods, they provide limited ability to visualize single particle behaviors, such as switching between fast and slow diffusion, or confined diffusion [9, 10]. Single molecule tracking (SMT) is a complementary technique that can analyze individual particle trajectories in detail, and thus is able to extract such information from recordings of diffusing particles.

For over 20 years, numerous authors have described approaches for SMT data acquisition, analysis, extraction of diffusion coefficients, and uncertainty estimation [11–15]. For each experimental paradigm, several factors that may introduce bias into the data need to be considered. The sample type and preparation (i.e. live cell, artificial membrane, mica or glass support) and the microscope setup, including the detector type, lens characteristics, labeling strategy and filter quality, all affect the signal-to-noise ratio, a crucial parameter for sensitive particle recognition and linking of detected particles into trajectories with high accuracy [16]. Acquisition parameters such as frame rate, detector gain, binning, and light intensity should be optimized. For example, a too low frame rate will result in motion- blur of moving particles. On the other hand, a too high frame rate might lead to a low signal-to-noise ratio. High light intensity increases the signal-to-noise ratio, but also results in rapid bleaching, shortening particle lifetimes (and thus trajectories). Moreover, light exposure over too long a period of time may cause sample photodamage i.e. by lipid oxidation, changing the diffusion characteristics of the sample [17]. Finally, acquired datasets must be analyzed with a view to the nature of the observed diffusion type. In both artificial and plasma membranes, diffusion is often more complex than simple Brownian diffusion in a homogenous medium, and anomalous or confined diffusion with multiple diffusing fractions are observed. This might be caused by membrane inhomogeneity, the existence of domains or impermeable clusters to the label used, or even the presence of fluorescent contaminants [13, 15, 18]. SMT datasets are relatively large and require initial filtering before further processing. Consequently, the final results of such analyses are extremely sensitive to the choice of proper fitting models and filtering parameters. Ideally, results on unknown data from real membranes should be supported by adequate simulations in silico. Thus, a meaningful characterization of probe dynamics requires not only good datasets, but also strong programming skills for their analysis. To simplify the process of SMT data analysis, and thereby to make it more accessible to a wide range of researchers, we designed TrackArt as a graphic user interface (GUI) implementing commonly used methods for diffusion coefficient estimation from acquired SMT data, and data filtering, as well as various modes of diffusion simulation.

Here we present features of the TrackArt interface for analysis of single molecule tracking data, and apply the workflow to describe the dynamic behavior of a fluorescently tagged sphingolipid analog, SM-Atto677N, on mica supported DOPC bilayers.

Diffusion simulation

As a method of validating implemented tracking data algorithms, by challenging acquired data with simulation, as well as for teaching and illustrative purposes, a simulation module was developed and included in the TrackArt ensemble. Trajectories are simulated using the Monte Carlo algorithm, for any given number of trajectories and steps, with an optional simulation of localization error (Figure 1A,B). Three simulation modes are available:

Simple diffusion mode - each particle moves with constant D throughout its lifetime. Particles can be divided into two separate populations, each moving with a different D (Figure 1C).

Switching mode - particles switch between two states, each one with a characteristic diffusion coefficients D ₁ and D ₂ with switch rates k _1-2 and k _2-1 (Figure 1D) according to an equilibrium:

(1)

Domains mode - particles diffuse among immobile domains, simulated as circles with a given number per area, diameter, and diameter variation. The probability that a simulated particle will enter or leave a domain is regulated by constant rates k _1-2 and k _2-1 . Depending on these constants, domains are more or less permeable to diffusing particles (Figure 2). In extreme cases, when k _1-2 or k _2-1 is equal to zero, domains act as impermeable obstacles, giving rise to anomalous diffusion (subdiffusion), or as permeable but viscous regions, giving rise to confined diffusion. Moreover, different diffusion coefficients can be defined for particles moving within or outside of domains. A very useful feature is that the domain map can also be imported from a binary image file, as shown in Figure 3A and 3B. This gives a user the option of running diffusion simulation on images derived from, e.g., atomic force microscopy (AFM) or other maps of actual membrane ‘landscapes’ where domains with different shapes and characteristics such as fractal dimensions, percolation, confined or hop diffusion, or grid-patterns occur. For each domain map (either simulated or imported), the pair correlation curve G(r) can also be calculated and plotted (Figure 3C,D). G(r) is the probability of finding a domain at distance r and allows more detailed domain map characterization [19, 20].

Data import

The import module is used to import trajectories into TrackArt from a file, such as an ImageJ plugin: Particle Tracker [21] results, or coordinates exported previously from TrackArt Simulation module. Data from other tracking software also can be imported after formatting (see Additional file 1). Once imported, one can inspect quality of tracks, and filter out unwanted trajectories, including trajectories which are too short, not linked properly, or derived from contaminants or aggregates. Filtering of imported experimental data is essential for meaningful diffusion coefficient estimation thereafter. There are several possible factors contributing to further error: samples (or surface) contamination by other fluorescent contaminants, probes forming aggregates, the existence of an immobile probe fraction (as can happen when probe sticks to a glass surface), spurious particle recognition (noise) or errors in linking coordinates into trajectories due to high particle concentration and/or fluorophore blinking. Although many of these factors can be minimized by careful surface cleaning procedures during sample preparation, the use of sensitive EMCCD cameras, high grade filters, ultra-pure lipids and solvents, and pre-bleaching of contaminants with a strong laser pulse, several exclusion criteria should be used to dismiss trajectories which may be inaccurate. In TrackArt, the aforementioned criteria are applied through various parameters: 1) a minimum number of frames required for each trajectory, 2) a minimum and maximum diffusion coefficient value calculated for each trajectory, 3) a minimum R-squared value of the linear MSD fit for each trajectory, and 4) minimum and maximum average trajectory intensity. The optimal value for each parameter is specific for the measurement conditions, equipment used, type of sample and fluorescent label. Thus, these must be determined empirically for each imaging setup. To aid in that process, TrackArt offers a wide variety of plots and data representations, such as histograms of individual D, trajectory length and intensity, MSD plots, and trajectory preview.

Mean square displacement fits

Analysis of the mean square displacement (MSD) curves is the most common approach for extracting the diffusion coefficient, when only one population of particles with a single characteristic diffusion is observed. There are four models of possible MSD fits implemented in TrackArt, all of which assume particle movement in 2-dimensional space:

where α is the intercept and t is time. The fit can be optionally weighted by the inverse of the MSD standard deviation. In analyzing the MSD curve (and thus estimating and minimizing the error in D), it is important to take into account effects such as localization uncertainty, finite camera exposure and the effect of diffusion on the MSD curve. TrackArt simplifies this process by providing on output consisting of MSD standard deviation, parameter errors for weighted and unweighted fits, static and dynamic localization error, reduced localization error, error in D and finally the optimum number of time-lags to use for fitting (minimizing the a and b error). For these calculations, TrackArt implements algorithms and methods described in detail by Michalet et al. [11, 12].

Remaining MSD fitting models include selected models described by Saxton et al. [22]:

Anomalous diffusion (subdiffusion) - particles diffuse among immobile obstacles, which cause deviation from Brownian diffusion;

Free diffusion with flow - particles undergo directional motion due to drift or active transport;

Confined/corralled diffusion –MSD approaches a maximum value for large time-lags, due to limitation of diffusion to within a region of confinement.

Extraction of multiple diffusion coefficients

Analysis of MSD curves is extremely valuable for diffusion coefficient extraction. However the tracked molecules often exist as populations with different diffusion behaviors, e.g. a slow and a fast population, or a single population of particles that switch intermittently between different states. Both situations can be effectively simulated in the TrackArt simulation module. When dealing with relatively large numbers of trajectories, in both cases the overall MSD fit will provide only the mean value of D. Different methods of analyzing tracking data can be used to distinguish between these fractions and extract their individual D s [15, 18, 23]. The one implemented in TrackArt was proposed by Schütz et al. [15] and was successfully used in several diffusion studies [13, 24–27]. Briefly, MSDs for each population and their fraction are extracted as parameters from multi-exponential fits to cumulative probability distribution (CPD) of square displacements. In TrackArt, the CPD module is used for CPD calculation and fits, whereas the FIT module calculates final values of D, the size of fractions diffusing with given Ds, and their errors. More detailed descriptions of each module and their algorithms can be found in Additional file 1 and user manual.

Diffusion in a mica-supported DOPC bilayer

To show the capabilities and standard workflow of TrackArt we used single molecule data derived from diffusion of a head-labeled sphingolipid analog Sphingomyelin-Atto647N in a mica supported DOPC bilayer. We chose this probe because of its sphingolipid backbone, which might be expected to have a more complex behavior than commonly used DHPE probes.

Image stacks were acquired using TIRF microscope setup, with 10 ms time resolution at 25°C. By visual inspection, the existence of separate populations diffusing with different speeds is clearly evident. Moreover, switching between these states was often observable. An example of such a trajectory is shown in Figure 4. The summed projection (the sum of values for each pixel through the whole stack) with additional color coding was overlaid into a trajectory, to better visualize regions where the particle was residing for longer times (diffusing more slowly). To ensure that the particles remain in a confined region longer than particles undergoing normal Brownian diffusion would remain, Analyzing Particle Movement (APM_GUI) software was used [28]. Some particles were observed to be immobile for the entirety of their lifetimes, which might be attributable to membrane defects or particle adherence to the surface.

For detailed analysis of the diffusion behavior, first Mosaic Particle Tracker plugin [21] was used to recognize single particles and link them into trajectories. At this stage, the data must be filtered to dismiss spurious or immobile trajectories. Although this process is not complicated per se, and can be done using a variety of available programming environments or statistical software, in all cases it requires good programming skills from the user. This is especially true when dealing with large datasets, which are typical for lipid bilayer diffusion data. In TrackArt, trajectories can be easily imported, inspected and filtered. For the case of the experiment discussed above, trajectories were filtered according to criteria summarized in Table 1, and the statistics, such as number of filtered coordinates, trajectories, average D value and trajectory size for each dataset before and after filtering are listed in Table 2. For better visualization of the filtering process, combined trajectories and their MSD curves in log-log scale are presented in Figure 5.

Exclusion criterion	Value
Min frames number	20
Min D (μm2/s)	0.1
Max D (μm2/s)	10
Min individual MSD fit R2	0.9
Min average trajectory intensity	0.3
Max average trajectory intensity	1.5

	DOPC SM-Atto647N on mica, 25°C
	Non-filtered	Filtered
Coordinates	166159	90954
Trajectories	2562	986
Average trajectory length	65	92

Datasets were then analyzed in TrackArt MSD module, by linear MSD fitting. Typically, calculation of MSDs and their linear fit to extract the diffusion coefficient can be done in a simple spreadsheet. However, a more detailed analysis returning MSD standard deviation, error in D (calculated using recently published algorithms [11, 12]), localization error and number of optimal time-lags to use, requires more complex programming tools. Although there are direct solutions that deal effectively with the calculation of parameters mentioned [11, 12], the raw code used for their implementation is daunting for those not familiar with Matlab or C++ environments. In contrast to these options, the TrackArt GUI in this example allowed easy calculation of the diffusion coefficient to 1.503 ± 0.009 μm²/s and the dynamic localization error to 71 nm.

Because of the aforementioned existence of multiple populations, the diffusion coefficient estimated from simple MSD fits gives only an average value of D. Thus, CPD and FIT modules are used to find individual D s of each population and their fractions. The cumulative probability distribution (CPD) of square displacements (SD) was calculated and fit in the TrackArt CPD module for the first 10 time-lags. Plots of CPD and fits aid in choosing the right model for analysis, based on residuals and calculated MSD values. As expected, a single population model failed to fit, in contrast to a two-population model (P1 and P2), which fit well (Figure 6). The three-population model did not show any fitting improvement according to an F-test and was dismissed as data over-fitting. Calculated ${\mathit{r}}_1^2$, ${\mathit{r}}_2^2$ and F₁ were then plotted in the TrackArt FIT module (Figure 7). Diffusion coefficients were estimated from the linear MSD fits, while the fraction was estimated by averaging F₁ parameters, resulting in: D ₁  = 2.57 ± 0.04 μm²/s, D ₂  = 0.20 ± 0.01 μm²/s and F ₁  = 53.8% ± 0.2%. The diffusion coefficient of the fast population, at 2.57 ± 0.04 μm²/s, is in general agreement with a recent report (2.7 ± 0.3 μm²/s) obtained from FCS studies on a similar mica supported bilayer [29]. In that case however, a one population model was validated and used.

A FRAP study on similar DMPC bilayers clearly indicated the existence of two populations with different diffusion rates, explained as particles diffusing in the upper and lower bilayer leaflet [30]. This explanation, however, is not consistent with our observation of switching between fast and slow states occurring in time range of seconds. Transmembrane lipid flip-flop transitions are known to occur at a rate several orders of magnitude lower [31], and will therefore be essentially unobservable. Thus, we conclude that the slowly diffusing component is more likely a result of direct interaction of individual lipid molecules with the surrounding bilayer.

Temperature effect on diffusion

Results of diffusion at different temperatures were displayed as Arrhenius plots of ln(D) as a function of 1/T, shown in Figure 8. Both populations showed highly correlated linear dependence, in perfect agreement with values expected from the Arrhenius plots, since experiments were conducted at temperatures above the DOPC melting point (T _m  = - 20°C). The effective activation energy E _Arr , was calculated from the slope of the least squares linear fit, yielding 30.61 ± 2.78 kJ/mol and 48.24 ± 7.20 kJ/mol for the fast and slow population, respectively. The > 1.5 times higher E _Arr value for the slow population supports the idea that the slower diffusion rate is due to lipid interaction with the mica surface. This would result in higher activation energy being required to overcome the surface adhesive energy, in addition to the forces from the surrounding lipids, in order to increase diffusion rate. Activation energy for the fast fraction was higher comparing to previous reports (17-20 kJ.mol) [32, 33]. In those cases however, only one diffusion component was observable in bilayers supported on glass, also different lipid marker was used, and for that reason the results cannot be directly compared.