APM_GUI: analyzing particle movement on the cell membrane and determining confinement
 Silvia A Menchón^{1, 2}Email author,
 Mauricio G Martín^{1, 3} and
 Carlos G Dotti^{1, 3}Email author
DOI: 10.1186/2046168254
© Menchón et al; licensee BioMed Central Ltd. 2012
Received: 30 August 2011
Accepted: 20 February 2012
Published: 20 February 2012
Abstract
Background
Singleparticle tracking is a powerful tool for tracking individual particles with high precision. It provides useful information that allows the study of diffusion properties as well as the dynamics of movement. Changes in particle movement behavior, such as transitions between Brownian motion and temporary confinement, can reveal interesting biophysical interactions. Although useful applications exist to determine the paths of individual particles, only a few software implementations are available to analyze these data, and these implementations are generally not userfriendly and do not have a graphical interface,.
Results
Here, we present APM_GUI (Analyzing Particle Movement), which is a MatLabimplemented application with a Graphical User Interface. This userfriendly application detects confined movement considering nonrandom confinement when a particle remains in a region longer than a Brownian diffusant would remain. In addition, APM_GUI exports the results, which allows users to analyze this information using software that they are familiar with.
Conclusions
APM_GUI provides an opensource tool that quantifies diffusion coefficients and determines whether trajectories have nonrandom confinements. It also offers a simple and userfriendly tool that can be used by individuals without programming skills.
Background
Informatics tools have become essential for biologists because they allow the analysis of a vast amount of data obtained using newly developed techniques and electronic devices. Many informatics tools are now available, which makes it possible to analyze various processes, such as the linear movement of particles, and to quantify fluorescence using easytouse software. However, more complex biological processes, such as the multidirectional, evanescent and at times frantic movement of proteins diffusing along the lateral plane of membranes, require sophisticated algorithms that run on complex software distributions. These applications sometimes require a thorough knowledge of programming, which makes their use difficult for biologists. The aim of this work is to provide a userfriendly, accessible and opensource tool for the analysis of data from twodimensional singleparticle tracking (SPT) experiments.
SPT is a useful technique for the study of the dynamics and movement of individual submicrometersized particles. SPT is frequently used to study the movement of receptors on the cell surface [1]. The development of quantum dots (Qdots) and the improved sensitivity of fluorescence microscopy allow the localization of each particle with a high resolution and precision for long periods of time [2]. SPT occurs in two important and distinct stages: first, the dots (representing the particles' positions) are localized and marked, and second, the dots are tracked over time [3]. The trajectories for each particle are obtained by trace reconnection. Although many sources of noise are present throughout the process, (e.g., the blinking of Qdots, which generates dark states), some algorithms are able to label and track the marked particles. The most commonly used implementations for Qdots are MTT (a set of MatLab scripts [4]), Particle Tracker (a ImageJ plugin [5]) and Imaris Track (Bitplane's software [6]). However, it is difficult to find a userfriendly application with a graphical interface that can analyze the dynamic properties of trajectories, such as variations in protein diffusion coefficients.
Here, an implementation for MatLab with a graphical user interface (GUI) is presented that allows the analysis of lateral diffusion properties using data obtained by SPT in two dimensions. In particular, it determines whether a particle has free Brownian motion or nonrandom confinement based on how long the particle stays in a given region [7, 8]. When a particle trajectory shows regions with confined movement, our implementation determines where it occurs, the sizes of the confined regions, the duration of the time that a particle stays in each of these regions and the characteristic diffusion coefficients. Although this application runs on MatLab, (and saves all of the data in a workspace for MatLab users), all generated data are also exported in .dat files that can be opened with any software and subjected to statistical analyses, which allows the users to analyze and plot this information using software that they are familiar with.
Implementation
Data import
Data obtained through SPT experiments must be converted to a MatLab format. The panel Converting calls the scripts to convert files from Imaris and ImageJ. An extra script is provided to convert files from MTT (see additional file 1). If Imaris is used to obtain the trajectories, its output has to be saved as .csv file. Then, using the "Browse" button in the panel "From Imaris (csv)", the .csv files are selected, and their conversion starts after the "Convert" button is pressed in the "From Imaris (csv)" panel. If the Particle Tracker of ImageJ is used to obtain the trajectories, its output has to be saved as .txt file. Then, the procedure is the same as in the case of data obtained through Imaris, but the "Browse" and "Convert" buttons in the panel "From ImageJ" are used instead.
An algorithm based on the Simson/Saxton approach
The coefficients in Eq. (1) can be obtained from the series expansion of the analytical solution (see Appendix A in Ref. [9]).
The index L is always a positive number, and nonrandom confinement zones are correlated with its highest values. To determine the confinement index for an experimental trajectory, which can be represented as a sequence of points, we proceed by breaking it down into shorter segments. Thus, each point on the trajectory is taken as a starting point for a series of segments with variable length, from four to S_{ m }. Then, to calculate the index L, we define R as the largest displacement from the starting point and t as the duration of the segment, (if the segment has n frames, t = (n  1)Δ, where Δ is the time between frames). We also take the diffusion coefficient in Eq. (1), D, for each trajectory from the highest instantaneous diffusion coefficient. Because each point on the trajectory is included in many segments, the final value for Lata given point is the average over all segments that it belongs to. Regions for nonrandom confinement are associated with the highest values of L. Thus, a period of confined diffusion is defined by the positions where L increases above a critical threshold L_{ c }for a duration of time longer than a critical time t_{ c }. A confinement zone position is defined by the center, which is the average position of all points with L ≥ L_{ c }, and the distance from the center to the furthest point into the confinement zone. Because the diffusion coefficient of a particle can change along the trajectory, we define L_{ c }similarly to Meilhac et al. [8]. In our algorithm, L_{ c }= α ⟨L⟩, where ⟨.⟩ represents the average over all the points along the trajectory. Because Brownian diffusants do not have nonrandom confined movement, we define a minimum possible value for L_{ c }. However, to prevent mistakes in defining the size of the confinement zone, we fix the value of the threshold L_{ c }if L has very high values. This value is fixed to ensure welldefined confinement zone sizes in the cases of experimental trajectories that are confined most of the time or in cases in which there is a very large difference between the outer and inner diffusion coefficients. Thus, for each trajectory, the threshold L_{ c }is generally defined as α⟨L⟩. However, if α⟨L⟩ is less than the minimum possible value, L_{ c }is defined as the minimum possible value, and if L has very large values, L_{ c }assumes another predefined value (see the section "The parameters").
Diffusion coefficients
where N is the total number of points in the trajectory. For small n, the MSD values are well averaged. However, longer time lags have greater uncertainty in the MSD value. Diffusion coefficient values can be obtained from the evaluation of a plot of the MSD vs. time. However, the localization uncertainty and finite camera exposure introduce an offset to the MSD curve. Michalet considered all of these effects (see Section III Ref. [13]) and proposed an algorithm to determine the optimal number of points to be considered when fitting the MSD curve, (see Section V Ref. [13]).
The characteristic diffusion coefficient of a given region is calculated as described by Michalet [13] using a subtrajectory containing only the points within the region under consideration. Instantaneous diffusion coefficients are calculated by computing an MSD curve for each subtrajectory of duration 10Δ. Although the uncertainty in the diffusion coefficient can be relatively large for such a short subtrajectory, instantaneous diffusion coefficients are useful in determining slow and fast diffusion regimes with durations equal to or greater than 10Δ (the used time window).
The parameters
The parameters S_{ m }, t_{ c }and all of the parameters involved in the definition of L_{ c }must be optimized. A random walk can temporarily mimic confinement. Then, the Lprofile would not be a horizontal line, even for a Brownian diffusant. However, the peaks for a random walk with mimicked confinement would be lower and narrower than those for nonrandom confinement. Then, the minimum value for L_{ c }has to ensure that the Lprofile for any Brownian diffusant would be below it (or above it, but only for durations shorter than t_{ c }). This parameter has to be introduced in the "Minimum L_c" text box. However, to prevent mistakes in the determination of confinement zone sizes, if L has a greater value than the parameter introduced in the "Maximum L value to fix a threshold" text box, then the threshold L_{ c }takes the value that has been introduced in the "Threshold for high L" text box. These two parameters cannot affect most trajectories; they are defined only for specific cases and obviously do not affect any trajectory when the parameter entered in the "Maximum L value to fix a threshold" text box is sufficiently high. The value of S_{ m }changes the Lprofile. If S_{ m }is too low, the Lprofile presents many peaks. Increasing the maximum segment size S_{ m }smooths the Lprofile. However, if S_{ m }is too large, the Lprofile is very smooth, and information about confinement is lost. This loss is caused by taking the average over very large segments of the trajectory. Then, the value of S_{ m }must be sufficiently high to suppress the mimicked confinement of Brownian motion. However, it cannot be too high because the Lprofile resulting from nonrandom confinement may also be suppressed. The optimization of the time t_{ c }depends on S_{ m }and L_{ c }. However, depending on the biological sample, it can sometimes be estimated from previous knowledge. For a more detailed description about how to optimize the parameter S_{ m }, see Ref. [7], as we kept the same notation.
Inputs and outputs
The files to analyze can be selected using the browser for the folder dialog box that appears after the "Browse" button in the panel "Analyzing" is pressed. For the analysis, APM_GUI uses the files that contain trajectory information that has been generated by the functions in the panel "Converting files", (see section Data import). When the files to analyze have been selected, and the required parameters have been given, the analysis will start after the "Finding confinement" button in the panel "Analyzing" is pressed.
The panel: Exporting a trajectory
Using the panel "Exporting a trajectory", it is possible to export the spatial coordinates, the confinement index L and the instantaneous diffusion coefficient over time as a .dat file. In this case, the number of the selected trajectory has to be entered, and the file that contains it has to be selected using the browser for the folder dialog box that appears after the "Browse" button is pressed in the "Exporting a trajectory" panel. The parameters required in the empty boxes in the panel "Analyzing" also have to be entered. After the "Export trajectory" button is pressed, a new .dat file is created and saved in the same folder where the selected file is located.
Results and Discussion
Testing Simson/Saxton approach with simulated data
To test our implementation and analyze its power of detection, we used simulated random walks. Particle trajectories were generated by using a jump size ℓ and choosing a random direction for each jump. After 100 jumps, the particle position was recorded. Each simulated trajectory consisted of 100 frames (i.e., the particle position was recorded 100 times), and for each setting (i.e., for each ℓ), 1000 particles were simulated. The fixed jump length was determined by $\ell =\sqrt{4Ddt}$, where D was the diffusion coefficient applied and dt was the time interval of a basic simulation step. To simulate the confined motion, we assumed that the particles were entrapped in circular domains of radius r_{ d }. The exit from the domain was restricted by rigid walls. To test the effects of different noise levels, we displaced every trajectory point of a simulated trajectory by a random distance that was generated based on Gaussian white noise with a standard deviation of σ_{ n }. Because we also tested our implementation with experimental data obtained from AMPA receptors (see next subsection), we used a similar setting for the simulations. Then, dt = 0.067/100 s and for the analysis, S_{ m }, α and t_{ c }were selected as 25, 0.5 and 0.67s (10 frames), respectively. The minimal value for L_{ c }was 4.3, and if L ≥ 100, L_{ c }took the value of 19.
First, we analyzed a set of pure random trajectories, considering eight different diffusion coefficients between 0.01 μm^{2}/s and 0.1 μm^{2}/s. In all cases without noise, the false positive rate was less than 2.5%. However, this false positive rate decreased when noise was added. Simulations with noise were performed using standard deviations between 0.01 μm and 0.06 μm. In particular, all of the cases tested had a false positive rate of less than 1% if σ_{ n }≥ 0.05 μm.
Testing the Simson/Saxton approach with experimental data
We also tested our application by studying the diffusion of AMPA receptors on the cell membrane of hippocampal neurons maintained for 1014 days in vitro under basal conditions of activity and after the addition of the excitatory neurotransmitter glutamate. For a detailed description of the material and methods, see additional file 2. We evaluated the data from five different neuronal cultures. The trajectories of single molecules were obtained by tracking with the Imaris program. Only trajectories containing at least 50 points were considered for the analysis; S_{ m }, α and t_{ c }were selected as 25, 0.5 and 0.67s (10 frames), respectively. The minimal value for L_{ c }was 4.3, and if L ≥ 100, then L_{ c }assumed the value of 19.
Conclusions
In conclusion, our application provides a robust tool to study confined movement and diffusion dynamics on the cell membrane. Although some parameters depend on the experimental equipment, many others have to be optimized according to the instructions given in the section "The parameters". This application is programmed in MatLab and has a GUI that allows it to be used even without any programming knowledge. However, expert users can modify the scripts according to their needs.
In general, the trajectories obtained by SPT are analyzed by fitting the MSD vs. time plot or by using a maximum likelihood estimator [17]. Both approaches give reliable diffusion coefficient values when they are used properly [13, 17]. However, to identify standard types of motion, such as pure diffusion, anomalous diffusion, directed motion or confined movement, a specific algorithm should be provided. The test presented here is an algorithm based on the Simson/Saxton approach. This test has as its null hypothesis, the particle has a pure random walk, and as its alternative hypothesis, the trajectory has confinement zones. Thus, our implementation tests whether a trajectory corresponds to a pure random walk or if it has confinement zones. This type of algorithm is generally used to analyze biological data, when trapping is caused not only by the particles encountering a more viscous region but also by some type of barrier, such as a membrane skeleton fence [18]. Therefore, confined motion may result, for instance, from cytoskeletal corrals or from restrictions to motion that can be imposed by lipid domains [1]. Our implementation determines the confinement zones and characteristic diffusion coefficients very well. Although the power of detection decreases when the confinement region is at the end of the trajectory, a high power of detection can be obtained with relatively short trajectories, even in the presence of noise.
However, if a particle has a pure random walk, and if we wish to test if its diffusion coefficient changes along the trajectory, the Simson/Saxton approach would fail. In this case, an approach such as that presented by Montiel and coauthors should be used [17]. The Montiel test always assumes pure random walks, and the question behind it is: are there changes in the diffusion coefficient values? A statistical analysis of Montiel's test is presented in Ref. [17]. Although it is possible to obtain a high power of detection for diffusion coefficients differing by one order of magnitude, for smaller differences, considerably long trajectories are needed, which can be a limitation for biological samples on the cell membrane (because of endocytosis).
APM_GUI is based on the Simson/Saxton approach, and it is an opensource application that is publicly available directly from its home page and it is also included in the additional file 1. It also allows an easy analysis of all results because of the generation of files with a universal format and relative small size, which can be imported by any software for statistical analyses and plotting.
Availability and requirements
Project name: AMP_GUI
Project home page: http://www.bits.vib.be/ under BioInfo at VIB  Developed at VIB.
Operating system(s): platformindependent.
Other requirements: MatLab.
License: APM_GUI is distributed under the terms of the GNU General Public License, as published by the Free Software Foundation, version 3.
Further information: a short manual with a user's guide and installation instructions is available with the code source, which is also included in the additional file 1.
List of abbreviations
 The abbreviations used throughout the article are SPT:

Single Particle Tracking
 Qdots:

Quantum dots
 GUI:

Graphical User Interface
 MSD:

Mean Square Displacement.
Declarations
Acknowledgements
Spanish Ministry of Science and Innovation: SAF 201014906, Consolider 201000045, Flamish Fund for Scientific Research (FWO), Federal Office for Scientific Affairs, IAP P6/43 and the Flemish Government for the Methusalem Funding to CGD. This project was partially supported by European Union FP7 IIF Marie Curie Actions (FP7PIIFGA2009252375).
Authors’ Affiliations
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.