Department of Molecular and Developmental Genetics, VIB Center for the Biology of Disease and Center for Human Genetics, KULeuven, Campus Gasthuisberg, Herestraat 49 - bus 602, 3000 Leuven, Belgium

IFEG-CONICET and FaMAF, Universidad Nacional de Córdoba, Córdoba, Argentina

Centro de Biología Molecular Severo Ochoa, CSIC-UAM, Campus Universidad Autónoma de Madrid, Madrid, Spain

Abstract

Background

Single-particle 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 user-friendly and do not have a graphical interface,.

Results

Here, we present APM_GUI (Analyzing Particle Movement), which is a MatLab-implemented application with a Graphical User Interface. This user-friendly application detects confined movement considering non-random 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 open-source tool that quantifies diffusion coefficients and determines whether trajectories have non-random confinements. It also offers a simple and user-friendly 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 easy-to-use software. However, more complex biological processes, such as the multi-directional, 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 user-friendly, accessible and open-source tool for the analysis of data from two-dimensional single-particle tracking (SPT) experiments.

SPT is a useful technique for the study of the dynamics and movement of individual sub-micrometer-sized particles. SPT is frequently used to study the movement of receptors on the cell surface

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 non-random confinement based on how long the particle stays in a given region

Implementation

APM_GUI is a complete GUI tool created using MatLab language and GUIDE. The MatLab development is platform-independent. The installation consists of unpacking the compressed folder that contains a collection of MatLab scripts and functions to the desired location and adding this location to the MatLab path. It is possible to add directories to the MatLab path by selecting

APM_GUI window

**APM_GUI window**. The APM_GUI window contains three panels:

**Source code of APM_GUI**. The file should be extracted using a suitable program (e.g. Winzip, 7-Zip or File-roller). The extracted folder Scripts_APM_GUI should be placed in MatLab's path. Then, the application can be started by typing APM_GUI in MatLab's Command Window. The folder Examples has a few trial files for the software, and the file instructions_and_installation provides a short manual.

Click here for file

Data import

Data obtained through SPT experiments must be converted to a MatLab format. The panel

An algorithm based on the Simson/Saxton approach

To detect the confinement zones on each trajectory, we implement an algorithm reported by Simson and co-workers

The coefficients in Eq. (1) can be obtained from the series expansion of the analytical solution (see Appendix A in Ref.

We are interested in regions where a particle with Brownian motion has a low probability of staying for a period of time

The index _{
m
}. Then, to calculate the index _{
c
}for a duration of time longer than a critical time _{
c
}. A confinement zone position is defined by the center, which is the average position of all points with _{
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 _{
c
}similarly to Meilhac _{
c
}= _{
c
}. However, to prevent mistakes in defining the size of the confinement zone, we fix the value of the threshold _{
c
}if _{
c
}is generally defined as _{
c
}is defined as the minimum possible value, and if _{
c
}assumes another predefined value (see the section "The parameters").

Diffusion coefficients

The diffusion coefficients were quantified by analyzing the mean square displacement (MSD). The MSD (

where

The characteristic diffusion coefficient of a given region is calculated as described by Michalet

The parameters

The parameters _{
m
}, _{
c
}and all of the parameters involved in the definition of _{
c
}must be optimized. A random walk can temporarily mimic confinement. Then, the _{
c
}has to ensure that the _{
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 _{
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 _{
m
}changes the _{
m
}is too low, the _{
m
}smooths the _{
m
}is too large, the _{
m
}must be sufficiently high to suppress the mimicked confinement of Brownian motion. However, it cannot be too high because the _{
c
}depends on _{
m
}and _{
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 _{
m
}, see Ref.

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 information from the analysis is saved in a .

Screen shot of a plot showing an AMPA receptor trajectory with confined regions

**Screen shot of a plot showing an AMPA receptor trajectory with confined regions**. A sample trajectory was registered for a single AMPA receptor in live hippocampal neurons under basal conditions (left panel). The green and red circles represent the first and last trajectory points, respectively. The confinement zones (light blue circles) correspond to regions in which the confinement index is above the critical threshold level, _{c}. The confinement index is shown in the upper-right panel, and the critical threshold, _{c}, is indicated by the light-blue line. The lower-right panel shows the instantaneous diffusion coefficient. In general, confinement zones associated with the movement of the AMPA receptor are correlated with lower values of the instantaneous diffusion coefficient. This trajectory corresponds to trajectory number 5591 in the file

The panel: Exporting a trajectory

Using the panel "Exporting a trajectory", it is possible to export the spatial coordinates, the confinement index

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 _{
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 _{
n
}. Because we also tested our implementation with experimental data obtained from AMPA receptors (see next sub-section), we used a similar setting for the simulations. Then, _{
m
}, _{
c
}were selected as 25, 0.5 and 0.67_{
c
}was 4.3, and if _{
c
}took the value of 19.

First, we analyzed a set of pure random trajectories, considering eight different diffusion coefficients between 0.01 ^{2}/^{2}/_{
n
}≥ 0.05

To determine the power of detection of our implementation, we simulated trajectories with confinement zones. Two different types of mixed trajectories were generated. First, we considered that a particle started at the center of a confinement zone with a rigid wall and that the wall vanished after _{
d
}/_{
d
}/_{
m
}positions (25 points) are not averaged well. Therefore, the power of detection for free-confined motion is much lower than that for confined-free motion. The simulations were performed for ^{2}/^{2}/^{2}/^{2}/^{2}/

Power of detection without noise

**Power of detection without noise**. The power of detection vs. the ratio _{d}/^{2}/^{2}/

Power of detection considering different noise levels

**Power of detection considering different noise levels**. Changes in the power of detection in response to different noise levels are shown for ^{2}/_{n }was assumed. The values of _{n }are indicated in the abscissa using a scale of 10 nm. In both panels (A and B), the first column corresponds to the ratio _{d}/_{d}/_{d}/_{d}/

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 10-14 days _{
m
}
_{
c
}were selected as 25, 0.5 and 0.67_{
c
}was 4.3, and if _{
c
}assumed the value of 19.

**Materials and Methods**. This file has a description of the materials and methods for the biological samples that were used to test our software. Hippocampal neurons from 18- day- old rat embryos were cultured until 10-14 DIV on glass coverslips, according to the Banker technique ^{2}). The protocol described in Ref.

Click here for file

In Figure ^{2}/^{2}/^{2}/^{2}/^{2}/

Frequency histograms of the durations, sizes and diffusion coefficients of the confined events for a single culture

**Frequency histograms of the durations, sizes and diffusion coefficients of the confined events for a single culture**. Analysis for AMPA receptors in living hippocampal neurons after bath application of glutamate. The results are normalized to the total number of mobile confined zones.

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

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 co-authors should be used

APM_GUI is based on the Simson/Saxton approach, and it is an open-source application that is publicly available directly from its home page and it is also included in the additional file

Availability and requirements

**Project name**: AMP_GUI

**Project home page**:

**Operating system(s)**: platform-independent.

**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

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.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

SAM designed and developed the software. MGM contributed to the evaluation of the software regarding the biological data management and aided in its design. CGD initiated and supervised the project. Each of the authors contributed to the drafting of the manuscript and have read and approved its final version.

Acknowledgements

Spanish Ministry of Science and Innovation: SAF 2010-14906, Consolider 2010-00045, 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 (FP7-PIIF-GA-2009-252375).