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SUMMARY:

This MATLAB graphical user interface allows the user to load a set of protein trajectories and run perturbation expectation-maximization to determine the number of diffusive states and determine the short-time diffusive properties of each state.

We have provided various sets of synthetic protein trajectories (Case&@#.mat, where & corresponds to the case number in the Table S1, @ corresponds to whether the static localization noise is constant (const) or variable (var), and # corresponds to the number of protein trajectories in the dataset). Each synthetic protein track begins on a different location of a square grid with a separation of 1 um for Case1 and 0.5 um for Cases 2.

The format of the protein trajectories that pEM requires to analyze is a cell array: X{1}, X{2}, … , X{M}, where M is the total number of particle tracks. Within each cell, X{m} = [xpositions ypositions], where positions are given by a column vector. Positions should be in um.

Example: Case1_var_500.mat takes up to 15 minutes to run on a standard laptop; while Case1_const_1000.mat can take up to 30 minutes to run. Running on a desktop with a powerful processor can certainly help to reduce these times.

To run pem_gui.m, copy “pem_gui” in the command prompt of MATLAB without the quotations. Also provided is a MATLAB script called main_pEM.m to allow a user to adjust the code to fit their needs.

Please cite:

Koo, P. K., Weitzman, M., Sabanaygam, C. R., van Golen, K. L., & Mochrie, S. G. J Extracting Diffusive States of Rho GTPase in Live Cells: Towards In Vivo Biochemistry. PLOS Computational Biology 2015.

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pem_gui.m - run down

1. Load Data - push button which prompts the user to select a mat file where the protein 	trajectories are stored.  This should be a cell array called X, where each element contains the 	2D protein trajectory.  Positions should be in um. (See Case1_500.mat for an example)
2. Filename - displays the filename of the selected file from Load Data

Movie Parameters -> 3. Frame Duration (s) - user has to set the frame duration between protein positions 4. Exposure time (s) - user has to set the exposure time

rEM parameters -> 5. No. of reinitializations - number of reinitializations to try. The minimum value should be 1. Increasing this value results in a longer time to run. This value is set at 3. This is because a very poor initialization may yield poor results regardless of the number of perturbation trials.

pEM parameters -> 6. Min. Model Size - smallest model size to start pEM 7. Max. Model Size - largest model size to consider 8. No. of Perturbations - number of perturbation trials to test Increasing the number of perturbations may yield more accurate results. Hence, when analyzing actual experimental data, we suggest this value be change to 50-100. However, the computational time will increase correspondingly.
9. Max. iterations - maximum iterations to allow within a single EM run 10. Convergence - convergence is when the change in likelihood falls below this value. Larger numbers lead to suboptimal results, while smaller numbers require longer time to converge. 11. Show Progress - plots the pEM parameter estimates at each iteration (will slow down computational time, so it is not recommended on a regular basis.)

12. RUN - push button to run rEM/pEM 
13. Display Results - displays pEM results on command window
14. Display Posterior MSD - plots the posterior-weighted average of the time-averaged MSDs 	for each diffusive state (shown in a different color)
15. Display Posterior Tracks - plots all of the protein trajectories rendered with a color 	proportional to the posterior probability of being in each diffusive state.
16. Save Results - push button to save the results structure of pEM with the output filename. 	The output file is saved in a Results directory which is generated if it does not already exist.

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Output:

Results structure: results - array of structures for each model size results(model size).structure elements: .numberOfStates - model size, i.e. number of states, K .BIC - Bayesian information criterion score for the model size (scalar) .optimalD - optimal diffusion coefficients for each state (vector, 1xK) .optimalS - optimal static localization noise for each state (vector, 1xK) .optimalP - optimal population fraction for each state (vector, 1xK) .optimalL - maximum likelihood value found (scalar) .posteriorProb - posterior probability of each protein track to be in a given diffusive state (matrix, MxK) .elapsedTime - elapsed time to run pEM for the given model size (scalar)

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List of functions within pEM directory:

main.m: matlab script to execute pEM pEM.m: main function to execute the perturbation expectation-maximization procedure EM.m: Expectation.m: executes the expectation by calculating the posterior probabilities Maximization.m: executes the maximization for each particle track LogDeterminant.m: calculates the log of the determinant with eigenvalue decomposition InitialParameters.m: manual parameters initialization for each state size RandomInitialization.m: random parameter initialization based on the CDF of the diffusion coefficient CovarianceProperties.m: calculates the features of the empirical covariance matrix for each particle track.
TrackLengthParameters: determines the length of each particle track and finds unique track lengths DisplayPosteriorTracks.m: displays the particle tracks as an image with a color proportional to the posterior probability for a given diffusive state DisplayWeightedMSD.m: displays the time-averaged mean square displacement of all particle tracks each weighed by the posterior probability for a given diffusive state

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For further support, please contact: [email protected]