WAVE

(By Ting Chen, Fengnan Gao and Yan-Wen Tan)

Implementation in MATLAB of WAVE (Wasserstein distance Analysis in steady-state Variations in smFRET) to detect and locate non-equilibrium transition positions in FRET trajectories, which is first introduced in Chen, Gao and Tan (2023).¹

Description of main functions

1. TestNonequilibrium3: The core of WAVE and the main function.

2. MakeNonequilibriumHMMPoissonData: This script generates simulated data (FRET trajectories) via HMM.

3. NonequilibriumCompare: This script evaluates the analysis result after TestNonequilibrium3 has finished processing the simulated data generated by MakeNonequilibriumHMMPoissonData.

User guide

Run TestNonequilibrium3 individually

Run TestNonequilibrium3 script in Matlab, and select a folder with structure as follows:

---

Folder_name (a folder containing all FRET trajectories)

-->XXX.txt (records of intensity-time trajectory, containing 2 columns data with same length. The first column is the intensity-time trajectory of donor channel, and the second column is the intensity-time trajectory of acceptor channel)
------E (a folder containing FRET efficiency and region information of all trajectories in FRET folder)
--------->XXX.txt Efficiency.txt (corresponding to XXX.txt, and recording FRET efficiency-time trajectory in the first column, of the same length as intensity-time trajectory. In FRET region: [FRETbegin, FRETend], the recorded FRET efficiency~=0, while in crosstalk region [Crosstalkbegin, Crosstalkend] and background region [Backgroundbegin, Backgroundend], the recorded FRET efficiency=0)
--------->XXX.txt Region.txt (corresponding to XXX.txt, records region boundaries. This file contains 6 elements, like follows [FRETbegin, FRETend, Crosstalkbegin, Crosstalkend, Backgroundbegin, Backgroundend])

---

We advise the user study the test folder for this specific structure of organizing data.

test
├── BestHMMParameters2.mat
├── BNESTAnanysis.mat
├── DataSetInformation.mat
├── E
│   ├── test1.txt Efficiency.txt
│   ├── test1.txt Region.txt
│   ├── test2.txt Efficiency.txt
│   ├── test2.txt Region.txt
│   ├── test3.txt Efficiency.txt
│   ├── test3.txt Region.txt
|   └── test3.txt Region.txt
├── test1.txt
├── test2.txt
└── test3.txt

Note: Set carefully the parameters in TestNonequilibrium3 before running, especially Changeframe, which is the time point at which the conditions change and depends on the experimental design.

Test TestNonequilibrium3 with simulated data

Follow the steps below:

1. Create an empty folder new_folder to save simulated data.
2. Run MakeNonequilibriumHMMPoissonData with the newly created empty folder new_folder.
3. Run TestNonequilibrium3 with the folder new_folder containing simulated data.
4. Evaluate the output with NonequilibriumCompare.

Note: The evaluation criteria in NonequilibriumCompare should match the kinetic rate coefficients set in MakeNonequilibriumHMMPoissonData. Read the comments in these scripts for details.

Additional information

Output of TestNonequilibrium3

BNESTAnanysis is the output of TestNonequilibrium3. It is a cell table, with the following format

• 1st row: the name of each FRET trajectory (.txt file)
• 2nd row: the length of FRET trajectory after BNEST
• 3rd row: the last state before BNEST
• 4th row: the first state after BNEST
• 5th row: the trajectory length after condition change and before BNEST
• 6th row: the Length of last segment before BNEST
• 7th row: the FRET trajectory after BNEST
• 8th row: the fitting trajectory after BNEST

Categories of provided functions

1. STaSI part: MDLMulit.m, StategroupingMulti.m, change_point_detection.
2. HMM part: HMM_Algorithm2.m, HMM_Core.m, HMM_Data_Preparation.m, HMM_FitTrace_Get_Distribution.m, HMM_MainSimple.m, HMM_Max_Likelihood.m Tcalculation.m
3. MWD analysis part: CountMatrixCalculation.m, FindMaximumWassersteinDistance3.m FindMaximumWassersteinDistanceHMMSequence.m, TcalculationC.m, FindMaximumWassersteinDistanceOutOrder.m
4. Forward/Backward algorithm part: FindBestTracePart2.m, MDLCompare.m
5. Data simulation and evaluation part: MakeHMMPoissonData.m, postcalculationTimeBin.m, precalculationTimeBin.m

Footnotes

1. Chen, T., Gao, F. and Tan, Y-W. (2023) Transition Time Determination of Single-Molecule FRET Trajectories via Wasserstein Distance Analysis in Steady-state Variations in smFRET (WAVE) ↩