savin-lab / potential-correction

A notebook to correct an energy landscape, as measured by particle tracking, for static and dynamic errors.

Correction scheme for a potential measured by particle tracking

A notebook implementing the algorithm to correct an energy landscape, as measured by particle tracking, for static and dynamic errors.

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Citation

Errors in energy landscapes measured with particle tracking
Michał J. Bogdan and Thierry Savin, Biophys. J. 115:139-149 (2018)
http://doi.org/10.1016/j.bpj.2018.05.035

@article{Bogdan:2018,
  author = {Bogdan, Micha\l{} J. and Savin, Thierry},
  title = {Errors in energy landscapes measured with particle tracking},
  volume = {115},
  number = {1},
  pages = {139--149},
  year = {2018},
  doi = {10.1016/j.bpj.2018.05.035},
  URL = {http://doi.org/10.1016/j.bpj.2018.05.035},
  eprint = {http://www.cell.com/biophysj/fulltext/S0006-3495(18)30675-1},
  journal = {Biophysical Journal}
}

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Requirements

• Wolfram Mathematica is required to execute the notebook. It can be obtained from http://www.wolfram.com/mathematica.
• The input data files should be provided as three columns .csv files:

• 1st column: locations at which the apparent potential is measured;
• 2nd column: values of the measured potential;
• 3rd column: error bars on the potential's measurements.

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Files

• "Potential-Correction.nb" is a Mathematica notebook implementing the true potential reconstruction algorithm using Eqs. (15) & (16) of the article referenced above;
• "Examples/" contains 8 example data files, with the simulation results used to generate Fig. 5 of the article; the names of the files provide information about which of the curves the data refers to: for example, "Data_fig5a_sig0.1_eps0.3_p10.csv" contains the data for Fig. 5a, with the dimensionless shutter time sigma=0.1, the dimensionless static localisation uncertainty epsilon=0.3, and the optimal polynomial order of potential fitting p=10.

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Structure of the notebook

• The section INPUTS specifies the information to be entered by the user;
• The section CALCULATIONS performs the reconstruction algorithm;
• The section OUTPUTS plots the reconstructed potential compared to the apparent measured potential, and gives the polynomial coefficients of the reconstructed potential.