Tweezercalib 2.0: Faster version of MatLab package for precise calibration of optical tweezers

Abstract

We present a vectorized version of the MatLab (MathWorks Inc.) package tweezercalib for calibration of optical tweezers with precision. The calibration is based on the power spectrum of the Brownian motion of a dielectric bead trapped in the tweezers. Precision is achieved by accounting for a number of factors that affect this power spectrum, as described in vs. 1 of the package [I.M. Tolić-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Matlab program for precision calibration of optical tweezers, Comput. Phys. Comm. 159 (2004) 225–240]. The graphical user interface allows the user to include or leave out each of these factors. Several “health tests” are applied to the experimental data during calibration, and test results are displayed graphically. Thus, the user can easily see whether the data comply with the theory used for their interpretation. Final calibration results are given with statistical errors and covariance matrix. New version program summary Title of program: tweezercalib Catalogue identifier: ADTV_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTV_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Reference in CPC to previous version: I.M. Tolić-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Comput. Phys. Comm. 159 (2004) 225 Catalogue identifier of previous version: ADTV Does the new version supersede the original program: Yes Computer for which the program is designed and others on which it has been tested: General computer running MatLab (Mathworks Inc.) Operating systems under with the program has been tested: Windows2000, Windows-XP, Linux Programming language used: MatLab (Mathworks Inc.), standard license Memory required to execute with typical data: Of order four times the size of the data file High speed storage required: none No. of lines in distributed program, including test data, etc.: 135 989 No. of bytes in distributed program, including test data, etc.: 1 527 611 Distribution format: tar. gz Nature of physical problem: Calibrate optical tweezers with precision by fitting theory to experimental power spectrum of position of bead doing Brownian motion in incompressible fluid, possibly near microscope cover slip, while trapped in optical tweezers. Thereby determine spring constant of optical trap and conversion factor for arbitrary-units-to-nanometers for detection system. Method of solution: Elimination of cross-talk between quadrant photo-diode's output channels for positions (optional). Check that distribution of recorded positions agrees with Boltzmann distribution of bead in harmonic trap. Data compression and noise reduction by blocking method applied to power spectrum. Full accounting for hydrodynamic effects: Frequency-dependent drag force and interaction with nearby cover slip (optional). Full accounting for electronic filters (optional), for “virtual filtering” caused by detection system (optional). Full accounting for aliasing caused by finite sampling rate (optional). Standard non-linear least-squares fitting. Statistical support for fit is given, with several plots facilitating inspection of consistency and quality of data and fit. Summary of revisions: A faster fitting routine, adapted from [J. Nocedal, Y.x. Yuan, Combining trust region and line search techniques, Technical Report OTC 98/04, Optimization Technology Center, 1998; W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986], is applied. It uses fewer function evaluations, and the remaining function evaluations have been vectorized. Calls to routines in Toolboxes not included with a standard MatLab license have been replaced by calls to routines that are included in the present package. Fitting parameters are rescaled to ensure that they are all of roughly the same size (of order 1) while being fitted. Generally, the program package has been updated to comply with MatLab, vs. 7.0, and optimized for speed. Restrictions on the complexity of the problem: Data should be positions of bead doing Brownian motion while held by optical tweezers. For high precision in final results, data should be time series measured over a long time, with sufficiently high experimental sampling rate: The sampling rate should be well above the characteristic frequency of the trap, the so-called corner frequency. Thus, the sampling frequency should typically be larger than 10 kHz. The Fast Fourier Transform used works optimally when the time series contain 2 n data points, and long measurement time is obtained with n > 12 – 15 . Finally, the optics should be set to ensure a harmonic trapping potential in the range of positions visited by the bead. The fitting procedure checks for harmonic potential. Typical running time: Seconds Unusual features of the program: None