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Extended Kalman filter estimates the contour length of a protein in single molecule atomic force microscopy experiments

Rev. Sci. Instrum. 80, 113104 (2009); doi:10.1063/1.3252982

Published 6 November 2009

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Vicente I. Fernandez,1 Pallav Kosuri,2 Vicente Parot,3 and Julio M. Fernandez4
1Department of Mechanical Engineering, MIT, Massachusetts 02139, USA
2Department of Biochemistry and Molecular Biophysics, Columbia University, New York 10027, USA
3Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
4Department of Biological Sciences, Columbia University, New York 10027, USA
Atomic force microscopy force spectroscopy has become a powerful biophysical technique for probing the dynamics of proteins at the single molecule level. Extending a polyprotein at constant velocity produces the now familiar sawtooth pattern force-length relationship. Customarily, manual fits of the wormlike chain (WLC) model of polymer elasticity to sawtooth pattern data have been used to measure the contour length Lc of the protein as it unfolds one module at a time. The change in the value of Lc measures the number of amino acids released by an unfolding protein and can be used as a precise locator of the unfolding transition state. However, manual WLC fits are slow and introduce inevitable operator-driven errors which reduce the accuracy of the Lc estimates. Here we demonstrate an extended Kalman filter that provides operator-free real time estimates of Lc from sawtooth pattern data. The filter design is based on a cantilever-protein arrangement modeled by a simple linear time-invariant cantilever model and by a nonlinear force-length relationship function for the protein. The resulting Kalman filter applied to sawtooth pattern data demonstrates its real time, operator-free ability to accurately measure Lc. These results are a marked improvement over the earlier techniques and the procedure is easily extended or modified to accommodate further quantities of interest in force spectroscopy. ©2009 American Institute of Physics
History: Received 13 September 2009; accepted 30 September 2009; published 6 November 2009
Permalink: http://link.aip.org/link/?RSINAK/80/113104/1
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KEYWORDS and PACS

Keywords
PACS
  • 87.80.Nj
    Single-molecule techniques (biophysical research methods)
  • 87.80.Dj
    Spectroscopies (biophysical research methods)
  • 87.14.E-
    Proteins
  • 87.15.bk
    Structure of biomolecular aggregates
  • 87.15.H-
    Biomolecular dynamics
  • 36.20.Ey
    Macromolecular conformation (statistics and dynamics)
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
0034-6748 (print)   1089-7623 (online)
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