Abstract

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 L c of the protein as it unfolds one module at a time. The change in the value of L c 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 L c estimates. Here we demonstrate an extended Kalman filter that provides operator-free real time estimates of L c 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 L c. 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.