Spectral analysis methods for the robust measurement of the flexural rigidity of biopolymers

The mechanical properties of biopolymers can be determined from a statistical analysis of the ensemble of shapes they exhibit when subjected to thermal forces. In practice, extracting information from fluorescence microscopy images can be challenging due to low signal/noise ratios and other artifacts. To address these issues, we develop a suite of tools for image processing and spectral data analysis that is based on a biopolymer contour representation expressed in a spectral basis of orthogonal polynomials. We determine biopolymer shape and stiffness using global fitting routines that optimize a utility function measuring the amount of fluorescence intensity overlapped by such contours. This approach allows for filtering of high-frequency noise and interpolation over sporadic gaps in fluorescence. We use benchmarking to demonstrate the validity of our methods, by analyzing an ensemble of simulated images generated using a simulated biopolymer with known stiffness and subjected to various types of image noise. We then use these methods to determine the persistence lengths of taxol-stabilized microtubules. We find that single microtubules are well described by the wormlike chain polymer model, and that ensembles of chemically identical microtubules show significant heterogeneity in bending stiffness, which cannot be attributed to sampling or fitting errors. We expect these approaches to be useful in the study of biopolymer mechanics and the effects of associated regulatory molecules.