ABSTRACT
Cellular biopolymers can exhibit significant compositional heterogeneities as a result of the non-uniform binding of associated proteins, the formation of microstructural defects during filament assembly, or the imperfect bundling of filaments into composite structures of variable diameter. These can lead to significant variations in the local mechanical properties of biopolymers along their length. Existing spectral analysis methods assume filament homogeneity and therefore report only a single average stiffness for the entire filament. However, understanding how local effects modulate biopolymer mechanics in a spatially resolved manner is essential to understanding how binding and bundling proteins regulate biopolymer stiffness and function in cellular contexts. Here, we present a new method to determine the spatially varying material properties of individual complex biopolymers from the observation of passive thermal fluctuations of the filament conformation. We develop new statistical mechanics-based approaches for heterogeneous filaments that estimate local bending elasticities as a function of the filament arc-length. We validate this methodology using simulated polymers with known stiffness distributions, and find excellent agreement between derived and expected values. We then determine the bending elasticity of microtubule filaments of variable composition generated by repeated rounds of tubulin polymerization using either GTP or GMPCPP, a nonhydrolyzable GTP analog. Again, we find excellent agreement between mechanical and compositional heterogeneities.
ABSTRACT
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.
