Understanding Mechanical Properties of Bio-filaments through Curvature
Cells are dynamic systems that generate and respond to forces through the complex interplay between biochemical and mechanical regulations. Since cellular processes often happen at the molecular level and are challenging to be observed under in vivo conditions due to limitations in optical microscopy, multiple analysis tools have been developed to gain insight into those processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring the persistence length of the filaments, including Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature can be used to quantify local deformations of cell shape and cellular components. We develop a novel technique, called curvature analysis, to measure the stiffness of bio-filaments from fluorescent images. We test our predictions with Monte-Carlo generated filaments. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of non-functional motors. The presented curvature analysis is significantly more accurate compared to existing approaches for small data sets. To study the effect of motors on filament deformations and velocities observed in gliding assays with functional and non-functional motors, we developed Langevin dynamics simulations of on glass and lipid surfaces. We found that generally the gliding velocity increases with an increase in motor density and a decrease in diffusion coefficient, and that motor density and diffusion coefficient have no clear effect on filament curvatures, except at a very low diffusion coefficients. Finally, we provide an ImageJ plugin to make curvature and persistence length measurements more accessible to everyone.