Title: KnotResolver: Tracking self-intersecting filaments in microscopy using directed graphs

Abstract: Quantification of microscopy time-series of in vitro reconstituted motor driven microtubule (MT) transport in 'gliding assays' is typically performed using computational object tracking tools. However, these are limited to non-intersecting and rod-like filaments. Here, we describe a novel computational image-analysis pipeline, KnotResolver, to track image time-series of highly curved self-intersecting looped filaments (knots) by resolving cross-overs. The code integrates filament segmentation and cross-over or 'knot' identification based on directed graph representation, where nodes represent cross-overs and edges represent the path connecting them. The graphs are mapped back to contours and the distance to a reference minimized. We demonstrate the utility of the tool by segmentation and tracking MTs from experiments with dynein-driven wave like filament looping. The accuracy of contour detection is sub-pixel accuracy, and Dice scores indicate a robustness to noise, better than currently used tools. Thus KnotResolver overcomes multiple limitations of widely used tools in microscopy of cytoskeletal filament-like structures.