Inferring spatially varying bending stiffness of biopolymers with deep-learning approach

Abstract The bendability of biopolymers, including DNA, actin filaments, and microtubules, is crucial to diverse biological processes, such as cell motility and cytoskeletal organization. While conventional polymer models like the worm-like chain model assume uniform bending stiffness along the contour, biopolymers in reality often attain spatially varying bending stiffness as a result of complex cellular interactions. For instance, the bending stiffness of actin filaments and microtubules varies in response to associated binding proteins or chemical modifications. Despite its biological implications, measuring the position-dependent persistence length along polymer contours remains challenging. Here, we present a deep-learning (DL)-based method that quantitatively predicts spatially varying bending stiffness of biopolymers. Our framework segments a polymer chain into short overlapping fragments, predicts local persistence lengths using a DL model, and reconstructs full profiles. Using simulated data, we demonstrate that our approach achieves high accuracy and robustness even under data-scarce conditions. Applied to various biological systems, our method reveals a spatially varying stiffness from tip to base in filopodia as well as spatially heterogeneous stiffness in microtubules. Additionally, we investigate the internal mechanism of our DL model and show that the model utilizes multiple physics-related features for persistence length estimation while adaptively adjusting its attention based on polymer stiffness.