Force-response statistics of semiflexible polymers



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Biomolecules perform key roles in the cell based on their mechanical responses to a variety of forces, and these responses are governed by their physical properties. A variety of single-molecule force-extension experiments have allowed the manipulation of biomolecules to probe the physical properties of these biopolymers in unprecedented detail. These methods have led to a greater understanding of a wide range of biologically relevant processes, including the dynamics of cytoskeletal filaments, the stability of DNA double helix, and the formation of histone-DNA complexes. The worm-like chain theory is a polymer-physics-based model and has been successfully applied to predict force-extension relations, bond correlations, and dynamics of semiflexible biopolymers. Despite these successes, the effects of non-uniform forces are not well understood. Examples include force-extension experiments of charged polymers under electric fields, or deformation forces in the actomyosin cortex causing the filaments to buckle forming defects or inhomogeneities in the actin bundles. In this dissertation, we develop a mean-field theory approach combined with molecular simulations to address the fundamental questions of how a single semiflexible filament responds to a) non-uniform stretching fields, b) compression forces, or c) contractile forces with memory, also known as an active force. An existing mean-field theory overcomes the analytical tractability challenge of the worm-like chain model and imposes inextensibility in a way that helps to extract various force-response statistics of a semiflexible polymer that are experimentally relevant. Naively using this model fails to account for the inhomogeneity in the system and predicts inaccurate statistics. We adapt and improve the model to explicitly account for non-uniform tension or compression forces or active forces and show that this simple theoretical approach can determine the force responses in a variety of systems. The current outlined analytical formalism and Monte Carlo or molecular dynamics simulations provide a pathway to building complex interactions for inhomogeneities in biological polymers like DNA or F-actin and further quantitatively determine the statistics.



Biophysics, Force-extension, Wormlike chains, Monte Carlo, Molecular Dynamics, Semiflexible Polymer, Statistics, Buckling, Activity, Mean-field


Portions of this document appear in: Mondal, Ananya, and Greg Morrison. "Compression-induced buckling of a semiflexible filament in two and three dimensions." The Journal of Chemical Physics 157, no. 10 (2022): 104903.