A mean-field theory to predict statistics of semiflexible biomolecules due to inhomogeneous forces

Biomolecules such as DNA perform key roles governed by their mechanical responses to tensile forces exerted by other biomolecules in vivo. Single-molecule force-extension experiments help us to study the mechanical responses of biopolymers to applied forces such as electrophoretic stretching in microfluidic devices used for DNA sequencing. The effects of inhomogeneous tension on the extension of charged biopolymers under electric fields are not well understood. In our work, we modify an existing analytically tractable mean-field approach to account for the heterogeneity in tension for electric fields. This model has been shown to successfully predict the force-extension relations of inextensible polymers under uniform tension. However, for non-uniform stretching, naively using this model results in local overstretching of the polymer under an electric field. So, we improve this approach by subdividing the chain into smaller segments while imposing the inextensibility of the chain and eventually predicting experimentally relevant observables like force-extension relations and fluctuations for non-uniform forces. The proposed method may be applied to the study of the extension of DNA in confined nanochannels and protein-DNA packaging statistics.