Field-extension statistics of charged semiflexible polymers stretched with uniform electric fields

Single-molecule force-extension experiments have allowed quantitative measurements of the mechanical responses of biomolecules to applied forces explaining their roles in key biological functions. Electrophoretic stretching of charged polymers such as DNA in uniform electric fields is one such example, currently, used for sequencing purposes. Field-extension statistics of charged polymers differ from laser optical tweezer setups due to a non-uniform tension along the backbone of the chain, the effects of which remain poorly understood. In this paper, we modify an existing analytically tractable mean-field (MF) approach to account for the heterogeneity in tension for electric fields. Naively using this model for stretching of charged polymers such as DNA under electric fields results in local overstretching of the chain and gives inaccurate field-extension statistics. We improve this approach and account for the inhomogeneity in the tension by subdividing the chain into smaller segments while imposing the inextensibility of the chain. We find that the subdivided MF model shows better agreement with the simulations for the force-extension plots. We also show that using an isotropic mean-field model overestimates the longitudinal fluctuations both for tension forces as well as for fields. We correct the quantitative predictions for the fluctuations in the mean extension by numerically differentiating the field-extension plots. We also find that the subdivided MF model can accurately predict the statistics of experimentally relevant quantities, such as transverse fluctuations, due to the analytical tractability of the model. These field-extension predictions may be further used to introduce confinement effects in the subdivided MF model and develop a comprehensive understanding of sequencing technologies.