  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.
