  Transcription is the first step of gene expression, in which a particular
segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite
many details of the complex interactions between DNA and RNA synthesis
disclosed experimentally, much of physical behavior of transcription remains
largely unknown. Understanding torsional mechanics of DNA and RNAP together
with its nascent RNA and RNA-bound proteins in transcription maybe the first
step towards deciphering the mechanism of gene expression. In this study, based
on the balance between viscous drag on RNA synthesis and torque resulted from
untranscribed supercoiled DNA template, a simple model is presented to describe
mechanical properties of transcription. With this model, the rotation and
supercoiling density of the untranscribed DNA template are discussed in detail.
Two particular cases of transcription are considered, transcription with
constant velocity and transcription with torque dependent velocity. Our results
show that, during the initial stage of transcription, rotation originated from
the transcribed part of DNA template is mainly released by the rotation of RNAP
synthesis. During the intermediate stage, the rotation is usually released by
both the supercoiling of the untranscribed part of DNA template and the
rotation of RNAP synthesis, with proportion depending on the friction
coefficient in environment and the length of nascent RNA. However, with the
approaching to the upper limit of twisting of the untranscribed DNA template,
the rotation resulted from transcription will then be mainly released by the
rotation of RNAP synthesis.
