  A methodology for the statistical mechanical analysis of polymeric chains
under tension introduced previously is extended to include torque. The response
of individual bonds between monomers or of entire groups of monomers to a
combination of tension and torque involves, in the framework of this method of
analysis, the (thermal or mechanical) activation of a specific mix of
statistically interacting particles carrying quanta of extension or contraction
and quanta of twist or supercoiling. The methodology, which is elucidated in
applications of increasing complexity, is capable of describing the conversion
between twist chirality and plectonemic chirality in quasistatic processes. The
control variables are force or extension and torque or linkage (a combination
of twist and writhe). The versatility of this approach is demonstrated in two
applications relevant and promising for double-stranded DNA under controlled
tension and torque. One application describes conformational transformations
between (native) B-DNA, (underwound) S-DNA, and (overwound) P-DNA in accord
with experimental data. The other application describes how the conversion
between a twisted chain and a supercoiled chain accommodates variations of
linkage and excess length in a buckling transition.
