  We study the dynamics of a double-stranded DNA (dsDNA) segment, as a
semiflexible polymer, in a shear flow, the strength of which is customarily
expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains
in shear flows are well-known to undergo tumbling motion. When the chain
lengths are much smaller than the persistence length, one expects a
(semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment
shorter than the persistence length does indeed tumble as a rigid rod. However,
for higher Wi the chain does not tumble as a rigid rod, even if the polymer
segment is shorter than the persistence length. In particular, from time to
time the polymer segment may assume a buckled form, a phenomenon commonly known
as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA
fragments, we first analyze Euler buckling in terms of the oriented
deterministic state (ODS), which is obtained as the steady-state solution of
the dynamical equations by turning off the stochastic (thermal) forces at a
fixed orientation of the chain. The ODS exhibits symmetry breaking at a
critical Weissenberg number Wi$_{\text c}$, analogous to a pitchfork
bifurcation in dynamical systems. We then follow up the analysis with
simulations and demonstrate symmetry breaking in computer experiments,
characterized by a unimodal to bimodal transformation of the probability
distribution of the second Rouse mode with increasing Wi. Our simulations
reveal that shear can cause strong deformation for a chain that is shorter than
its persistence length, similar to recent experimental observations.
