Buckling Transitions in Superhelical DNA: Dependence on the Elastic Constants
and DNA Size
Buckling transitions in superhelical DNA are sudden changes in shape
that accompany a smooth variation in a key parameter, such as superhelical
density. Here we explore the dependence of these transitions on the elastic
constants for bending and twisting, A and C, important characteristics
of DNA's bending and twisting persistence lengths. The large
range we explore extends to other elastic materials with self-contact interactions,
modeled here by a Debye-Hückel electrostatic potential.
Our collective description of DNA shapes and energies over a wide range
of = A/C reveals
a dramatic dependence of DNA shape and associated configurational
transitions on :
transitions are sharp for large but masked for small.
In particular, at small ,
a nonplanar circular family emerges, in agreement with Jülicher's
recent analytical predictions; a continuum of forms (and associated writhing
numbers) is also observed.
The relevance of these buckling transitions to DNA in solution is examined
through studies of size dependence and thermal effects. Buckling transitions
smooth considerably as size increases, and this can be explained in part
by the lower curvature in larger plasmids. This trend suggests that buckling
transitions should not be detectable for isolated (i.e., unbound)
DNA plasmids of biological interest, except possibly for very large .
Buckling phenomena would nonetheless be relevant for small DNA loops,
particularly for higher values of
, and might have a role in regulatory mechanisms: a small change
in superhelical stress could lead to a large configurational change.
Writhe distributions as a function of ,
generated by Langevin dynamics simulations, reveal the importance of thermal
fluctuations. Each distribution range (and multipeacked shape) can be interpreted
by our buckling profiles. Significantly, the distributions for moderate
to high superhelical densities are most sensitive to ,
isolating different distribution patterns. If this effect could be
captured experimentally for small plasmids by currently available imaging
techniques, such results suggest a slightly different experimental procedure
for estimating the torsional stiffness of supercoiled DNA than considered
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