The formation of a topologically closed DNA loop is important in many
biological processes, including the regulation of transcription, recombination,
and replication. Modeling DNA as an isotropic elastic rod, we have in the
past period used finite element analysis to show that the dependence of
the twist (*Tw) and the writhe (Wr) upon the linking number deficit (*Lk)
of such loops is strongly influenced by intrinsic bends. In particular,
we have determined the geometry of DNA containing uniformly spaced coplanar 20° bends,
oriented so as to open towards the center of the loop. We have shown how
varying the numbers of bends changes the dependence of Wr and *Tw upon
changes in *Lk. We have also calculated the geometry of DNA rods that are
smoothly bent to the same extent. The response of both *Tw and Wr of a
bent DNA to a change in *Lk can be divided into three categories, depending
upon the total number of bends. For one bend of 20°, Wr increases monotonically
with *Lk and the change in *Tw with distance is constant along the entire DNA axis. For two to ten 20°
bends, Wr passes first through a local maximum, then through a local minimum,
and finally increases monotonically as *Lk increases. The profile of *Tw
per unit length depends upon the distribution of intrinsic bends, being constant
between any two adjoining bends but varying with their position relative
to the cut location. For eleven to eighteen 20° bends, Wr again varies
monotonically with *Lk. These results raise the possibility that intrinsic bends can serve as a control
factor in the biological functions associated with loop formation in DNA.
A paper has been published on these results. In addition, we have investigated
the effect upon the geometry and geometric parameters, Tw and Wr of varying
the positions and angles of the intrinsic bends, as well as the position
of place in the DNA at which the change in linking number is made with
respect to the placement of the bends. This is resulting in the preparation
of a new manuscript detailing the new major changes found. |
