Three-dimensional shapes of looped DNA
The equilibrium shapes of a closed DNA are investigated
by employing a model of a thin, homogeneous, isotropic, linearly
elastic rod of circular cross section. An equilibrium
configuration of such an initially straight and twisted rod,
submitted to external forces and moments at its ends only, obeys
equations identical to those governing the rotation of a symmetric
gyrostat spinning about a fixed point in a gravitational field
(the Kirchhoff analogy). To represent the equilibrium of the
looped DNA, the model rod must be smoothly closed into a ring. The
corresponding BVP results in a system of four nonlinear equations
with respect to four parameters. The perturbation analysis and the
parameter continuation approach are used to find nonplanar
solutions. The conformation change is discussed for various values
of parameters.
E.L.Starostin
Meccanica,
1996, v. 31, No. 3, pp. 235-271.
Abstract