ELASTICITY THEORY AND NUMERICAL-ANALYSIS OF DNA SUPERCOILING - AN APPLICATION TO DNA LOOPING

A DNA polymer with 1000 base pairs (bp's) is modeled as an elastic rod at the base pair level. The elastic theory of rods is used to express the free energy of a double helix that has been deformed by stresses. After including a Lagrange multiplier in the energy expression to con strain the ends of the rod, an expression for the equilibrium configur ation of the rod is obtained through the use of the appropriate Euler- Lagrange equations. The resulting set of differential equations is sim plified to a set of nonlinear algebraic equations by discretizing the rod into individual elements. Because each element can have its own ph ysical characteristics, base sequence effects can be taken into accoun t. The methods developed are applied to DNA loops that are either nick ed (i.e., torsionally relaxed) or unnicked (i.e., supercoiled). Small changes in the orientations and displacements of the ends of the loops can cause large changes in the overall configuration of the DNA. The nicked DNA shows a greater propensity to change configuration than the same unnicked DNA. DNA loops that contain regions of intrinsic curvat ure require less elastic energy for loop formation and facilitate conv ersion between different looped configurations.