Looping mechanics of rods and DNA with non-homogeneous and discontinuous stiffness

DNA molecules may form loops in response to binding with regulatory proteins that control the expression of genes. While DNA looping is a widely accepted gene regulatory mechanism, basic questions regarding the mechanics of the looping process remain open. The present paper contributes a computational rod model that accounts for non-homogeneous and discontinuous changes in stiffness to support the analysis of DNA looping. We pursue this objective in two steps. First, we illustrate the effects of non-homogeneous stiffness on the looping of generic rods under pure torsion. Results computed for this idealized case support our intuition that elastic deformation and strain energy localize in ‘soft’ regions and that equilibrium bifurcations are sensitive to non-homogenous stiffness. Next, we extend the formulation to describe the combined bending, torsion and compression induced on DNA by the LacR protein. We demonstrate that while moderate stiffness variations have only modest influence on LacR-mediated DNA looping, highly localized softening (e.g., ‘kinkable’ or ‘melted’ subdomains) may substantially reduce the energetic cost of looping and profoundly affect loop geometry.