Multiple folding and packing for DNA modeling

In this paper we introduce and analyze a set of equations to study geometric and energetic aspects associated with the kinematics of multiple folding and coiling of closed filaments for DNA modeling. By these equations we demonstrate that a high degree of coiling may be achieved at relatively low energy costs through appropriate writhe and twist distribution, and independently from the number of coils formed. For sufficiently high twist we show that coiling is actually favoured by elastic energy relaxation, when the deformation energy is due to curvature and the mean twist of the filament. We give estimates for the writhing process based purely on curvature information and the number of coils produced. We also determine the packing rate associated with filament compaction in the case of a hierarchical helical coiling. These results find useful applications in DNA biology, especially in modeling DNA wrapping in proteic regions, where there is a strong connection between high coiling, efficient compaction and energy localization.