The double-helical nature of DNA imparts interesting topological properties on the molecule: small changes in the local twisting of base pairs can affect the folding, or writhing, of long, closed DNA polymers. The classical methods used to describe the twisting and writhing assume that the base pairs remain intact and are not suitable to study the topology of DNA containing melted or unusual fragments like bubbles or cruciforms (four-way junctions). In order to treat such structures we have developed a model to address the topology of DNA at the strand level. Our model is based on the derivation of a discrete ribbon representation from the atomic coordinates of a DNA molecule. Use of such a discrete setting makes it possible to characterize the topology of each strand of the duplex, with writhing and total twist numbers, and then to reveal typical features of melted and unusual structures. The writhing number of each strand can be calculated using a discrete dihedral-angle formulation of the Gaussian integral while the total twist density (and thus the total twisting number) can be evaluated using a parallel transport method along the centerline of the discrete ribbon representation.
A-DNA with ribbon representations of both strand
Our model can be used to analyze numerical data from molecular dynamic simulations or crystallographic structures such as the ones found in the Protein Data Bank. In addition to that, the discrete setting we build to describe DNA geometry and topology is well adapted to set up Monte Carlo simulations taking into account topological constraints (such as fixed linking number) and local twist fluctuations.
