Writhing number of supercoiled DNA from its scanning force microscopy imaging

Scanning force microscopy can routinely image supercoiled DNA molecules under liquids or in air and the complete three-dimensional path of the chain can be identified. This makes it possible to evaluate the writhing number (Wr) of the coiled curve described by the chain axis in the imaged conformation of the molecule. Wr is a much better descriptor of supercoiling than the linking deficit (ΔLk) which has been commonly used so far. Wr of the DNA axis curve can be roughly estimated by the signed-intersection approach or calculated as the Gauss integral of the curve itself. We applied both methods to a model closed simple curve and to coiled DNA molecules exhibiting one or two turns of the chain about their superhelical axis.