Alignment of partial denaturation maps of circularly permuted DNA by computer.

In the accompanying paper, it was necessary to align partial denaturation maps of linear but circularly permuted DNA molecules in order to determine the relative positions of the ends. As mentioned in Materials and Methods, this was accomplished by visual alignment of maps plotted on paper strips, a tedious process of possibly questionable objectivity. This Appendix describes a technique for the automated analysis by objective criteria of these maps, which yields essentially the same result with some improvement in the resolution of 6.ne structure. Each partially denatured P22 DNA molecule is entered into a PDP9 computer by tracing its electron micrograph on a Computek Tablet (model GT50/10). Each molecule is divided into 1024 equal segments, each of which is coded to indicate whether it is in a native (level = 0) or denatured (level = 1) region. There are 1024 such segments per DNA molecule, so that each segment corresponds to about 40 base pairs. A two-level curve x(m) is thus produced, an example of which is shown in Plate AI. Of the total length, 2% is deleted from an end of each curve to eliminate the terminal repetition (Tye et al., 1974). The resulting curve (which corresponds to one genome length) is treated as a circle and the displacements required to match the denaturation maps are treated as angles. The program (described below) determines the relative shifts (i.e. angles) of the denaturation maps when their numerical representations (curves) are optimally aligned. In a set of N curves, a pairwise cross-correlation for all pairs (i,j) is performed. The cross-correlation function is given by