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We describe a method for determining the position of a cloned internal sequence with respect to the ends of a DNA molecule. The molecules are randomly broken at low frequency and the fragments are subjected to electrophoresis. Southern hybridization using the cloned DNA as a probe identifies only those fragments containing the sequence. The size distribution of these fragments is such that two threshold changes in intensity of signal are seen in the smear pattern below the unbroken molecules. The positions of the changes represent the distances from the sequence to each molecular end. The intensity changes arise because the natural ends of the molecules influence the fragment distribution obtained. From once-broken molecules, no fragments can arise that contain a given sequence and are shorter than the distance between that sequence and the nearest molecular end. We tested the method by using x-rays to induce breakage in yeast DNA. Genes of independently known position were mapped within whole chromosomes or Not I restriction fragments using Southern blots from gels of irradiated molecules. We present equations to predict fragment distribution as a function of break-frequency and position of the probed sequence.

Random-breakage mapping, a rapid method for physically locating an internal sequence with respect to the ends of a DNA molecule