Ligase requires precisely positioned 5'PO4 and 3'OH groups to catalyse phosphodiester bond formation. The best and probably the most common physiological substrate for the reaction is a double helix with a single break in one of the two phosphodiester backbones in which free 5'-PO4 and 3'-OH groups are held in close proximity by stacked bases which remain hydrogen bonded to the intact DNA strand. Free DNA ends can be ligated only when base stacking or both stacking and hydrogen bonding interactions can create transient pseudo-continuous DNA double helices with structures similar to that. The stability, and therefore probability of finding such structures depends on the strength and number of interactions between the free ends. Complementary single stranded ends (cohesive ends) with either 5' or 3' overhangs such as those formed by the action of some restriction enzymes or the lambda terminase protein are better substrates than blunt ended molecules. The probability of finding ligatable complexes between the free ends increases with increasing concentration of substrate when the ends in question are on different molecules. For unimolecular circularization reactions, the end-joining probabilities are determined by the length of the intervening DNA and are indepedent of concentration. This cyclization probability can be thought of as an effective concentration of one end in the vicinity in the other. The effective concentration is equivalent to the bulk concentration of ends when dimerization and cyclization are equally probable.