Repression of transcription of the Escherichia coli Lac operon by the Lac repressor (LacR) is accompanied by the simultaneous binding of LacR to two operators and the formation of a DNA loop. A recently developed theory of sequence-dependent DNA elasticity enables one to relate the fine structure of the LacR-DNA complex to a wide range of heretofore-unconnected experimental observations. Here, that theory is used to calculate the configuration and free energy of the DNA loop as a function of its length and base-pair sequence, its linking number, and the end conditions imposed by the LacR tetramer. The tetramer can assume two types of conformations. Whereas a rigid V-shaped structure is observed in the crystal, EM images show extended forms in which two dimer subunits are flexibly joined. Upon comparing our computed loop configurations with published experimental observations of permanganate sensitivities, DNase I cutting patterns, and loop stabilities, we conclude that linear DNA segments of short-to-medium chain length (50 -180 bp) give rise to loops with the extended form of LacR and that loops formed within negatively supercoiled plasmids induce the V-shaped structure.lac operon ͉ sequence-dependent DNA elasticity ͉ DNase I footprinting M any genetic processes are controlled by proteins that bind at separate, often widely spaced, sites on DNA and hold the intervening double helix in a loop (1-3). The classical example is the lac operon of Escherichia coli (4). The Lac repressor (LacR) is a tetrameric protein assembly that represses the expression of the lac operon by simultaneously binding to two DNA sites, i.e., operators, in the vicinity of the nucleotides at which transcription starts. The structure and elastic properties of DNA determine which spacings of the operators are optimal for functionality. For the lac operon, a change in spacing by five to six nucleotides can induce a 50-fold alteration in the efficiency of repression (5, 6).Although there is a large amount of literature on genetic and biochemical aspects of expression in the lac system, less is known about the actual configuration of the LacR-DNA loop assembly. In the crystalline state the two dimer subunits of LacR are joined to form a V (7, 8), and contact with DNA is made at the tips of each arm of the V (Fig. 1). On the other hand, electron microscopy and solution studies (9-12) indicate that the angle between the dimer subunits, i.e., the angle of aperture ␣, can vary. A change in ␣ affects the configuration of the DNA loop through its influence on the distance and orientation of the operators. We are here concerned with loops formed between the primary operator site O1 and the weaker auxiliary site O3. As each operator binds to the protein in one of two possible orientations, there are four distinct loop types that are analogous to those considered by Geanacopoulos et al. (13) in their treatment of DNA loops in the E. coli gal operon. We write A1, A2, P1, and P2 for these loop types, where the A and P refer to antiparallel and parallel ...