The lac repressor, a tetrameric protein of identical subunits [molecular weight (MW) 4 x 38,500], interacts specifically with the lac operator, preventing the expression of the structural genes of the lac operon. The presence of an inducer (such as isopropyl-beta-D-thiogalactoside; IPTG) which binds to the repressor, prevents operator binding by lowering the association constant by a factor of 10(3) (ref. 3). Genetic and biochemical analysis have shown that the major part--if not all--of the binding site for the lac operator is located in the 60 N-terminal residues of the protein. In certain conditions, limited trypsinolysis of the protein yields four N-terminal 'headpieces' each containing 51 or 59 residues, and a tetrameric core with full inducer binding activity. It was shown recently that this headpiece is able to bind nucleic acids, and interacts with the lac operator, giving the same pattern of sensitivity with respect to the methylation of the bases as does the intact repressor. We are studying the interaction of lac repressor with DNA by neutron scattering using contrast variation and discuss here measurements on the protein, its tryptic core and their complexes with IPTG. Our results demonstrate that the headpieces are located far (67 +/- 10 A) from the centre of mass of a somewhat elongated core, and that the inducer does not significantly change the radius of gyration of the protein.