Analysis of the gel electrophoresis of looped protein-DNA complexes by computer simulation

The theory of mass transport coupled to reversible interactions under chemical kinetic control forms the basis of a numerical model that has been applied to systems such as lac repressor-lac operator DNA, in which a protein binds in two different modes to linear DNA carrying two specific binding sites. Three complexes may be formed: (1) a linear 1:1 complex with one protein molecule bound to one site on the DNA molecule; (2) a 1:1 complex in which a single protein molecule is bound to both sites simultaneously, thereby inducing a large DNA loop; and (3) a 2:1 linear complex in which two protein molecules are bound in tandem, each occupying a single site. The computational model affords a quantitative numerical simulation of the observed gel electrophoretic patterns produced by titration of the DNA with protein and provides new insights into the shape and nature of the patterns. In particular, the patterns may represent unimodal or bimodal reaction zones. Nevertheless, analysis of the peaks in the patterns obtained at low DNA and high protein concentration provides essential information as to the stoichiometry of the complexes and satisfactory estimates of association constants. The theory thus provides the experimenter with guidelines for quantitative evaluation of the results of gel retardation assays of the particular system under investigation, once protein-induced DNA (or RNA) loops have been established by independent physical or chemical methods. It is suggested that these insights might also find application to systems involving the binding of two or three different proteins to DNA with loop formation.