Abstract

We have investigated the question of whether the gel mobility-shift assay can provide data that are useful to the demonstration of cooperativity in the site-specific binding of proteins to DNA. Three common patterns of protein-DNA interaction were considered: (i) the cooperative binding of a protein to two sites (illustrated by the Escherichia coli Gal repressor); (ii) the cooperative binding of a bidentate protein to two sites (illustrated by the E. coli Lac repressor); and (iii) the cooperative binding of a protein to three sites (illustrated by the lambda cI repressor). A simple, rigorous, and easily extendable statistical mechanical approach to the derivation of the binding equations for the different patterns is presented. Both simulated and experimental data for each case are analyzed. The mobility-shift assay provides estimates of the macroscopic binding constants for each step of ligation based on its separation of liganded species by the number of ligands bound. Resolution of the binding constants depends on the precision with which the equilibrium distribution of liganded species is determined over the entire range of titration of each of the sites. However, the evaluation of cooperativity from the macroscopic binding constants is meaningful only for data that are also accurate. Some criteria that are useful in evaluating accuracy are introduced and illustrated. Resolution of cooperative effects is robust only for the simplest case, in which there are two identical protein binding sites. In this case, cooperative effects of up to 1,000-fold are precisely determined. For heterogeneous sites, cooperative effects of greater than 1,000-fold are resolvable, but weak cooperativity is masked by the heterogeneity. For three-site systems, only averaged pair-wise cooperative effects are resolvable.

Highlights

  • Of cooperativityfrom the macroscopic binding constants is meaningful only for data thatare accurate

  • (1961) for the original operon model) to complex regulatory amounts of these intermediate ligation states are extremely assemblies. The latter can contain bonthegative and positive sensitive tocooperative interactions between regulatory protranscription factors that interact with one another and wittehins bound at the different sites

  • Areobtainedintothe microscopic bindingconstantsthat describe the intrinsic affinity of theprotein ligandfora particular site and the cooperative interactions betweenliganded sites

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Summary

Configurationsand associated free energy states for protein binding to DNA

Binding sites aredenoted by L if liganded. The total Gibbs free energy of each configuration (AG.) relative to the unliganded reference state is given as the sum of contributions from six energy changes (column 3). AG, (i = 1, 2, or 3 ) are the intrinsic free energy changes for binding to the individual operator sites; AGi, are the free energies of cooperative interaction between liganded sites, defined as thedifference in free energy to fill the sites simultaneously (AGT) andthe free energy to fill them individually (E AG,)

AGz AGl
SA N DD ISCUSSION
The direct detector offers no advantage in the precision of
Microscopic binding constants used for simulations
Total free enerm
CONCLUSIONS
Fitted parameters
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