Analytic binding isotherms describing competitive interactions of a protein ligand with specific and nonspecific sites on the same DNA oligomer.

Many studies of specific protein-nucleic acid binding use short oligonucleotides or restriction fragments, in part to minimize the potential for nonspecific binding of the protein. However, when the specificity ratio is low, multiple nonspecifically bound proteins may occupy the region of DNA corresponding to one specific site; this situation was encountered in our recent calorimetric study of binding of integration host factor (IHF) protein to its specific 34-bp H' DNA site. Here, beginning from the analytical McGhee and von Hippel infinite-lattice nonspecific binding isotherm, we derive a novel analytic isotherm for nonspecific binding of a ligand to a finite lattice. This isotherm is an excellent approximation to the exact factorial-based Epstein finite lattice isotherm even for short lattices and therefore is of great practical significance for analysis of experimental data and for analytic theory. Using this isotherm, we develop an analytic treatment of the competition between specific and nonspecific binding of a large ligand to the same finite lattice (i.e., DNA oligomer) containing one specific and multiple overlapping nonspecific binding sites. Analysis of calorimetric data for IHF-H' DNA binding using this treatment yields enthalpies and binding constants for both specific and nonspecific binding and the nonspecific site size. This novel analysis demonstrates the potential contribution of nonspecific binding to the observed thermodynamics of specific binding, even with very short DNA oligomers, and the need for reverse (constant protein) titrations or titrations with nonspecific DNA to resolve specific and nonspecific contributions. The competition treatment is useful in analyzing low-specificity systems, including those where specificity is weakened by mutations or the absence of specificity factors.

Two-dimensional reaction of biological molecules studied by Weighted-Ensemble Brownian dynamics.

Computer simulations offer critical insights into the reaction of biological macromolecules, especially when the molecular shapes are too complex to be amenable to analytical solution. In this work, the Weighted-Ensemble Brownian (WEB) Dynamics simulation algorithm is adapted to a reaction of two unlike biological molecules, with the interaction modeled by a two-parameter system: a spherical molecular depositing on a target region of an infinite cylinder with a periodic boundary conditions. The original algorithm of Huber and Kim is streamlined for this class of reactive models. The reaction rate constant is calculated as a function of relative sizes of the reactive to non-reactive regions of the cylindrical molecule. An analytical expression for the rate constant is also obtained from the solution of the diffusion equation for the special case of a constant-flux boundary condition. Good agreement between analytical and simulation results validates the applicability of WEB Dynamics to a reaction of molecules of complicated shape. On the other hand, the simple form of our analytical expression is useful as a testing case for other simulation and numerical techniques.