Limited co-operativity in protein-nucleic acid interactions: A thermodynamic model for the interactions of Escherichia coli single strand binding protein with single-stranded nucleic acids in the “beaded”, (SSB) 65 mode

Abstract

We present, a statistical thermodynamic model (“tetramer/octamer” model) that describes the equilibrium binding of the Escherichia coli single strand binding (SSB) protein to single-stranded nucleic acids in its “beaded” binding mode, which seems to be equivalent to the high site size, (SSB) 65 binding mode. The method of sequence-generating functions is used to derive the model, which accounts for the observation that clustering of bound SSB tetramers is limited to the formation of octamers, which have been observed as “beads” in the electron microscope. The model also accounts for the overlap of potential protein binding sites on the nucleic acid. The “tetramer/octamer” model is fully described by only three parameters: the site size, n; the intrinsic equilibrium constant, K; and the co-operativity parameter, ω, and we obtain exact, closed form expressions for the binding isotherm as well as the distribution of DNA-bound SSB tetramers and octamers. The closed form expressions allow one to calculate easily average binding properties and analyze experimental binding isotherms to obtain estimates of K and ω. In order to test the tetramer/octamer model, we have determined the equilibrium binding isotherm for the E. coli SSB protein-poly(U) interaction in 0.2 m-NaCl over a wide range of binding densities. These are conditions in which the low co-operativity (SSB) 65 binding mode solely exists. The tetramer/octamer model provides a much better description of the experimental isotherm over the entire binding density range than a model that assumes the formation of clusters of unlimited size. A co-operativity parameter of ω = 420 ± 80 provides a good fit to data for SSB binding to poly(dA) and poly(U), corresponding to an interaction free energy of −3.6 kcal/mol of SSB octamer formed. On the basis of this moderate value of ω, the tetramer/octamer model predicts that at low to intermediate binding densities, a significant fraction of bound SSB exists in the form of tetramers co-existing with octamers. In the case of E. coli SSB protein binding in the “beaded”, (SSB) 65 mode this model provides a significant improvement over previous treatments which assume unlimited nearest-neighbor interactions, since the binding parameters, K and ω, represent physically meaningful interaction constants rather than fitting parameters.