Model of DNA Bending by Cooperative Binding of Proteins

We present a model of nonspecific cooperative binding of proteins to DNA in which the binding of isolated proteins generates local bends but binding of proteins at neighboring sites on DNA straightens the polymer. We solve the statistical mechanical problem and calculate the effective persistence length, site occupancy, and cooperativity. Cooperativity leads to nonmonotonic variation of the persistence length with protein concentration, and to an unusual shape of the binding isotherm. The results are in qualitative agreement with recent single molecule experiments on nucleoid protein HU-DNA complexes.

Figure 1

Sketch of the model. (a)–(d) are described in the text. (e) 2D realization of the lowest energy conformation of the DNA-protein complex.

Figure 2

Plot of effective persistence length $\xi =l_p/l_0$ versus effective chemical potential $\mu$, for ${\kappa }_0=0$ (red solid line), 0.1 (green dotted curve), 0.3 (cyan dashed curve), and $1/\sqrt{2}$ (blue dash-dotted curve).

Figure 3

The mean site occupancy $\varphi$ (a) and cooperativity $C$ (b) are plotted as function of effective chemical potential $\mu$, for ${\kappa }_0=0$ (red solid line), 0.1 (green dotted line), 0.3 (cyan dashed line), and $1/\sqrt{2}$ (blue dash-dotted line).