Binding dynamics of single-stranded DNA binding proteins to fluctuating bubbles in breathing DNA

We investigate the dynamics of a single local denaturation zone in a DNA molecule, a so-called DNA bubble, in the presence of single-stranded DNA binding proteins (SSBs). In particular, we develop a dynamical description of the process in terms of a two-dimensional master equation for the time evolution of the probability distribution of having a bubble of size m with n bound SSBs, for the case when m and n are the slowest variables in the system. We derive explicit expressions for the equilibrium statistical weights for a given m and n, which depend on the statistical weight a associated with breaking a base-pair interaction, the loop closure exponent c, the cooperativity parameter sigma(0), the SSB size lambda, and binding strength kappa. These statistical weights determine, through the detailed balance condition, the transfer coefficient in the master equation. For the case of slow and fast binding dynamics the problem can be reduced to one-dimensional master equations. In the latter case, we perform explicitly the adiabatic elimination of the fast variable n. Furthermore, we find that for the case that the loop closure is neglected and the binding dynamics is vanishing (but with arbitrary sigma(0)) the eigenvalues and the eigenvectors of the master equation can be obtained analytically, using an orthogonal polynomial approach. We solve the general case numerically (i.e., including SSB binding and the loop closure) as a function of statistical weight u, binding protein size;,, and binding strength K, and compare to the fast and slow binding limits. In particular, we find that the presence of SSBs in general increases the relaxation time, compared to the case when-no binding proteins are present. By tuning the parameters, we can drive the system from regular bubble fluctuation in the absence of SSBs to full denaturation, reflecting experimental and in vivo situations.