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

Abstract

We investigate the dynamics of a single local denaturation zone in a DNA molecule, aso-called DNA bubble, in the presence of single-stranded DNA binding proteins (SSBs). Inparticular, we develop a dynamical description of the process in terms of a two-dimensionalmaster equation for the time evolution of the probability distribution of having a bubble of sizem withn bound SSBs, forthe case when m and n arethe slowest variables in the system. We derive explicit expressions for the equilibrium statistical weights for agiven m andn, which depend onthe statistical weight u associated with breaking a base-pair interaction, the loop closure exponentc, the cooperativityparameter σ0, theSSB size λ, andbinding strength κ. These statistical weights determine, through the detailed balance condition, thetransfer coefficient in the master equation. For the case of slow and fast bindingdynamics the problem can be reduced to one-dimensional master equations. In thelatter case, we perform explicitly the adiabatic elimination of the fast variablen. Furthermore, we find that for the case that the loop closure isneglected and the binding dynamics is vanishing (but with arbitraryσ0) 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 weightu, binding proteinsize λ, andbinding strength κ, and compare to the fast and slow binding limits. In particular, we find that the presenceof SSBs in general increases the relaxation time, compared to the case when no bindingproteins are present. By tuning the parameters, we can drive the system from regularbubble fluctuation in the absence of SSBs to full denaturation, reflecting experimental andin vivo situations.