Weak frustration regulates sliding and binding kinetics on rugged protein-DNA landscapes

A fundamental step in gene-regulatory activities, such as repression, transcription, and recombination, is the binding of regulatory DNA-binding proteins (DBPs) to specific targets in the genome. To rapidly localize their regulatory genomic sites, DBPs reduce the dimensionality of the search space by combining three-dimensional (3D) diffusion in solution with one-dimensional (1D) sliding along DNA. However, the requirement to form a thermodynamically stable protein-DNA complex at the cognate genomic target sequence imposes a challenge on the protein because, as it navigates one-dimensionally along the genome, it may come in close contact with sites that share partial or even complete sequence similarity with the functional DNA sequence. This puzzling issue creates a conflict between two basic requirements: finding the cognate site quickly and stably binding it. Here, we structurally assessed the interface adopted by a variety of DBPs to bind DNA specifically and nonspecifically, and found that many DBPs utilize one interface to specifically recognize a DNA sequence and another to assist in propagating along the DNA through nonspecific associations. While these two interfaces overlap each other in some proteins, they present partial overlap in others and frustrate the protein-DNA interface. Using coarse-grained molecular dynamics simulations, we demonstrate that the existence of frustration in DBPs is a compromise between rapid 1D diffusion along other regions in the genome (high frustration smoothens the landscape for sliding) and rapid formation of a stable and essentially active protein-DNA complex (low frustration reduces the free energy barrier for switching between the two binding modes).