Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative charac
teristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. We consider a simple theoretical model for two interacting transcription factor (TF) species, searching for and binding to two adjacent target sites hidden in the genomic background. We study the kinetic competition of a dimer search pathway and a monomer search pathway, as well as the steady-state regulation function mediated by the two TFs over a broad range of TF-TF interaction strengths. Using a transcriptional AND-logic as exemplary functional context, we identify the functionally desirable regime for the interaction. We find that both weak and very strong TF-TF interactions are favorable, albeit with different characteristics. However, there is also an unfavorable regime of intermediate interactions where the genetic response is prohibitively slow.
We study a protein-DNA target search model with explicit DNA dynamics applicable to in vitro experiments. We show that the DNA dynamics plays a crucial role for the effectiveness of protein jumps between sites distant along the DNA contour but close
in 3D space. A strongly binding protein that searches by 1D sliding and jumping alone, explores the search space less redundantly when the DNA dynamics is fast on the timescale of protein jumps than in the opposite frozen DNA limit. We characterize the crossover between these limits using simulations and scaling theory. We also rationalize the slow exploration in the frozen limit as a subtle interplay between long jumps and long trapping times of the protein in islands within random DNA configurations in solution.
