Theory on the mechanisms of combinatorial binding of transcription factors with DNA

We develop a theoretical framework on the mechanism of combinatorial binding of transcription factors (TFs) with their specific binding sites on DNA. We consider three possible mechanisms viz. monomer, hetero-oligomer and coordinated recruitment pathways. In the monomer pathway, combinatorial TFs search for their targets in an independent manner and the protein-protein interactions among them will be insignificant. The protein-protein interactions are very strong so that the hetero-oligomer complex of TFs as a whole searches for the cognate sites in case of hetero-oligomer pathway. The TF which arrived first will recruit the adjacent TFs in a sequential manner in the recruitment pathway. The free energy released from the protein-protein interactions among TFs will be in turn utilized to stabilize the TFs-DNA complex. Such coordinated binding of TFs in fact emerges as the cooperative effect. Monomer and hetero-oligomer pathways are efficient only when few TFs are involved in the combinatorial regulation. Detailed random walk simulations suggest that when the number of TFs in a combination increases then the searching efficiency of TFs in these pathways decreases with the increasing number of TFs in a power law manner. The power law exponent associated with the monomer pathway seems to be strongly dependent on the number of TFs, distance between the initial position of TFs from their specific binding sites and the hop size associated with the dynamics of TFs on DNA. Here hop size is positively correlated with the degree of condensation or supercoiling of DNA. The searching efficiency of TFs in the coordinated recruitment pathway with propagating cooperative effects decreases with increasing number of TFs in a logarithmic manner. Since the combinatorial regulation is mandatory for eukaryotic systems to avoid the speed-fidelity issues related to the searching of TFs over large genome size and nuclear volume, the recruitment pathway with cooperative effects is the paramount mechanism for most of the eukaryotic systems. Mechanisms of combinatorial binding of transcription factors 3