Facilitated Diffusion In Crowded Environments

The search of DNA-binding proteins,such as transcription factors and DNA-repair proteins,for their specific target sites among a vast excess of nonspecific DNA plays a very important role in many cellular processes,such as gene expression and regulation.In the 1970s,Riggs et al.revealed in vitro experiments that the search for target is both rapid and efficient,about two orders of magnitude faster than the rate for the three-dimensional(3D)diffusion limit.To resolve this discrepancy,Berg et al.in several seminal papers developed a facilitated diffusion mechanism that is currently the most known and widely utilized.The main underlying idea of this mechanism is that the search process is a combination of three-dimensional motions in the solution and one-dimensional slidings along the DNA chain.Subsequently,considerable theoretical,experimental,and numerical effort has been devoted to developing the mechanism of facilitated diffusion.In chapter one,we offer a review of research progress on facilitated diffusion.In recent decade,more attentions have been paid on the study of facilitated diffusion mechanism in vivo cellular environment.There exist a large number of macromolecules,such as proteins、ribosomes,inside the cells.The macromolecules occupy 10-40%of the total cellular volume and lead to a crowded environment in the cell.The effect of molecular crowding plays a very important role on the facilitated diffusion in vivo.In chapter two,using analytical techniques and Langevin dynamics simulations in two dimensions,we investigate the effect of molecular crowding on facilitated diffusion mechanism.We find that the average search time τ always increases with increasing the density of crowding agents φ.Moreover,by analyzing the dynamics details of the target search deeply,we find that the consequence of the monotonous increase mainly results from monotonous increases of the average search rounds and the average 1D diffusion time,as well as the constant behavior of the average 2D diffusion time.In addition,for 2D diffusion the molecular crowding decreases the jumping length and narrows its distribution due to the cage effect from crowders.In living cells,about 30%of the DNA is associated with macromolecules,such as proteins.These macromolecules serve as roadblocks to specific binding proteins and impede the 1D sliding of them.In chapter three,we have investigated the influence of the blocker(roadblock)on the search dynamics based on 3D Langevin dynamics simulations.For a pair of symmetrically placed blockers with respect to the target,we find that the search time τ rapidly decreases and then saturates with increasing the distance between the blocker and the target.For randomly placed blockers with density φ,τ may initially increase to its maximum and then unexpectedly decreases with increasing φ,or always increase with φ,depending on the nonspecific interaction strength and the volume fraction of DNA in the system.The previous contradicted results on the role of the blocker in search time are reconciled by these findings.Particularly,the nonmonotonic behavior of τ with φindicates that blockers may facilitate the search after a critical φ.In chapter four,the implications of crowding and protein subdiffusion in solution are our main focuses here.In the bulk,we use fractional Brownian motion(FBM)to mimic a non-Brownian and subdiffusive motion of proteins.We demonstrated that the target search time features a pronounced minimum versus the strength of protein-DNA binding ￡,for normal and subdiffusive motions.The optimal target search time is found to rise significantly as a function of ￡ for smaller exponents a.We characterized this increase of τ as the bulk motion slows down due to a more local space sampling by FBM.We believe that our results shed light on the role of facilitated diffusion in DNA targeting kinetics in vivo.