Facilitated diffusion with DNA coiling

Abstract

When DNA-binding proteins search for their specific binding site on a DNA molecule they alternate between linear 1-dimensional diffusion along the DNA molecule, mediated by nonspecific binding, and 3-dimensional volume excursion events between successive dissociation from and rebinding to DNA. If the DNA molecule is kept in a straight configuration, for instance, by optical tweezers, these 3-dimensional excursions may be divided into long volume excursions and short hops along the DNA. These short hops correspond to immediate rebindings after dissociation such that a rebinding event to the DNA occurs at a site that is close to the site of the preceding dissociation. When the DNA molecule is allowed to coil up, immediate rebinding may also lead to so-called intersegmental jumps, i.e., immediate rebindings to a DNA segment that is far away from the unbinding site when measured in the chemical distance along the DNA, but close by in the embedding 3-dimensional space. This effect is made possible by DNA looping. The significance of intersegmental jumps was recently demonstrated in a single DNA optical tweezers setup. Here we present a theoretical approach in which we explicitly take the effect of DNA coiling into account. By including the spatial correlations of the short hops we demonstrate how the facilitated diffusion model can be extended to account for intersegmental jumping at varying DNA densities. It is also shown that our approach provides a quantitative interpretation of the experimentally measured enhancement of the target location by DNA-binding proteins.gene regulation | search processes | random processes | intersegmental jumps | single-molecule biophysics A t any given instant of time a biological cell only uses part of its genes for production of other molecules (RNA, proteins). During the development of the cell, or the organism the cell belongs to, different genes may be turned on. A classical example is the lactose metabolism of bacteria: in absence of lactose the Lac repressor is specifically bound at the lacZ gene and prevents unnecessary production of the lactose enzyme used to digest the milk sugar; when only lactose and no glucose is present the lacZ gene is activated and lactose-digesting enzymes are produced. Equally famed is the λ switch in Escherichia coli bacteria that are infected by bacteriophage λ. There, the λ switch decides between the dormant lysogenic state or the state of lysis that leads to the production of new phages and ultimate death of the E.coli host cell. Molecularly, the regulation of a gene relies on the presence of certain DNA-binding proteins, so-called transcription factors, that bind to a specific binding site close to the starting sequence of the related gene. The transcription factor then promotes or inhibits binding of RNA polymerase and thus regulates the transcription of this gene. This strategy allows eukaryotic and prokaryotic cells as well as viruses to respond to different internal or external signals (1, 2).The binding of the protein to its specific bindin...

Comparison of pure and combined search strategies for single and multiple targets

“…Slutsky and Mirny [92] argue that the one-dimensional search needs to consist of search and recognition modes such that the protein can slide sufficiently fast while retaining its binding selectivity. Including intersegmental transfers or jumps of the protein between chemically remote but physically close segments of the DNA chain further improves the search efficiency, especially when the three-dimensional search mode is repressed, for instance, at certain salt conditions [34,93,94]. Interestingly, in the limit of long DNA chains and sufficiently fast reorganisation of the DNA conformation, intersegmental jumps effect an LF search by the binding protein [34].…”

The dynamic interplay between DNA topoisomerases and DNA topology

“…The altered topology impacts the geometry and dynamics of DNA bending, as well as the probabilities of DNA melting and distal site juxtaposition (Vologodskii 2009;Vologodskii andCozzarelli 1993, 1994). These physical changes in turn affect the interaction of DNA-modifying proteins with their DNA substrates (Lomholt et al 2009;Vologodskii and Cozzarelli 1994). The impact of DNA supercoiling on enzymatic activity is particularly clear for RNA transcription.…”

A new approach to the problem of bulk-mediated surface diffusion

“…The latter describes effective diffusion of the particle in the absence of the constraint that the particle should be on the surface at time t, 5) where P eq b is the equilibrium probability of finding the particle in the bulk layer above the surface,…”

“…Their initial treatment was extended in subsequent studies to allow for a more careful consideration of DNA structural features and spatial arrangements [1][2][3][4][5][6][8][9][10] making a quantitative foundation for interpreting experimental findings. [24][25][26] One can find a detailed discussion of the problem in a recent review article.…”