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The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here we analyze existing experimental data and demonstrate that the Hill coefficient characterizing the binding of transcription factors to their cognate sites can in fact be larger than one -- the standard indication of cooperativity -- even in the absence of any standard cooperative binding mechanism. By studying the problem analytically, we demonstrate that this effect occurs due to the disordered binding energy of the transcription factor to the DNA molecule and the steric interactions between the different copies of the transcription factor. We show that the enhanced Hill coefficient implies a significant reduction in the number of copies of the transcription factors which is needed to occupy a cognate site and, in many cases, can explain existing estimates for numbers of the transcription factors in cells. The mechanism is general and should be applicable to other biological recognition processes.
In gene expression, various kinds of proteins need to bind to specific locus of DNA. It is still not clear how these proteins find their target locus. In this study, the mean first-passage time (FPT) of protein binding to its target locus on DNA chai
Positioning of nucleosomes along eukaryotic genomes plays an important role in their organization and regulation. There are many different factors affecting the location of nucleosomes. Some can be viewed as preferential binding of a single nucleosom
Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, mu
A swarm of preys when attacked by a predator is known to rely on their cooperative interactions to escape. Understanding such interactions of collectively moving preys and the emerging patterns of their escape trajectories still remain elusive. In th
We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature. On the one hand, a quite widespread