A Brownian ratchet model for DNA loop extrusion by the cohesin complex.

The cohesin complex topologically encircles DNA to promote sister chromatid cohesion. Alternatively, cohesin extrudes DNA loops, thought to reflect chromatin domain formation. Here, we propose a structure-based model explaining both activities. ATP and DNA binding promote cohesin conformational changes that guide DNA through a kleisin N-gate into a DNA gripping state. Two HEAT-repeat DNA binding modules, associated with cohesin’s heads and hinge, are now juxtaposed. Gripping state disassembly, following ATP hydrolysis, triggers unidirectional hinge module movement, which completes topological DNA entry by directing DNA through the ATPase head gate. If head gate passage fails, hinge module motion creates a Brownian ratchet that, instead, drives loop extrusion. Molecular-mechanical simulations of gripping state formation and resolution cycles recapitulate experimentally observed DNA loop extrusion characteristics. Our model extends to asymmetric and symmetric loop extrusion, as well as z-loop formation. Loop extrusion by biased Brownian motion has important implications for chromosomal cohesin function

Rapid movement and transcriptional re-localization of human cohesin on DNA

The spatial organization, correct expression, repair, and segregation of eukaryotic genomes depend on cohesin, ring-shaped protein complexes that are thought to function by entrapping DNA It has been proposed that cohesin is recruited to specific genomic locations from distal loading sites by an unknown mechanism, which depends on transcription, and it has been speculated that cohesin movements along DNA could create three-dimensional genomic organization by loop extrusion. However, whether cohesin can translocate along DNA is unknown. Here, we used single-molecule imaging to show that cohesin can diffuse rapidly on DNA in a manner consistent with topological entrapment and can pass over some DNA-bound proteins and nucleosomes but is constrained in its movement by transcription and DNA-bound CCCTC-binding factor (CTCF). These results indicate that cohesin can be positioned in the genome by moving along DNA, that transcription can provide directionality to these movements, that CTCF functions as a boundary element for moving cohesin, and they are consistent with the hypothesis that cohesin spatially organizes the genome via loop extrusion

Decision making under incompleteness based on soft set theory

[EN]Decision making with complete and accurate information is ideal but infrequent. Unfortunately, in most cases the available infor- mation is vague, imprecise, uncertain or unknown. The theory of soft sets provides an appropriate framework for decision making that may be used to deal with uncertain decisions. The aim of this paper is to propose and analyze an effective algorithm for multiple attribute decision-making based on soft set theory in an incomplete information environment, when the distribution of incomplete data is unknown. This procedure provides an accurate solution through a combinatorial study of possible cases in the unknown data. Our theoretical development is complemented by practical examples that show the feasibility and implementability of this algorithm. Moreover, we review recent research on decision making from the standpoint of the theory of soft sets under incomplete information

Filament Depolymerization Can Explain Chromosome Pulling during Bacterial Mitosis

Chromosome segregation is fundamental to all cells, but the force-generating mechanisms underlying chromosome translocation in bacteria remain mysterious. Caulobacter crescentus utilizes a depolymerization-driven process in which a ParA protein structure elongates from the new cell pole, binds to a ParB-decorated chromosome, and then retracts via disassembly, pulling the chromosome across the cell. This poses the question of how a depolymerizing structure can robustly pull the chromosome that disassembles it. We perform Brownian dynamics simulations with a simple, physically consistent model of the ParABS system. The simulations suggest that the mechanism of translocation is “self-diffusiophoretic”: by disassembling ParA, ParB generates a ParA concentration gradient so that the ParA concentration is higher in front of the chromosome than behind it. Since the chromosome is attracted to ParA via ParB, it moves up the ParA gradient and across the cell. We find that translocation is most robust when ParB binds side-on to ParA filaments. In this case, robust translocation occurs over a wide parameter range and is controlled by a single dimensionless quantity: the product of the rate of ParA disassembly and a characteristic relaxation time of the chromosome. This time scale measures the time it takes for the chromosome to recover its average shape after it is has been pulled. Our results suggest explanations for observed phenomena such as segregation failure, filament-length-dependent translocation velocity, and chromosomal compaction

Mechanochemical modeling of dynamic microtubule growth involving sheet-to-tube transition

Microtubule dynamics is largely influenced by nucleotide hydrolysis and the resultant tubulin configuration changes. The GTP cap model has been proposed to interpret the stabilizing mechanism of microtubule growth from the view of hydrolysis effects. Besides, the microtubule growth involves the closure of a curved sheet at its growing end. The curvature conversion also helps to stabilize the successive growth, and the curved sheet is referred to as the conformational cap. However, there still lacks theoretical investigation on the mechanical-chemical coupling growth process of microtubules. In this paper, we study the growth mechanisms of microtubules by using a coarse-grained molecular method. Firstly, the closure process involving a sheet-to-tube transition is simulated. The results verify the stabilizing effect of the sheet structure, and the minimum conformational cap length that can stabilize the growth is demonstrated to be two dimers. Then, we show that the conformational cap can function independently of the GTP cap, signifying the pivotal role of mechanical factors. Furthermore, based on our theoretical results, we describe a Tetris-like growth style of microtubules: the stochastic tubulin assembly is regulated by energy and harmonized with the seam zipping such that the sheet keeps a practically constant length during growth.Comment: 23 pages, 7 figures. 2 supporting movies have not been uploaded due to the file type restriction

On the fixed point theory of soft metric spaces

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