September 2017
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7 Reads
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September 2017
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7 Reads
September 2017
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526 Reads
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39 Citations
In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.
September 2017
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9 Reads
September 2017
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65 Reads
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1 Citation
In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif -FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.
August 2015
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192 Reads
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16 Citations
Frontiers in Molecular Biosciences
Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.
... In the real world, where fluids are not ideal, knots decay and can change their topology. The study of the sequences of knots, knot cascades, that can occur during such processes is an active area of research [11,12], see also [13] for a study of knot cascades in DNA. Static solutions that describe physical systems that contain a knot are stable in another sense: the topology does not change under sufficiently small perturbations. ...
Reference:
Complex optical vortex knots
September 2017
... In [14,16], it is shown that the XerCD-dif-FtsK system unlinks replication DNA catenanes in a stepwise manner. The link types of the replication catenanes are torus link T (2, c). ...
Reference:
Signature and crossing number of links
September 2017
... They are facilitated by the general osmotic stress and confinement pressure in the cell nucleus as well as by the additional pressure of DNA supercoiling acting near CTCF sites due to cohesion molecular motors, which actively form chromatin loops at these sites [91]. In addition, different polymer models have widely shown that non-equilibrated knotting and linking probability rapidly grows upon confinement [92]. Therefore, the same result achieved by air-drying and by localization microscopy and mathematical operations on the recorded data set of the freshly fixed cells corroborates that heterochromatin networks with certain topology and determinants in nucleus organization are predestined by the "physics of this compartment". ...
August 2015
Frontiers in Molecular Biosciences