Chromatin Is Frequently Unknotted at the Megabase Scale.

Knots in the human genome would greatly impact diverse cellular processes ranging from transcription to gene regulation. To date, it has not been possible to directly examine the genome in vivo for the presence of knots. Recently, methods for serial fluorescent in situ hybridization have made it possible to measure the three-dimensional position of dozens of consecutive genomic loci in vivo. However, the determination of whether genomic trajectories are knotted remains challenging because small errors in the localization of a single locus can transform an unknotted trajectory into a highly knotted trajectory and vice versa. Here, we use stochastic closure analysis to determine if a genomic trajectory is knotted in the setting of experimental noise. We analyze 4727 deposited genomic trajectories of a 2-Mb-long chromatin interval from human chromosome 21. For 243 of these trajectories, their knottedness could be reliably determined despite the possibility of localization errors. Strikingly, in each of these 243 cases, the trajectory was unknotted. We note a potential source of bias insofar as knotted contours may be more difficult to reliably resolve. Nevertheless, our data are consistent with a model in which, at the scales probed, the human genome is often free of knots

Studies of global and local entanglements of individual protein chains using the concept of knotoids.

We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely, knotoids are diagrams representing projections of open curves in 3D space, in contrast to knot diagrams which represent projections of closed curves in 3D space. The intrinsic difference with classical knot theory is that the generalization provided by knotoids admits non-trivial topological entanglement of the open curves provided that their geometry is frozen as it is the case for crystallized proteins. Consequently, our approach doesn't require the closure of chains into loops which implies that the geometry of analysed chains does not need to be changed by closure in order to characterize their topology. Our study revealed that the knotoid approach detects protein regions that were classified earlier as knotted and also new, topologically interesting regions that we classify as pre-knotted

Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids

In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins

Chromatin Loop Extrusion and Chromatin Unknotting.

It has been a puzzle how decondensed interphase chromosomes remain essentially unknotted. The natural expectation is that in the presence of type II DNA topoisomerases that permit passages of double-stranded DNA regions through each other, all chromosomes should reach the state of topological equilibrium. The topological equilibrium in highly crowded interphase chromosomes forming chromosome territories would result in formation of highly knotted chromatin fibres. However, Chromosome Conformation Capture (3C) methods revealed that the decay of contact probabilities with the genomic distance in interphase chromosomes is practically the same as in the crumpled globule state that is formed when long polymers condense without formation of any knots. To remove knots from highly crowded chromatin, one would need an active process that should not only provide the energy to move the system from the state of topological equilibrium but also guide topoisomerase-mediated passages in such a way that knots would be efficiently unknotted instead of making the knots even more complex. We perform coarse-grained molecular dynamics simulations of the process of chromatin loop extrusion involving knotted and catenated chromatin fibres to check whether chromatin loop extrusion may be involved in active unknotting of chromatin fibres. Our simulations show that the process of chromatin loop extrusion is ideally suited to actively unknot, decatenate and demix chromatin fibres in interphase chromosomes

In Silico Transcriptomic Analysis of Wound-Healing-Associated Genes in Malignant Pleural Mesothelioma.

Background and objectives: Malignant pleural mesothelioma (MPM) is a devastating malignancy with poor prognosis. Reliable biomarkers for MPM diagnosis, monitoring, and prognosis are needed. The aim of this study was to identify genes associated with wound healing processes whose expression could serve as a prognostic factor in MPM patients. Materials and Methods: We used data mining techniques and transcriptomic analysis so as to assess the differential transcriptional expression of wound-healing-associated genes in MPM. Moreover, we investigated the potential prognostic value as well as the functional enrichments of gene ontologies relative to microRNAs (miRNAs) of the significantly differentially expressed wound-healing-related genes in MPM. Results: Out of the 82 wound-healing-associated genes analyzed, 30 were found significantly deregulated in MPM. Kaplan-Meier analysis revealed that low ITGAV gene expression could serve as a prognostic factor favoring survival of MPM patients. Finally, gene ontology annotation enrichment analysis pointed to the members of the hsa-miR-143, hsa-miR-223, and the hsa-miR-29 miRNA family members as important regulators of the deregulated wound healing genes. Conclusions: 30 wound-healing-related genes were significantly deregulated in MPM, which are potential targets of hsa-miR-143, hsa-miR-223, and the hsa-miR-29 miRNA family members. Out of those genes, ITGAV gene expression was a prognostic factor of overall survival in MPM. Our results highlight the role of impaired tissue repair in MPM development and should be further validated experimentally

KnotProt 2.0: a database of proteins with knots and other entangled structures.

The KnotProt 2.0 database (the updated version of the KnotProt database) collects information about proteins which form knots and other entangled structures. New features in KnotProt 2.0 include the characterization of both probabilistic and deterministic entanglements which can be formed by disulfide bonds and interactions via ions, a refined characterization of entanglement in terms of knotoids, the identification of the so-called cysteine knots, the possibility to analyze all or a non-redundant set of proteins, and various technical updates. The KnotProt 2.0 database classifies all entangled proteins, represents their complexity in the form of a knotting fingerprint, and presents many biological and geometrical statistics based on these results. Currently the database contains >2000 entangled structures, and it regularly self-updates based on proteins deposited in the Protein Data Bank (PDB)

A generalized skein relation for Khovanov homology and a categorification of the θ-invariant

The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are able to generalize the Khovanov homology in order to obtain a categorification of the θ-invariant, which is itself a generalization of the Jones polynomial. Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

Knoto-ID: a tool to study the entanglement of open protein chains using the concept of knotoids.

The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluating the entanglement of open curves without the need to close them, using the recent concept of knotoids which is a generalization of the classical knot theory to open curves. Knoto-ID can analyse the global topology of the full chain as well as the local topology by exhaustively studying all subchains or only determining the knotted core. Knoto-ID permits to localize topologically non-trivial protein folds that are not detected by informatics tools detecting knotted protein folds. Knoto-ID is written in C++ and includes R (www.R-project.org) scripts to generate plots of projections maps, fingerprint matrices and disk matrices. Knoto-ID is distributed under the GNU General Public License (GPL), version 2 or any later version and is available at https://github.com/sib-swiss/Knoto-ID. A binary distribution for Mac OS X, Linux and Windows with detailed user guide and examples can be obtained from https://www.vital-it.ch/software/Knoto-ID

A topological selection of folding pathways from native states of knotted proteins

Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins

In silico transcriptomic analysis of wound-healing-associated genes in malignant pleural mesothelioma

Background and objectives: Malignant pleural mesothelioma (MPM) is a devastating malignancy with poor prognosis. Reliable biomarkers for MPM diagnosis, monitoring, and prognosis are needed. The aim of this study was to identify genes associated with wound healing processes whose expression could serve as a prognostic factor in MPM patients. Materials and Methods: We used data mining techniques and transcriptomic analysis so as to assess the differential transcriptional expression of wound-healing-associated genes in MPM. Moreover, we investigated the potential prognostic value as well as the functional enrichments of gene ontologies relative to microRNAs (miRNAs) of the significantly differentially expressed wound-healing-related genes in MPM. Results: Out of the 82 wound-healing-associated genes analyzed, 30 were found significantly deregulated in MPM. Kaplan–Meier analysis revealed that low ITGAV gene expression could serve as a prognostic factor favoring survival of MPM patients. Finally, gene ontology annotation enrichment analysis pointed to the members of the hsa-miR-143, hsa-miR-223, and the hsa-miR-29 miRNA family members as important regulators of the deregulated wound healing genes. Conclusions: 30 wound-healing-related genes were significantly deregulated in MPM, which are potential targets of hsa-miR-143, hsa-miR-223, and the hsa-miR-29 miRNA family members. Out of those genes, ITGAV gene expression was a prognostic factor of overall survival in MPM. Our results highlight the role of impaired tissue repair in MPM development and should be further validated experimentally. © 2019 by the authors. Licensee MDPI, Basel, Switzerland