Journal ArticleDOI
The spectrum of filament entanglement complexity and an entanglement phase transition
Gregory Buck,Jonathan Simon +1 more
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TLDR
In this paper, the authors classify entanglement patterns by the rate with which entagglement complexity grows with the length of the filament, and identify a fundamental phase transition between linear and nonlinear entaglement rates.Abstract:
DNA, hair, shoelaces, vortex lines, rope, proteins, integral curves, thread, magnetic flux tubes, cosmic strings and extension cords; filaments come in all sizes and with diverse qualities. Filaments tangle, with profound results: DNA replication is halted, field energy is stored, polymer materials acquire their remarkable properties, textiles are created and shoes stay on feet. We classify entanglement patterns by the rate with which entanglement complexity grows with the length of the filament. We show which rates are possible and which are expected in arbitrary circumstances. We identify a fundamental phase transition between linear and nonlinear entanglement rates. We also find (perhaps surprising) relationships between total curvature, bending energy and entanglement.read more
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On the derivation of the HOMFLYPT polynomial invariant for fluid knots
Xin Liu,Renzo L. Ricca +1 more
TL;DR: In this article, Liu et al. derived the skein relations of the HOMFLYPT polynomial for ideal fluid knots from helicity, thus providing a rigorous proof that the HOFT invariant is a new, powerful invariant of topological fluid mechanics.
Journal ArticleDOI
Protein droplets in systems of disordered homopeptides and the amyloid glass phase
TL;DR: A novel amyloid glass phase is identified that is substantially cross linked forming amorphous and anisotropic spatial patterns and the existence of fluid-like phenomena, like droplet fusion and fission is demonstrated.
Journal ArticleDOI
Structural entanglements in protein complexes
TL;DR: It is argued that entanglement enhances the thermodynamic stability of the system but it may have other functions: burying the hydrophobic residues at the interface and increasing the DNA or RNA binding area.
Journal ArticleDOI
Active entanglement enables stochastic, topological grasping
Kaitlyn P. Becker,Clark B. Teeple,N. Charles,Yeon-Hee Jung,Danielle Baum,James C. Weaver,Lakshminarayanan Mahadevan,Robert Wood +7 more
TL;DR: In this paper , the authors introduce the notion of entanglement grasping, a non-deterministic approach that circumvents challenges of object recognition, grasp planning, and feedback via a randomly distributed array of contacts via filament-like soft actuators.
Journal ArticleDOI
Link lengths and their growth powers
TL;DR: For a certain infinite family of knots or links, this article studied the growth power ratios of their stick number, lattice stick number and minimum lattice length compared with their minimum crossing number c(K) for every.
References
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Journal ArticleDOI
Comprehensive mapping of long-range interactions reveals folding principles of the human genome.
Erez Lieberman Aiden,Nynke L. van Berkum,Louise Williams,Maxim Imakaev,Tobias Ragoczy,Tobias Ragoczy,Agnes Telling,Agnes Telling,Ido Amit,Bryan R. Lajoie,Peter J. Sabo,Michael O. Dorschner,Richard Sandstrom,Bradley E. Bernstein,Bradley E. Bernstein,Michaël Bender,Mark Groudine,Mark Groudine,Andreas Gnirke,John A. Stamatoyannopoulos,Leonid A. Mirny,Eric S. Lander,Eric S. Lander,Job Dekker +23 more
TL;DR: Hi-C is described, a method that probes the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing and demonstrates the power of Hi-C to map the dynamic conformations of entire genomes.
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Principles of Biochemistry
TL;DR: The third edition, coming ten years after the first, emphasizes both the flowering of biochemical research and the prodigious effort by busy teachers and scientists to keep up to date this popular text and reference.
Book
Knots and Links
TL;DR: In this paper, the fundamental group of three-dimensional PL geometry Seifert surfaces Finite cyclic coverings and the torsion invariants Infinite cyclic covers and the Alexander invariant Matrix invariants 3-manifolds and surgery on links Foliations, branched covers, fibrations and so on.
Book
Statistical physics of macromolecules
TL;DR: In this article, the authors introduce the concept of a single macromolecule with volume interaction and the notion of a blob in the theory of volume interactions in polymer systems.