Topology in soft and biological matter. (English) Zbl 07886110
Summary: The last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterization of knots in single polymers and proteins to that of whole chromosomes and polymer melts. At the same time, considerable advances have been made in the description of the interplay between topological and physical properties in complex fluids, with the development of techniques that now allow researchers to control the formation of and interaction between defects in diverse classes of liquid crystals. Thanks to technological progress and the integration of experiments with increasingly sophisticated numerical simulations, topological biological and soft matter is a vibrant area of research attracting scientists from a broad range of disciplines. However, owing to the high degree of specialization of modern science, many results have remained confined to their own particular fields, with different jargon making it difficult for researchers to share ideas and work together towards a comprehensive view of the diverse phenomena at play. Compelled by these motivations, here we present a comprehensive overview of topological effects in systems ranging from DNA and genome organization to entangled proteins, polymeric materials, liquid crystals, and theoretical physics, with the intention of reducing the barriers between different fields of soft matter and biophysics. Particular care has been taken in providing a coherent formal introduction to the topological properties of polymers and of continuum materials and in highlighting the underlying common aspects concerning the emergence, characterization, and effects of topological objects in different systems. The second half of the review is dedicated to the presentation of the latest results in selected problems, specifically, the effects of topological constraints on the viscoelastic properties of polymeric materials; their relation with genome organization; a discussion on the emergence and possible effects of knots and other entanglements in proteins; the emergence and effects of topological defects and solitons in complex fluids. This review is dedicated to the memory of Marek Cieplak.
Keywords:
topology in soft condensed matter; polymers and polymer melts; topology in living matter – protein folding; entangled proteins; DNA topology & genome organization; topologically complex fluidsBiographic References:
Cieplak, MarekReferences:
| [1] | Ashley, C. W., The Ashley Book of Knots, 1944, Doubleday |
| [2] | Adams, C. C., The Knot Book, 1994, Freeman · Zbl 0840.57001 |
| [3] | Kauffman, L. H., Knots and Applications, 1995, World Scientific · Zbl 0838.00015 |
| [4] | Burton, B. A., The next 350 million knots, (36th International Symposium on Computational Geometry (SoCG 2020), 2020, Schloss Dagstuhl-Leibniz-Zentrum für Informatik), 25:1-25:17 · Zbl 07760154 |
| [5] | Jones, V. F.R., Hecke algebra representations of braid groups and link polynomials, (New Developments in the Theory of Knots, 1987, World Scientific), 20-73 |
| [6] | Kauffman, L. H., Knots and Physics, 2001, World Scientific · Zbl 1057.57001 |
| [7] | Freyd, P.; Yetter, D.; Hoste, J.; Lickorish, W. B.R.; Millett, K.; Ocneanu, A., A new polynomial invariant of knots and links, Bull. (new series) Am. Math. Soc., 12, 2, 239-246, 1985 · Zbl 0572.57002 |
| [8] | Przytycki, J. H.; Traczyk, P., Invariants of links of conway type, Kobe J. Math., 4, 115-139, 1987 · Zbl 0655.57002 |
| [9] | Vologodskii, A. V.; Lukashin, A. V.; Frank-Kamenetskii, M. D.; Anshelevich, V. V., The knot problem in statistical mechanics of polymer chains, Sov. Phys.-JETP, 39, 1059-1063, 1974 |
| [10] | Tubiana, L.; Polles, G.; Orlandini, E.; Micheletti, C., Kymoknot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers, Eur. Phys. J. E, 41, 6, 72, 2018 |
| [11] | Micheletti, C.; Marenduzzo, D.; Orlandini, E., Polymers with spatial or topological constraints: Theoretical and computational results, Phys. Rep., 504, 1-73, 2011 · Zbl 1211.82070 |
| [12] | Dabrowski-Tumanski, P.; Rubach, P.; Niemyska, W.; Gren, B. A.; Sulkowska, J. I., Topoly: Python package to analyze topology of polymers, Brief. Bioinform., 000, 1-8, 2020 |
| [13] | Scharein, R. G., Knotplot, 1998, https://www.knotplot.com/ |
| [14] | Stein, W.; Joyner, D., Sage: System for algebra and geometry experimentation, Acm Sigsam Bull., 39, 2, 61-64, 2005 · Zbl 1341.68315 |
| [15] | Trefz, B.; Siebert, J.; Virnau, P., How molecular knots can pass through each other, Proc. Natl. Acad. Sci., 111, 22, 7948-7951, 2014 |
| [16] | Tubiana, L., Computational study on the progressive factorization of composite polymer knots into separated prime components, Phys. Rev. E, 89, 5, Article 052602 pp., 2014 |
| [17] | Najafi, S.; Podgornik, R.; Potestio, R.; Tubiana, L., Role of bending energy and knot chirality in knot distribution and their effective interaction along stretched semiflexible polymers, Polymers, 8, 10, 347, 2016 |
| [18] | Ricca, R. L.; Nipoti, B., Gauss’ linking number revisited, J. Knot Theory Ramifications, 20, 10, 1325-1343, 2011 · Zbl 1230.57009 |
| [19] | Douglas, J., Solution of the problem of plateau, Trans. Amer. Math. Soc., 33, 1, 263-321, 1931 · JFM 57.1542.03 |
| [20] | Smrek, J.; Grosberg, A. Y., Minimal surfaces on unconcatenated polymer rings in melt, ACS Macro Lett., 5, 6, 750-754, 2016 |
| [21] | Lang, M., Ring conformations in bidisperse blends of ring polymers, Macromolecules, 46, 3, 1158-1166, 2013 |
| [22] | Brakke, K. A., The surface evolver, Exp. Math., 1, 2, 141-165, 1992 · Zbl 0769.49033 |
| [23] | Van Wijk, J. J.; Cohen, A. M., Visualization of seifert surfaces, IEEE Trans. Vis. Comput. Graph., 12, 485, 2006 |
| [24] | Conway, J. H., An enumeration of knots and links, and some of their algebraic properties, (Computational Problems in Abstract Algebra, 1970, Elsevier), 329-358 · Zbl 0202.54703 |
| [25] | Sumners, D. W., Lifting the curtain: Using topology to probe the hidden action of enzymes, Notices Amer. Math. Soc., 42, 528-537, 1995 · Zbl 1003.92515 |
| [26] | Hu, S.; Lundgren, M.; Niemi, A. J., Discrete frenet frame, inflection point solitons, curve visualization with applications to folded proteins, Phys. Rev. E, 83, Article 061908 pp., 2011 |
| [27] | Călugăreanu, G., Sur les classes d’isotopie des noeuds tridimensionnels et leurs invariants, Czechoslovak Math. J., 11, 4, 588-625, 1961 · Zbl 0118.16005 |
| [28] | Moffatt, H. K.; Ricca, R. L., Helicity and the Călugăreanu invariant, Proc. R. Soc. London. Ser. A: Math. Phys. Sci., 439, 1906, 411-429, 1992 · Zbl 0771.57013 |
| [29] | White, J. H., Self-linking and the Gauss integral in higher dimensions, Am. J. Math., 91, 683-728, 1969 · Zbl 0193.50903 |
| [30] | Fuller, F. B., The writhing number of a space curve, Proc. Natl. Acad. Sci. U S A, 68, 815-819, 1971 · Zbl 0212.26301 |
| [31] | Dennis, M. R.; Hannay, J. H., Geometry of Călugăreanu’s theorem, Proc. R. Soc. A: Math., Phys. Eng. Sci., 461, 2062, 3245-3254, 2005 · Zbl 1370.53003 |
| [32] | Kamien, R. D., The geometry of soft materials: A primer, Rev. Modern Phys., 74, 4, 953-971, 2002 |
| [33] | Moriuchi, H., An enumeration of theta-curves with up to seven crossings, J. Knot Theory Ramifications, 18, 2, 2009 · Zbl 1200.57002 |
| [34] | Yamada, S., An invariant of spatial graphs, J. Graph Theory, 13, 5, 537-551, 1989 · Zbl 0682.57003 |
| [35] | Tubiana, L.; Orlandini, E.; Micheletti, C., Probing the entanglement and locating knots in ring polymers: A comparative study of different arc closure schemes, Progr. Theoret. Phys. Suppl., 191, 192-204, 2011 |
| [36] | Sumners, D. W.; Whittington, S. G., Detecting knots in self-avoiding walks, J. Phys. A: Math. Gen., 23, 1471-1472, 1990 |
| [37] | Van Rensburg, E. J.J.; Sumners, D. W.; Wasserman, E.; Whittington, S. G., Entanglement complexity of self-avoiding walks, J. Phys. A: Math. Gen., 25, 6557-6566, 1992 · Zbl 0770.60099 |
| [38] | Mansfield, M. L., Are there knots in proteins?, Nature Structural Biology, 1, 4, 213-214, 1994 |
| [39] | Marcone, B.; Orlandini, E.; Stella, A. L.; Zonta, F., What is the length of a knot in a polymer?, J. Phys. A: Math. Gen., 38, L15-L21, 2005 · Zbl 1067.82531 |
| [40] | Millett, K.; Dobay, A.; Stasiak, A., Linear random knots and their scaling behavior, Macromolecules, 38, 2, 601-606, 2005 |
| [41] | Tubiana, L.; Orlandini, E.; Micheletti, C., Multiscale entanglement in ring polymers under spherical confinement, Phys. Rev. Lett., 107, Article 188302 pp., 2011 |
| [42] | Tubiana, L.; Kobayashi, H.; Potestio, R.; Dünweg, B.; Kremer, K.; Virnau, P.; Daoulas, K., Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators, J. Phys.: Condens. Matter, 33, 20, Article 204003 pp., 2021 |
| [43] | Caraglio, M.; Micheletti, C.; Orlandini, E., Physical links: defining and detecting inter-chain entanglement, Sci. Rep., 7, 2017, art no. 1156 |
| [44] | Barbensi, A.; Yerolemou, N.; Vipond, O.; Mahler, B. I.; Dabrowski-Tumanski, P.; Goundaroulis, D., A topological selection of folding pathways from native states of knotted proteins, Symmetry, 13, 1670, 2021 |
| [45] | Goundaroulis, D.; Dorier, J.; Benedetti, F.; Stasiak, A., Studies of global and local entanglements of individual protein chains using the concept of knotoids, Sci. Rep., 7, 1, 6309, 2017 |
| [46] | Goundaroulis, D.; Gügümcü, N.; Lambropoulou, S.; Dorier, J.; Stasiak, A.; Kauffman, L., Topological models for open-knotted protein chains using the concepts of knotoids and bonded knotoids, Polymers, 9, 9, 444, 2017 |
| [47] | Dorier, J.; Goundaroulis, D.; Benedetti, F.; Stasiak, A., Knoto-ID: A tool to study the entanglement of open protein chains using the concept of knotoids, Bioinformatics, 34, 19, 3402-3404, 2018 |
| [48] | Barbensi, A.; Goundaroulis, D., f-distance of knotoids and protein structure, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 477, 2246, Article 20200898 pp., 2021 |
| [49] | Turaev, V., Knotoids, Osaka J. Math., 49, 1, 195-223, 2012 · Zbl 1271.57030 |
| [50] | Gügümcü, N.; Kauffman, L. H., New invariants of knotoids, European J. Combin., 65, 186-229, 2017 · Zbl 1373.57012 |
| [51] | Goundaroulis, D.; Dorier, J.; Stasiak, A., A systematic classification of knotoids on the plane and on the sphere, 2019, arXiv preprint arXiv:1902.07277 |
| [52] | Barbensi, A.; Buck, D.; Harrington, H. A.; Lackenby, M., Double branched covers of knotoids, Comm. Anal. Geom., 2018 |
| [53] | Goundaroulis, D.; Dorier, J.; Stasiak, A., Knotoids and protein structure, Topol. Geom. Biopolym., 746, 185, 2020 · Zbl 1447.92302 |
| [54] | Dabrowski-Tumanski, P.; Rubach, P.; Goundaroulis, D.; Dorier, J.; Sułkowski, P.; Millett, K. C.; Rawdon, E. J.; Stasiak, A.; Sulkowska, J. I., KnotProt 2.0: A database of proteins with knots and other entangled structures, Nucleic Acids Res., 47, D1, D367-D375, 2018 |
| [55] | Panagiotou, E.; Kauffman, L. H., Knot polynomials of open and closed curves, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 476, 2240, Article 20200124 pp., 2020 · Zbl 1472.57011 |
| [56] | Panagiotou, E.; Kauffman, L. H., Vassiliev measures of complexity of open and closed curves in 3-space, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 477, 2254, Article 20210440 pp., 2021 |
| [57] | Viro, O., Khovanov homology, its definitions and ramifications, Fund. Math., 184, 317-342, 2004 · Zbl 1078.57013 |
| [58] | King, N. P.; Yeates, E. O.; Yeates, T. O., Identification of rare slipknots in proteins and their implications for stability and folding, J. Mol. Biol., 373, 1, 153-166, 2007 |
| [59] | Sulkowska, J. I.; Rawdon, E. J.; Millett, K. C.; Onuchic, J. N.; Stasiak, A., Conservation of complex knotting and slipknotting patterns in proteins, Proc. Natl. Acad. Sci., 109, 26, E1715-E1723, 2012 |
| [60] | Witten, E.; Mitra, A. N., Quantum field theory and the jones polynomial, Comm. Math. Phys., 121, 351-399, 1989 · Zbl 0667.57005 |
| [61] | Kleman, M.; Lavrentovich, O. D., Soft Matter Physics: An Introduction, 2003, Springer: Springer New York |
| [62] | Mermin, N. D., The topological theory of defects in ordered media, Rev. Modern Phys., 51, 3, 591-648, 1979 |
| [63] | Vachaspati, T., A class of kinks in SU(N) x Z(2), Phys. Rev. D, 63, Article 105010 pp., 2001 |
| [64] | Pogosian, L.; Vachaspati, T., Space of kink solutions in SU(N) * Z(2), Phys. Rev. D, 64, Article 105023 pp., 2001 |
| [65] | Kamien, R. D.; Selinger, J. V., Order and frustration in chiral liquid crystals, J. Phys.: Condens. Matter, 13, 3, R1, 2001 |
| [66] | Frank, F. C., I. Liquid crystals. On the theory of liquid crystals, Discuss. Faraday Soc., 25, 19-28, 1958 |
| [67] | Čopar, S.; Žumer, S., Quaternions and hybrid nematic disclinations, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469, 2156, 20130204, 2013 |
| [68] | Nash, C.; Sen, S., Topology and Geometry for Physicists, 1988, Academic Press · Zbl 0666.53001 |
| [69] | Volovik, G. E.; Lavrentovich, O. D., Topological dynamics of defects: boojums in nematic drops, Sov. Phys.—JETP, 58, December 1983, 1159-1166, 1983 |
| [70] | Ondris-Crawford, R.; Boyko, E. P.; Wagner, B. G.; Erdmann, J. H.; Žumer, S.; Doane, J. W., Microscope textures of nematic droplets in polymer dispersed liquid crystals, J. Appl. Phys., 69, 9, 6380-6386, 1991 |
| [71] | Škarabot, M.; Ravnik, M.; Žumer, S.; Tkalec, U.; Poberaj, I.; Babič, D.; Osterman, N.; Muševič, I., Two-dimensional dipolar nematic colloidal crystals, Phys. Rev. E, 76, Article 051406 pp., 2007 |
| [72] | Alexander, G. P.; Chen, B. G.; Matsumoto, E. A.; Kamien, R. D., Colloquium: Disclination loops, point defects, all that in nematic liquid crystals, Rev. Modern Phys., 84, 2, 497, 2012 |
| [73] | Göbel, B.; Mertig, I.; Tretiakov, O. A., Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles, Phys. Rep., 895, 1, 2021 · Zbl 1489.82093 |
| [74] | Wu, J.-S.; Smalyukh, I. I., Hopfions, heliknotons, skyrmions, torons and both abelian and nonabelian vortices in chiral liquid crystals, Liquid Cryst. Rev., 1-35, 2022 |
| [75] | Ackerman, P. J.; Smalyukh, I. I., Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and Hopfions, Phys. Rev. X, 7, 1, Article 011006 pp., 2017 |
| [76] | Chen, B. G.-g.; Ackerman, P. J.; Alexander, G. P.; Kamien, R. D.; Smalyukh, I. I., Generating the Hopf fibration experimentally in nematic liquid crystals, Phys. Rev. Lett., 110, 23, Article 237801 pp., 2013 |
| [77] | Ackerman, P. J.; Smalyukh, I. I., Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids, Nature Mater., 16, 4, 426-432, 2017 |
| [78] | Tai, J.-S. B.; Smalyukh, I. I., Static Hopf solitons and knotted emergent fields in solid-state noncentrosymmetric magnetic nanostructures, Phys. Rev. Lett., 121, 401, 2018 |
| [79] | Whitehead, J. H.C., An expression of Hopf’s invariant as an integral, Proc. Natl. Acad. Sci., 33, 5, 117-123, 1947 · Zbl 0030.07902 |
| [80] | Woltjer, L., A theorem on force-free magnetic fields, Proc. Natl. Acad. Sci., 44, 6, 489-491, 1958 · Zbl 0081.21703 |
| [81] | Moffatt, H. K., The degree of knottedness of tangled vortex lines, J. Fluid Mech., 35, 1, 117-129, 1969 · Zbl 0159.57903 |
| [82] | Moreau, J. J., Constantes d’un îlot tourbillonnaire en fluide parfait barotrope, C. R. Hebd. Séances l’Acad. Sci., 252, 2810-2812, 1961 · Zbl 0151.41703 |
| [83] | Berger, M. A.; Field, G. B., The topological properties of magnetic helicity, J. Fluid Mech., 147, 133-148, 1984 |
| [84] | Liu, X.; Ricca, R. L., The Jones polynomial for fluid knots from helicity, J. Phys. A: Math. Theor., 45, Article 205501 pp., 2012 · Zbl 1310.76047 |
| [85] | Liu, X.; Ricca, R. L., On the derivation of the HOMFLYPT polynomial invariant for fluid knots, J. Fluid Mech., 773, 34-48, 2015 · Zbl 1331.76009 |
| [86] | Knotted Fields, R.L. Ricca, X. Liu (Eds.), in: Lecture Notes in Mathematics, Springer-Verlag, in press. |
| [87] | Rubinstein, M.; Colby, R. H., Polymer Physics, 2003, Oxford University Press: Oxford University Press New York |
| [88] | Edwards, S. F., Statistical mechanics with topological constraints: I, Proc. Phys. Soc., 91, 3, 513-519, 1967 · Zbl 0181.57001 |
| [89] | Edwards, S. F., Statistical mechanics with topological constraints: II, J. Phys. A: Math. Gen., 1, 15-28, 1968 · Zbl 0181.57002 |
| [90] | Doi, M.; Edwards, S. F., The Theory of Polymer Dynamics, 1986, Clarendon: Clarendon Oxford |
| [91] | Cloizeaux, J.; Jannink, G., Polymers in Solution : their Modelling and Structure, 1990, Clarendon Press Oxford University Press: Clarendon Press Oxford University Press Oxford New York |
| [92] | Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, 1990, World Scientific: World Scientific Singapore Teaneck, NJ · Zbl 0941.81575 |
| [93] | Vernizzi, G.; Orland, H.; Zee, A., Classification and predictions of RNA pseudoknots based on topological invariants, Phys. Rev. E, 94, Article 042410 pp., 2016 |
| [94] | Molochkov, A.; Begun, A.; Niemi, A., Gauge symmetries and structure of proteins, (Foka, Y.; Brambilla, N.; Kovalenko, V., EPJ Web of Conferences, vol. 137, 2017, EDP Sciences), 04004 |
| [95] | Manna, R. K.; Kumar, P. B.S., Emergent topological phenomena in active polymeric fluids, Soft Matter, 15, 3, 477-486, 2019 |
| [96] | De Gennes, P. G., Exponents for the excluded volume problem as derived by the Wilson method, Phys. Lett. A, 38, 5, 339-340, 1972 |
| [97] | Schäfer, L., Renormalized perturbation theory and field-theoretic renormalization group, (Excluded Volume Effects in Polymer Solutions, 1999, Springer: Springer Berlin, Heidelberg), 179-205 |
| [98] | Ferrari, F.; Paturej, J.; Pia̧tek, M.; Zhao, Y., Knots, links, anyons and statistical mechanics of entangled polymer rings, Nuclear Phys. B, 945, Article 114673 pp., 2019 · Zbl 1430.82016 |
| [99] | Ferrari, F., A new strategy to microscopic modeling of topological entanglement in polymers based on field theory, Nuclear Phys. B, 948, Article 114778 pp., 2019 · Zbl 1435.82048 |
| [100] | Flory, P. J., Statistical Mechanics of Chain Molecules, 1969, Hanser |
| [101] | Grosberg, A. Y.; Khokhlov, A. R., Statistical physics of macromolecules, AIP series in polymers and complex materials, 1994, American Institute of Physics: American Institute of Physics New York |
| [102] | De Gennes, P.-G., Scaling Concepts in Polymer Physics, 1979, Cornell University Press: Cornell University Press Ithaca, New York |
| [103] | Grest, G. S.; Kremer, K., Molecular dynamics simulation for polymers in the presence of a heat bath, Phys. Rev. A, 33, 3628-3631, 1986 |
| [104] | Frenkel, D.; Smit, B., Understanding Molecular Simulation, 2002, Academic Press: Academic Press San Diego |
| [105] | Michieletto, D., Make or break: building soft materials with DNA, Phys. World, 34, 3, 48-52, 2021 |
| [106] | Watson, J. D.; Crick, F. H.C., Molecular structure of nucleic acids, Nature, 171, 737-738, 1953 |
| [107] | Bates, A. D.; Maxwell, A., DNA Topology, 2005, Oxford University Press |
| [108] | Calladine, C. R.; Drew, H.; Luisi, F. B.; Travers, A. A., Understanding DNA: the Molecule and How It Works, 1997, Elsevier Academic Press |
| [109] | Wikipedia contributors, C. R., Dna, 2024, https://en.wikipedia.org/wiki/DNA |
| [110] | Gao, X.; Hong, Y.; Ye, F.; Inman, J. T.; Wang, M. D., Torsional stiffness of extended and plectonemic DNA, Phys. Rev. Lett., 127, 2, 28101, 2021 |
| [111] | Smith, S. B.; Cui, Y.; Bustamante, C., Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules, Science, 271, 5250, 795-799, 1996 |
| [112] | Bustamante, C. J.; Chemla, Y. R.; Liu, S.; Wang, M. D., Optical tweezers in single-molecule biophysics, Nat. Rev. Methods Primers, 1, 1, 25, 2021 |
| [113] | Wang, J. C., Untangling the Double Helix: DNA Entanglement and the Action of the DNA Topoisomerases, 2009, Cold Spring Harbor Laboratory Press |
| [114] | Arsuaga, J.; Vázquez, M.; McGuirk, P.; Trigueros, S.; Sumners, D. W.; Roca, J., DNA knots reveal a chiral organization of DNA in phage capsids, Proc. Natl. Acad. Sci. USA, 102, 9165-9169, 2005 |
| [115] | Gellert, M., Formation of covalent circles of lambda DNA by E. coli extracts, Proc. Natl. Acad. Sci., 57, 1, 148-155, 1967 |
| [116] | Becker, A.; Murialdo, H., Bacteriophage lambda DNA: the beginning of the end, J. Bacteriol., 172, 6, 2819-2824, 1990 |
| [117] | Michieletto, D.; Neill, P.; Weir, S.; Evans, D.; Crist, N.; Martinez, V. A.; Robertson-Anderson, R. M., Topological digestion drives time-varying rheology of entangled DNA fluids, Nature Commun., 13, 1, 2022 |
| [118] | Kreuzer, K. N.; Cozzarelli, N. R., Formation and resolution of DNA catenanes by DNA gyrase, Cell, 20, May, 245-254, 1980 |
| [119] | Dans, P. D.; Walther, J.; Gómez, H.; Orozco, M., Multiscale simulation of DNA, Curr. Opin. Struct. Biol., 37, 29-45, 2016 |
| [120] | Schlick, T.; Portillo-Ledesma, S., Biomolecular modeling thrives in the age of technology, Nat. Comput. Sci., 1, 5, 321-331, 2021 |
| [121] | Smrek, J.; Garamella, J.; Robertson-Anderson, R.; Michieletto, D., Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids, Sci. Adv., 7, 20, 2021 |
| [122] | Marko, J. F.; Siggia, E. D., Bending and twisting elasticity of DNA, Macromolecules, 27, 4, 981-988, 1994 |
| [123] | Snodin, B. E.; Randisi, F.; Mosayebi, M.; Šulc, P.; Schreck, J. S.; Romano, F.; Ouldridge, T. E.; Tsukanov, R.; Nir, E.; Louis, A. A., Introducing improved structural properties and salt dependence into a coarse-grained model of DNA, J. Chem. Phys., 142, 23, 2015 |
| [124] | Skoruppa, E.; Nomidis, S. K.; Marko, J. F.; Carlon, E., Bend-induced twist waves and the structure of nucleosomal DNA, Phys. Rev. Lett., 121, 8, 2-6, 2018 |
| [125] | Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G., Theory of protein folding: The energy landscape perspective, Annu. Rev. Phys. Chem., 48, 1, 545-600, 1997 |
| [126] | Lubensky, T. C.; Pettey, D.; Currier, N.; Stark, H., Topological defects and interactions in nematic emulsions, Phys. Rev. E, 57, 610, 1998 |
| [127] | Tkalec, U.; Ravnik, M.; Čopar, S.; Žumer, S.; Muševič, I., Reconfigurable knots and links in chiral nematic colloids, Science, 333, 62, 2011 · Zbl 1355.82069 |
| [128] | Pollard, J.; Posnjak, G.; Čopar, S.; Muševič, I.; Alexander, G. P., Point defects, topological chirality, and singularity theory in cholesteric liquid-crystal droplets, Phys. Rev. X, 9, 1442, 2019 |
| [129] | Muševič, I., Nematic colloids, topology and photonics, Phil. Trans. R. Soc. A, 371, Article 20120266 pp., 2013 |
| [130] | Wikipedia contributors, I., Liquid crystal, 2022, https://en.wikipedia.org/wiki/Liquid_crystal |
| [131] | Nikkhou, M.; Škarabot, M.; Čopar, S.; Muševič, I., Dynamics of topological monopoles annihilation on a fibre in a thick and thin nematic layer, Eur. Phys. J. E, 39, 10, 1-7, 2016 |
| [132] | Chaikin, P. M.; Lubensky, T. C., Principles of Condensed Matter Physics, 1995, Cambridge University Press: Cambridge University Press Cambridge |
| [133] | Ravnik, M.; Žumer, S., Landau-De Gennes modelling of nematic liquid crystal colloids, Liq. Cryst., 36, 10-11, 1201-1214, 2009 |
| [134] | Frisch, H. L.; Wasserman, E., Chemical topology, J. Am. Chem. Soc., 83, 3789-3795, 1961 |
| [135] | Delbruck, M., Knotting problems in biology, Plant Genome Data Inf. Cent. Collect. Comput. Mol. Biol. Genet., 1961 |
| [136] | Liu, L. F.; E., D. R.; C., W. J., Knotted single-stranded DNA rings: A novel topological isomer of circular single-stranded DNA formed by treatment with Escherichia coli \(\omega\) protein, J. Mol. Biol., 106, 2, 439-452, 1976 |
| [137] | Liu, L. F.; Perkocha, L.; Calendar, R.; Wang, J. C., Knotted DNA from bacteriophage capsids, Proc. Natl. Acad. Sci., 78, 9, 5498-5502, 1981 |
| [138] | Liu, L. F.; Davis, J. L.; Calendar, R., Novel topologically knotted DNA from bacteriophage P4 capsids: studies with DNA topoisomerases, Nucleic Acids Res., 9, 16, 3979-3989, 1981 |
| [139] | Sumners, D. W.; Whittington, S. G., Knots in self-avoiding walks, J. Phys. A: Math. Gen., 21, 1689-1694, 1988 · Zbl 0659.57003 |
| [140] | Diao, Y.; Pippenger, N.; Sumners, D. W., On random knots, J. Knot Theory Ramifications, 3, 03, 419-429, 1994 · Zbl 0846.57003 |
| [141] | Diao, Y., The knotting of equilateral polygons in R \({}^3\), J. Knot Theory Ramifications, 4, 189-196, 1995 · Zbl 0846.57004 |
| [142] | Orlandini, E.; Tesi, M. C.; Van Rensburg, E. J.J.; Whittington, S. G., Asymptotics of knotted lattice polygons, J. Phys. A: Math. Gen., 31, 5953-5967, 1998 · Zbl 0953.82031 |
| [143] | Wasserman, S. A.; Cozzarelli, N. R., Biochemical topology: applications to DNA recombination and replication, Science, 232, 951-960, 1986 |
| [144] | Valdés, A.; Segura, J.; Dyson, S.; Martínez-García, B.; Roca, J., DNA knots occur in intracellular chromatin, Nucleic Acids Res., 46, 2, 650-660, 2018 |
| [145] | Ernst, C.; Sumners, D. W., A calculus for rational tangles: Applications to DNA recombination, Math. Proc. Camb. Phil. Soc., 108, 3, 489-515, 1990 · Zbl 0727.57005 |
| [146] | Rybenkov, V. V.; Cozzarelli, N. R.; Vologodskii, A. V., Probability of DNA knotting and the effective diameter of the DNA double helix, Proc. Natl. Acad. Sci. USA, 90, 5307-5311, 1993 |
| [147] | Tesi, M. C.; Van Rensburg, E. J.J.; Orlandini, E.; Sumners, D. W.; Whittington, S. G., Knotting and supercoiling in circular DNA: A model incorporating the effect of added salt, Phys. Rev. E, 49, 1, 868, 1994 |
| [148] | Vinograd, J.; Lebowitz, J.; Radloff, R.; Watson, R.; Laipis, P., The twisted circular form of polyoma viral DNA, Proc. Natl. Acad. Sci. USA, 53, 5, 1104-1111, 1965 |
| [149] | Menissier, J.; De Murcia, G.; Lebeurier, G.; Hirth, L., Electron microscopic studies of the different topological forms of the cauliflower mosaic virus DNA: knotted encapsidated DNA and nuclear minichromosome, EMBO J., 2, 7, 1067-1071, 1983 |
| [150] | Arsuaga, J.; Vázquez, M.; Trigueros, S.; Sumners, D.; Roca, J., Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids, Proc. Natl. Acad. Sci. USA, 99, 8, 5373-5377, 2002 |
| [151] | Shishido, K.; Komiyama, N.; Ikawa, S., Increased production of a knotted form of plasmid pBR322 DNA in Escherichia coli DNA topoisomerase mutants, J. Mol. Biol., 195, 1, 215-218, 1987 |
| [152] | Sogo, J. M.; Stasiak, A.; Martínez-Robles, M. L.; Krimer, D. B.; Hernández, P.; Schvartzman, J. B., Formation of knots in partially replicated DNA molecules, J. Mol. Biol., 286, 3, 637-643, 1999 |
| [153] | Goundaroulis, D.; Lieberman Aiden, E.; Stasiak, A., Chromatin is frequently unknotted at the megabase scale, Biophys. J., 118, 9, 2268-2279, 2020 |
| [154] | Marenduzzo, D.; Orlandini, E.; Stasiak, A.; Sumners, d. W.; Tubiana, L.; Micheletti, C., DNA-DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting, Proc. Natl. Acad. Sci. U. S. A., 106, 52, 22269-22274, 2009 |
| [155] | Grosberg, A. Y., Critical exponents for random knots, Phys. Rev. Lett., 85, 3858-3862, 2000 |
| [156] | Deutsch, J. M., Equilibrium size of large ring molecules, Phys. Rev. E, 59, 3, R2539-R2541, 1999 |
| [157] | des Cloizeaux, J., Ring polymers in solution: Topological effects, J. Physique - Lett., 42, L433-L436, 1981 |
| [158] | Rohwer, C. M.; Müller-Nedebock, K. K., Operator formalism for topology-conserving crossing dynamics in planar knot diagrams, J. Stat. Phys., 159, 1, 120-157, 2015 · Zbl 1319.82028 |
| [159] | Grosberg, A. Y.; Feigel, A.; Rabin, Y., Flory-type theory of a knotted ring polymer, Phys. Rev. E, 54, 6618-6622, 1996 |
| [160] | Katritch, V.; Bednar, J.; Michoud, D.; Scharein, R. G.; Dubochet, J.; Stasiak, A., Geometry and physics of knots, Nature, 384, 142-145, 1996 · Zbl 1369.57010 |
| [161] | Stasiak, A.; Katritch, V.; Bednar, J.; Michoud, D.; Dubochet, J., Electrophoretic mobility of DNA knots, Nature, 384, 6605, 122, 1996 |
| [162] | Tubiana, L.; Rosa, A.; Fragiacomo, F.; Micheletti, C., Spontaneous knotting and unknotting of flexible linear polymers: Equilibrium and kinetic aspects, Macromolecules, 46, 3669-3678, 2013 |
| [163] | Orlandini, E., Statics and dynamics of DNA knotting, J. Phys. A, 51, 5, Article 053001 pp., 2017 · Zbl 1385.92036 |
| [164] | Orlandini, E.; Whittington, S. G., Statistical topology of closed curves: Some applications in polymer physics, Rev. Modern Phys., 79, 2, 611, 2007 · Zbl 1205.82153 |
| [165] | Kremer, K.; Grest, G. S., Dynamics of entangled linear polymer melts: A molecular-dynamics simulation, J. Chem. Phys., 92, 8, 5057, 1990 |
| [166] | Rieger, F. C.; Virnau, P., A Monte Carlo study of knots in long double-stranded DNA chains, PLoS Comput. Biol., 12, 9, Article e1005029 pp., 2016 |
| [167] | Virnau, P.; Kantor, Y.; Kardar, M., Knots in globule and coil phases of a model polyethylene, J. Am. Chem. Soc., 127, 15102-15106, 2005 |
| [168] | Micheletti, C.; Orlandini, E., Numerical study of linear and circular model DNA chains confined in a slit: Metric and topological properties, Macromolecules, 45, 2113-2121, 2012 |
| [169] | Grosberg, A. Y.; Rabin, Y., Metastable tight knots in a wormlike polymer, Phys. Rev. Lett., 99, Article 217801 pp., 2007 |
| [170] | Tang, J.; Ning, D.; Doyle, P. S., Compression and self-entanglement of single DNA molecules under uniform electric field, Proc. Natl. Acad. Sci. U. S. A., 108, 39, 16153-16158, 2011 |
| [171] | Renner, C. B.; Doyle, P. S., Untying knotted DNA with elongational flows, ACS Macro Lett., 3, 963-967, 2014 |
| [172] | Dai, L.; Renner, C. B.; Doyle, P. S., Origin of metastable knots in single flexible chains, Phys. Rev. Lett., 114, Article 037801 pp., 2015 |
| [173] | Sulkowska, J. I.; Sułkowski, P.; Onuchic, J., Dodging the crisis of folding proteins with knots, Proc. Natl. Acad. Sci., 106, 9, 3119-3124, 2009 · Zbl 1202.92030 |
| [174] | Wettermann, S.; Brems, M.; Siebert, J. T.; Vu, G. T.; Stevens, T. J.; Virnau, P., A minimal Gō-model for rebuilding whole genome structures from haploid single-cell Hi-C data, Comput. Mater. Sci., 173, April 2019, 2020 |
| [175] | Plesa, C.; Verschueren, D.; Pud, S.; van der Torre, J.; Ruitenberg, J. W.; Witteveen, M. J.; Jonsson, M. P.; Grosberg, A. Y.; Rabin, Y.; Dekker, C., Direct observation of DNA knots using a solid-state nanopore, Nature Nanotechnol., 11, 12, 1093-1097, 2016 |
| [176] | Kumar Sharma, R.; Agrawal, I.; Dai, L.; Doyle, P. S.; Garaj, S., Complex DNA knots detected with a nanopore sensor, Nat. Commun., 10, 1, 4473, 2019 |
| [177] | Bao, X. R.; Lee, H. J.; Quake, S. R., Behavior of complex knots in single DNA molecules, Phys. Rev. Lett., 91, Article 265506 pp., 2003 |
| [178] | Reifenberger, J. G.; Dorfman, K. D.; Cao, H., Topological events in single molecules of e. coli DNA confined in nanochannels, Analyst, 140, 14, 4887-4894, 2015 |
| [179] | Welch, R. L.; Sladek, R.; Dewar, K.; Reisner, W. W., Denaturation mapping of saccharomyces cerevisiae, Lab Chip, 12, 18, 3314-3321, 2012 |
| [180] | Arai, Y.; Yasuda, R.; Akashi, K.; Harada, Y.; Miyata, H.; Kinosita, T.; Itoh, H., Tying a molecular knot with optical tweezers, Nature, 399, 446-448, 1999 |
| [181] | Amin, S.; Khorshid, A.; Zeng, L.; Zimny, P.; Reisner, W., A nanofluidic knot factory based on compression of single DNA in nanochannels, Nature Commun., 9, 1, 1506, 2018 |
| [182] | Ma, Z.; Dorfman, K. D., Diffusion of knots along DNA confined in nanochannels, Macromolecules, 53, 15, 6461-6468, 2020 |
| [183] | Klotz, A. R.; Soh, B. W.; Doyle, P. S., An experimental investigation of attraction between knots in a stretched DNA molecule, Europhys. Lett., 129, 68001, 2020 |
| [184] | Renner, C. B.; Doyle, P. S., Stretching self-entangled DNA molecules in elongational fields, Soft Matter, 11, 3105-3114, 2015 |
| [185] | Metzler, R.; Reisner, W.; Riehn, R.; Austin, R.; Tegenfeldt, J. O.; Sokolov, I. M., Diffusion mechanisms of localised knots along a polymer, Europhys. Lett., 76, 4, 696, 2006 |
| [186] | Ma, Z.; Dorfman, K. D., Diffusion of knotted DNA molecules in nanochannels in the extended de gennes regime, Macromolecules, 54, 9, 4211-4218, 2021 |
| [187] | Ma, Z.; Dorfman, K. D., Interactions between two knots in nanochannel-confined DNA molecules, J. Chem. Phys., 155, 15, Article 154901 pp., 2021 |
| [188] | Rothörl, J.; Wettermann, S.; Virnau, P.; Bhattacharya, A., Knot formation of dsDNA pushed inside a nanochannel, Sci. Rep., 12, 1, 5342, 2022 |
| [189] | Klotz, A. R.; Narsimhan, V.; Soh, B. W.; Doyle, P. S., Dynamics of DNA knots during chain relaxation, Macromolecules, 50, 10, 4074-4082, 2017 |
| [190] | Michieletto, D.; Marenduzzo, D.; Orlandini, E., Topological patterns in two-dimensional gel electrophoresis of DNA knots, Proc. Natl. Acad. Sci. USA, E5471-E5477, 2015 · Zbl 1355.92082 |
| [191] | Dai, L.; Doyle, P. S., Universal knot spectra for confined polymers, ACS Macro Lett., 51, 6327-6333, 2018 |
| [192] | Mansfield, M. L.; Douglas, J. F., Properties of knotted ring polymers. I. Equilibrium dimensions, J. Chem. Phys., 133, 4, Article 044903 pp., 2010 |
| [193] | Radhakrishnan, K.; Singh, S. P., Compression of a confined semiflexible polymer under direct and oscillating fields, Phys. Rev. E, 108, 1, Article 014501 pp., 2023 |
| [194] | Narsimhan, V.; Klotz, A. R.; Doyle, P. S., Steady-state and transient behavior of knotted chains in extensional fields, ACS Macro Lett., 6, 11, 1285-1289, 2017 |
| [195] | Soh, B. W.; Klotz, A. R.; Doyle, P. S., Untying of complex knots on stretched polymers in elongational fields, Macromolecules, 51, 9562-9571, 2018 |
| [196] | Caraglio, M.; Baldovin, F.; Marcone, B.; Orlandini, E.; Stella, A. L., Topological disentanglement dynamics of torus knots on open linear polymers, ACS Macro Lett., 8, 5, 576-581, 2019 |
| [197] | Klotz, A. R.; Soh, B. W.; Doyle, P. S., Motion of knots in DNA stretched by elongational fields, Phys. Rev. Lett., 120, 120, Article 188003 pp., 2018 |
| [198] | Soh, B. W.; Klotz, A. R.; Dai, L.; Doyle, P. S., Conformational state hopping of knots in tensioned polymer chains, ACS Macro Lett., 8, 905-911, 2019 |
| [199] | Soh, B. W.; Khorshid, A.; Al Sulaiman, D.; Doyle, P. S., Ionic effects on the equilibrium conformation of catenated DNA networks, Macromolecules, 53, 19, 8502-8508, 2020 |
| [200] | Matthews, R.; Louis, A. A.; Yeomans, J. M., Knot-controlled ejection of a polymer from a virus capsid, Phys. Rev. Lett., 102, Article 088101 pp., 2009 |
| [201] | Rosa, A.; Di Ventra, M.; Micheletti, C., Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore, Phys. Rev. Lett., 109, Article 118301 pp., 2012 |
| [202] | San Martín, Á.; Rodriguez-Aliaga, P.; Molina, J. A.; Martin, A.; Bustamante, C.; Baez, M., Knots can impair protein degradation by ATP-dependent proteases, Proc. Natl. Acad. Sci., 114, 37, 9864-9869, 2017 |
| [203] | Ziegler, F.; Lim, N. C.H.; Mandal, S. S.; Pelz, B.; Ng, W.-P.; Schlierf, M.; Jackson, S. E.; Rief, M., Knotting and unknotting of a protein in single molecule experiments, Proc. Natl. Acad. Sci. USA, 113, 27, 7533-7538, 2016 |
| [204] | Sriramoju, M. K.; Chen, Y.; Lee, Y.-T. C.; Hsu, S.-T. D., Topologically knotted deubiquitinases exhibit unprecedented mechanostability to withstand the proteolysis by an aaa+ protease, Sci. Rep., 8, 1, 1-9, 2018 |
| [205] | Sivertsson, E. M.; Jackson, S. E.; Itzhaki, L. S., The AAA+ protease clpxp can easily degrade a 3 1 and a 5 2-knotted protein, Sci. Rep., 9, 1, 1-14, 2019 |
| [206] | Jackson, S. E., Why are there knots in proteins?, Topol. Geom. Biopolym., 746, 129, 2020 · Zbl 1444.57004 |
| [207] | Soh, B. W.; Narsimhan, V.; Klotz, A. R.; Doyle, P. S., Knots modify the coil-stretch transition in linear DNA polymers, Soft Matter, 14, 1689-1698, 2018 |
| [208] | Caraglio, M.; Orlandini, E.; Micheletti, C., Stretching response of knotted and unknotted polymer chains, Phys. Rev. Lett., 115, Article 188301 pp., 2015 |
| [209] | Di Stefano, M.; Tubiana, L.; Di Ventra, M.; Micheletti, C., Driving knots on DNA with AC/DC electric fields: topological friction and memory effects, Soft Matter, 10, 6491-6498, 2014 |
| [210] | Richardson, J. S., \( \beta \)-Sheet topology and the relatedness of proteins, Nature, 268, 5620, 495-500, 1977 |
| [211] | Taylor, W. R., A deeply knotted protein structure and how it might fold, Nature, 406, 916-919, 2000 |
| [212] | Jarmolinska, A. I.; Perlinska, A. P.; Runkel, R.; Trefz, B.; Ginn, H. M.; Virnau, P.; Sulkowska, J. I., Proteins’ knotty problems, J. Mol. Biol., 431, 2, 244-257, 2019 |
| [213] | Jackson, S. E.; Suma, A.; Micheletti, C., How to fold intricately: using theory and experiments to unravel the properties of knotted proteins, Current opinion in structural biology, 42, 6-14, 2017 |
| [214] | Sulkowska, J. I., On folding of entangled proteins: knots, lassos, links and \(\theta \)-curves, Curr. Opin. Struct. Biol., 60, 131-141, 2020 |
| [215] | Schmidberger, J. W.; Wilce, J. A.; Weightman, A. J.; Whisstock, J. C.; Wilce, M. C.J., The crystal structure of dehi reveals a new \(\alpha \)-haloacid dehalogenase fold and active-site mechanism, J. Mol. Biol., 378, 1, 284-294, 2008 |
| [216] | Bölinger, D.; Sulkowska, J. I.; Hsu, H.-P.; Mirny, L. A.; Kardar, M.; Onuchic, J. N.; Virnau, P., A Stevedore’s protein knot, PLoS Comput. Biol., 6, 4, Article e1000731 pp., 2010 |
| [217] | Vologodskii, A. V.; Lukashin, A. V.; Frank-Kamenetskii, M. D., Topological interaction between polymer chains, Sov. Phys.-JETP, 40, 5, 932-936, 1975 |
| [218] | Khokhlov, A. R.; Nechaev, S. K., Polymer chain in an array of obstacles, Phys. Lett. A, 112, 3, 156-160, 1985 |
| [219] | Rubinstein, M., Dynamics of ring polymers in the presence of fixed obstacles, Phys. Rev. Lett., 57, 3023-3026, 1986 |
| [220] | Cates, M. E.; Deutsch, J. M., Conjectures on the statistics of ring polymers, J. Physique, 47, 12, 2121-2128, 1986 |
| [221] | Sakaue, T., Ring polymers in melts and solutions: Scaling and crossover, Phys. Rev. Lett., 106, Article 167802 pp., 2011 |
| [222] | Kapnistos, M.; Lang, M.; Vlassopoulos, D.; Pyckhout-Hintzen, W.; Richter, D.; Cho, D.; T., C.; Rubinstein, M., Unexpected power-law stress relaxation of entangled ring polymers, Nature Mater., 7, 997-1002, 2008 |
| [223] | Milner, S. T.; Newhall, J. D., Stress relaxation in entangled melts of unlinked ring polymers, Phys. Rev. Lett., 105, Article 208302 pp., 2010 |
| [224] | Tsolou, G.; Stratikis, N.; Baig, C.; Stephanou, P. S.; Mavrantzas, V. G., Melt structure and dynamics of unentangled poluethylene rings: Rouse theory, atomistic molecular dynamics simulation, comparison with the linear analogues, Macromolecules, 43, 10692, 2010 |
| [225] | Halverson, J. D.; Lee, W. B.; Grest, G. S.; Grosberg, A. Y.; Kremer, K., Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics, J. Chem. Phys., 134, Article 204905 pp., 2011 |
| [226] | Goossen, S.; Brás, A. R.; Krutyeva, M.; Sharp, M.; Falus, P.; Feoktystov, A.; Gasser, U.; Pyckhout-Hintzen, W.; Wischnewski, A.; Richter, D., Molecular scale dynamics of large ring polymers, Phys. Rev. Lett., 113, 16, Article 168302 pp., 2014 |
| [227] | Smrek, J.; Grosberg, A. Y., Understanding the dynamics of rings in the melt in terms of the annealed tree model, J. Phys.: Condens. Matter, 27, 6, Article 064117 pp., 2015 |
| [228] | Ge, T.; Panyukov, S.; Rubinstein, M., Self-similar conformations and dynamics in entangled melts and solutions of nonconcatenated ring polymers, Macromolecules, 49, 2, 708-722, 2016 |
| [229] | Tsalikis, D. G.; Koukoulas, T.; Mavrantzas, V. G.; Pasquino, R.; Vlassopoulos, D.; Pyckhout-Hintzen, W.; Wischnewski, A.; Monkenbusch, M.; Richter, D., Microscopic structure, conformation, dynamics of ring and linear poly(ethylene oxide) melts from detailed atomistic molecular dynamics simulations: Dependence on chain length and direct comparison with experimental data, Macromolecules, 50, 6, 2565-2584, 2017 |
| [230] | Tu, M. Q.; Davydovich, O.; Mei, B.; Singh, P. K.; Grest, G. S.; Schweizer, K. S.; O’Connor, T. C.; Schroeder, C. M., Unexpected slow relaxation dynamics in pure ring polymers arise from intermolecular interactions, ACS Polym. Au, 3, 4, 307-317, 2023 |
| [231] | Chen, D.; Molnar, K.; Kim, H.; Helfer, C. A.; Kaszas, G.; Puskas, J. E.; Kornfield, J. A.; McKenna, G. B., Linear viscoelastic properties of putative cyclic polymers synthesized by reversible radical recombination polymerization (R3P), Macromolecules, 56, 3, 1013-1032, 2023 |
| [232] | Halverson, J. D.; Smrek, J.; Kremer, K.; Grosberg, A. Y., From a melt of rings to chromosome territories: The role of topological constraints in genome folding, Rep. Progr. Phys., 77, 2, Article 022601 pp., 2014 |
| [233] | Cremer, T.; Cremer, C., Chromosome territories, nuclear architecture and gene regulation in mammalian cells, Nature Rev. Genet., 2, 4, 292-301, 2001 |
| [234] | Rosa, A.; Everaers, R., Structure and dynamics of interphase chromosomes, PLOS Comp. Biol., 4, Article e1000153 pp., 2008 |
| [235] | Grosberg, A.; Rabin, Y.; Havlin, S.; Neer, A., Crumpled globule model of the three-dimensional structure of DNA, Europhys. Lett., 23, 5, 373-378, 1993 |
| [236] | Needleman, D.; Dogic, Z., Active matter at the interface between materials science and cell biology, Nat. Rev. Mater., 2, 9, 1-14, 2017 |
| [237] | Vale, R. D., The molecular motor toolbox for intracellular transport, Cell, 112, 4, 467-480, 2003 |
| [238] | Zidovska, A.; Weitz, D. A.; Mitchison, T. J., Micron-scale coherence in interphase chromatin dynamics, Proc. Natl. Acad. Sci., 110, 39, 15555-15560, 2013 |
| [239] | Winkler, R. G.; Gompper, G., The physics of active polymers and filaments, J. Chem. Phys., 153, 4, Article 040901 pp., 2020 |
| [240] | Joshi, A.; Putzig, E.; Baskaran, A.; Hagan, M. F., The interplay between activity and filament flexibility determines the emergent properties of active nematics, Soft Matter, 15, 1, 94-101, 2019 |
| [241] | Zhang, R.; Redford, S. A.; Ruijgrok, P. V.; Kumar, N.; Mozaffari, A.; Zemsky, S.; Dinner, A. R.; Vitelli, V.; Bryant, Z.; Gardel, M. L.; de Pablo, J. J., Spatiotemporal control of liquid crystal structure and dynamics through activity patterning, Nat. Mater., 20, 6, 875-882, 2021 |
| [242] | Vliegenthart, G. A.; Ravichandran, A.; Ripoll, M.; Auth, T.; Gompper, G., Filamentous active matter: Band formation, bending, buckling, and defects, Sci. Adv., 6, 30, eaaw9975, 2020 |
| [243] | Smrek, J.; Chubak, I.; Likos, C. N.; Kremer, K., Active topological glass, Nature Commun., 11, 1, 26, 2020 |
| [244] | Saintillan, D.; Shelley, M. J.; Zidovska, A., Extensile motor activity drives coherent motions in a model of interphase chromatin, Proc. Natl. Acad. Sci. USA, 115, 45, 11442-11447, 2018 |
| [245] | Patil, V. P.; Tuazon, H.; Kaufman, E.; Chakrabortty, T.; Qin, D.; Dunkel, J.; Bhamla, M. S., Ultrafast reversible self-assembly of living tangled matter, Science, 380, 6643, 392-398, 2023 |
| [246] | Deblais, A.; Maggs, A. C.; Bonn, D.; Woutersen, S., Phase separation by entanglement of active polymerlike worms, Phys. Rev. Lett., 124, 20, Article 208006 pp., 2020 |
| [247] | Mahajan, A.; Yan, W.; Zidovska, A.; Saintillan, D.; Shelley, M. J., Euchromatin activity enhances segregation and compaction of heterochromatin in the cell nucleus, Phys. Rev. X, 12, 4, Article 041033 pp., 2022 |
| [248] | Chubak, I.; Likos, C. N.; Kremer, K.; Smrek, J., Emergence of active topological glass through directed chain dynamics and nonequilibrium phase segregation, Phys. Rev. Res., 2, Article 043249 pp., 2020 |
| [249] | Michieletto, D.; Turner, M. S., A topologically driven glass in ring polymers, Proc. Natl. Acad. Sci. USA, 113, 19, 5195-5200, 2016 |
| [250] | Michieletto, D.; Nahali, N.; Rosa, A., Glassiness and heterogeneous dynamics in dense solutions of ring polymers, Phys. Rev. Lett., 119, Article 197801 pp., 2017 |
| [251] | Locatelli, E.; Bianco, V.; Malgaretti, P., Activity-induced collapse and arrest of active polymer rings, Phys. Rev. Lett., 126, 9, Article 097801 pp., 2021 |
| [252] | Tejedor, A. R.; Ramirez, J., Reptation of active entangled polymers, Macromolecules, 52, 22, 8788-8792, 2019 |
| [253] | Tejedor, A. R.; Carracedo, R.; Ramírez, J., Molecular dynamics simulations of active entangled polymers reptating through a passive mesh, Polymer, Article 125677 pp., 2023 |
| [254] | Savoie, W.; Tuazon, H.; Tiwari, I.; Bhamla, M. S.; Goldman, D. I., Amorphous entangled active matter, Soft Matter, 2023 |
| [255] | Deblais, A.; Woutersen, S.; Bonn, D., Rheology of entangled active polymer-like t. tubifex worms, Phys. Rev. Lett., 124, 18, Article 188002 pp., 2020 |
| [256] | Deblais, A.; Prathyusha, K.; Sinaasappel, R.; Tuazon, H.; Tiwari, I.; Patil, V. P.; Bhamla, M. S., Worm blobs as entangled living polymers: from topological active matter to flexible soft robot collectives, Soft Matter, 19, 37, 7057-7069, 2023 |
| [257] | Baiesi, M.; Orlandini, E.; Trovato, A.; Seno, F., Linking in domain-swapped protein dimers, Sci. Rep., 6, 1, 1-11, 2016 |
| [258] | Niemyska, W.; Dabrowski-Tumanski, P.; Kadlof, M.; Haglund, E.; Sułkowski, P.; Sulkowska, J. I., Complex lasso: new entangled motifs in proteins, Sci. Rep., 6, 1, 36895, 2016 |
| [259] | Dabrowski-Tumanski, P.; Sulkowska, J. I., To tie or not to tie? That is the question, Polymers, 9, 9, 2017 |
| [260] | Nissley, D. A.; Jiang, Y.; Trovato, F.; Sitarik, I.; Narayan, K. B.; To, P.; Xia, Y.; Fried, S. D.; O’Brien, E. P., Universal protein misfolding intermediates can bypass the proteostasis network and remain soluble and less functional, Nat. Commun., 13, 1, 3081, 2022 |
| [261] | Jiang, Y.; Neti, S. S.; Sitarik, I.; Pradhan, P.; To, P.; Xia, Y.; Fried, S. D.; Booker, S. J.; O’Brien, E. P., How synonymous mutations alter enzyme structure and function over long timescales, Nature Chem., 15, 3, 308-318, 2023 |
| [262] | Baiesi, M.; Orlandini, E.; Seno, F.; Trovato, A., Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding, Sci. Rep., 9, 1, 1-12, 2019 |
| [263] | Baiesi, M.; Orlandini, E.; Seno, F.; Trovato, A., Exploring the correlation between the folding rates of proteins and the entanglement of their native states, J. Phys. A, 50, Article 504001 pp., 2017 · Zbl 1383.82077 |
| [264] | Simpson, L. P., Morphogenesis and the function of the kinetoplast in “leishmania”, Atlas Symposia Sobre Biota Amazonica (Pathologia), 6, 231-234, 1967 |
| [265] | Chen, J.; Rauch, C. A.; White, J. H.; Englund, P. T.; Cozzarelli, N. R., The topology of the kinetoplast DNA network, Cell, 80, 61-69, 1995 |
| [266] | Brack, C.; Delain, E.; Riou, G.; Festy, B., Molecular organization of the kinetoplast DNA of trypanosoma cruzi treated with berenil, a DNA interacting drug, J. Ultrasruct. Res., 39, 5-6, 568-579, 1972 |
| [267] | Simpson, L.; da Silva, A., Isolation and characterization of kinetoplast DNA from leishmania tarentolae, J. Mol. Biol., 56, 3, 443-473, 1971 |
| [268] | Klotz, A. R.; Soh, B. W.; Doyle, P. S., Equilibrium structure and deformation response of 2D kinetoplast sheets, Proc. Natl. Acad. Sci. USA, 117, 1, 121-127, 2020 |
| [269] | He, P.; Katan, A. J.; Tubiana, L.; Dekker, C.; Michieletto, D., Single-molecule structure and topology of kinetoplast DNA networks, Phys. Rev. X, 13, Article 021010 pp., 2023 |
| [270] | Diao, Y.; Hinson, K.; Kaplan, R.; Vazquez, M.; Arsuaga, J., The effects of density on the topological structure of the mitochondrial DNA from trypanosomes, J. Math. Biol., 64, 1087-1108, 2012 · Zbl 1311.92145 |
| [271] | Michieletto, D.; Marenduzzo, D.; Orlandini, E., Is the kinetoplast DNA a percolating network of linked rings at its critical point?, Phys. Biol., 12, 1, Article 036001 pp., 2015 |
| [272] | Wu, Q.; Rauscher, P. M.; Lang, X.; Wojtecki, R. J.; de Pablo, J. J.; Hore, M. J.A.; Rowan, S. J., Poly[n]catenanes: Synthesis of molecular interlocked chains, Science, 358, 6369, 1434-1439, 2017 |
| [273] | Krasnow, M. A.; Cozzarelli, N. R., Catenation of DNA rings by topoisomerases. Mechanism of control by spermidine, J. Biol. Chem., 257, 5, 2687-2693, 1982 |
| [274] | Krajina, B. A.; Zhu, A.; Heilshorn, S. C.; Spakowitz, A. J., Active DNA olympic hydrogels driven by topoisomerase activity, Phys. Rev. Lett., 121, 14, Article 148001 pp., 2018 |
| [275] | Vilgis, T. A.; Otto, M., Elasticity of entangled polymer loops: Olympic gels, Phys. Rev. E, 56, R1314-R1317, 1997 |
| [276] | Lang, M.; Fischer, J.; Werner, M.; Sommer, J.-U., Swelling of olympic gels, Phys. Rev. Lett., 112, Article 238001 pp., 2014 |
| [277] | Ahmadian Dehaghani, Z.; Chubak, I.; Likos, C. N.; Ejtehadi, M. R., Effects of topological constraints on linked ring polymers in solvents of varying quality, Soft Matter, 16, 3029-3038, 2020 |
| [278] | Alberts, B.; Johnson, A.; Lewis, J.; Raff, M.; Roberts, K.; Walter, P., Molecular Biology of the Cell: fifth edition, 2007, (Garland Science (Taylor and Francis)): (Garland Science (Taylor and Francis)) New York |
| [279] | Postow, L.; Hardy, C. D.; Arsuaga, J.; Cozzarelli, N. R., Topological domain structure of the Escherichia coli chromosome, Genes Dev., 18, 14, 1766-1779, 2004 |
| [280] | Peter, B. J.; Arsuaga, J.; Breier, A. M.; Khodursky, A. B.; Brown, P. O.; Cozzarelli, N. R., Genomic transcriptional response to loss of chromosomal supercoiling in Escherichia coli, Genome Biol., 5, 11, R87, 2004 |
| [281] | Goriely, A., Twisted elastic rings and the rediscoveries of Michell’s instability, J. Elasticity, 84, 281-299, 2006 · Zbl 1098.74034 |
| [282] | Wasserman, S.; Dungan, J.; Cozzarelli, N., Discovery of a predicted DNA knot substantiates a model for site-specific recombination, Science, 229, 4709, 171-174, 1985 |
| [283] | Olorunniji, F. J.; Buck, D. E.; Colloms, S. D.; McEwan, A. R.; Smith, M. C.; Stark, W. M.; Rosser, S. J., Gated rotation mechanism of site-specific recombination by \(\Phi\) C31 integrase, Proc. Natl. Acad. Sci. USA, 109, 48, 19661-19666, 2012 |
| [284] | Cozzarelli, N. R.; De Witt, S.; Cozzarelli, N. R., Analysis of the mechanism of DNA recombination using tangles, Q. Rev. Biophys., 28, 3, 253-313, 1995 |
| [285] | Saka, Y.; Vazquez, M., TangleSolve: topological analysis of site-specific recombination, Bioinformatics, 18, 7, 1011-1012, 2002 |
| [286] | Darcy, I. K.; Scharein, R. G., TopoICE-R: 3D visualization modeling the topology of DNA recombination, Bioinformatics, 22, 14, 1790-1791, 2006 |
| [287] | Darcy, I. K., Modeling protein-DNA complexes with tangles, Comput. Math. Appl., 55, 5, 924-937, 2008 · Zbl 1137.92011 |
| [288] | Stark, W. M.; Sherratt, D. J.; Boocock, M. R., Site-specific recombination by Tn3 resolvase: topological changes in the forward and reverse reactions, Cell, 58, 4, 779-790, 1989 |
| [289] | Colloms, S. D.; Bath, J.; Sherratt, D. J., Topological selectivity in xer site-specific recombination, Cell, 88, 6, 855-864, 1997 |
| [290] | Vazquez, M.; Colloms, S. D.; Sumners, D. W., Tangle analysis of xer recombination reveals only three solutions, all consistent with a single three-dimensional topological pathway, J. Mol. Biol., 346, 2, 493-504, 2005 |
| [291] | Pieranski, P.; Kasas, S.; Dietler, G.; Dubochet, J.; Stasiak, A., Localization of breakage points in knotted strings, New J. Phys., 3, 1, 10, 2001 |
| [292] | Uehara, H.; Kimura, H.; Aoyama, A.; Yamanobe, T.; Komoto, T., Effects of knot characteristics on tensile breaking of a polymeric monofilament, New J. Phys., 9, 3, 65, 2007 |
| [293] | Saitta, A. M.; Soper, P. D.; Wasserman, E.; Klein, M. L., Influence of a knot on the strength of a polymer strand, Nature, 399, 6731, 46-48, 1999 |
| [294] | Jawed, M. K.; Dieleman, P.; Audoly, B.; Reis, P. M., Untangling the mechanics and topology in the frictional response of long overhand elastic knots, Phys. Rev. Lett., 115, 11, Article 118302 pp., 2015 |
| [295] | Audoly, B.; Clauvelin, N.; Neukirch, S., Elastic knots, Phys. Rev. Lett., 99, 16, Article 164301 pp., 2007 |
| [296] | Johanns, P.; Baek, C.; Grandgeorge, P.; Guerid, S.; Chester, S. A.; Reis, P. M., The strength of surgical knots involves a critical interplay between friction and elastoplasticity, Sci. Adv., 9, 23, eadg8861, 2023 |
| [297] | Patil, V. P.; Sandt, J. D.; Kolle, M.; Dunkel, J., Topological mechanics of knots and tangles, Science, 367, 6473, 71-75, 2020 · Zbl 1478.57010 |
| [298] | Moestopo, W. P.; Shaker, S.; Deng, W.; Greer, J. R., Knots are not for naught: Design, properties, and topology of hierarchical intertwined microarchitected materials, Sci. Adv., 9, 10, eade6725, 2023 |
| [299] | Farago, O.; Kantor, Y.; Kardar, M., Pulling knotted polymers, Europhys. Lett., 60, 53-59, 2002 |
| [300] | Pierański, P.; Przybył, S.; Stasiak, A., Tight open knots, Eur. Phys. J. E, 6, 123-128, 2001 |
| [301] | Maddocks, J. H.; Keller, J. B., Ropes in equilibrium, SIAM J. Appl. Math., 47, 6, 1185-1200, 1987 · Zbl 0627.73100 |
| [302] | Wegst, U. G.; Bai, H.; Saiz, E.; Tomsia, A. P.; Ritchie, R. O., Bioinspired structural materials, Nat. Mater., 14, 1, 23-36, 2015 |
| [303] | Greco, G.; Pantano, M. F.; Mazzolai, B.; Pugno, N. M., Imaging and mechanical characterization of different junctions in spider orb webs, Sci. Rep., 9, 5776, 2019 |
| [304] | Cranford, S. W.; Tarakanova, A.; Pugno, N. M.; Buehler, M. J., Nonlinear material behaviour of spider silk yields robust webs, Nature, 482, 72-78, 2012 |
| [305] | Pugno, N. M., The “egg of columbus” for making the world’s toughest fibres, PLoS One, 9, 4, Article e93079 pp., 2014 |
| [306] | Agnarsson, I.; Kuntner, M.; Blackledge, T. A., Bioprospecting finds the toughest biological material: Extraordinary silk from a giant riverine orb spider, PLoS One, 5, 9, Article e11234 pp., 2010 |
| [307] | Ritchie, R. O., The conflicts between strength and toughness, Nat. Mater., 10, 11, 817-822, 2011 |
| [308] | Snyder, R.; Pargellis, A. N.; Graham, P. A.; Yurke, B., Light-transmission study of coarsening in a nematic liquid crystal, Phys. Rev. A, 45, R2169, 1992 |
| [309] | Chuang, I.; Yurke, B.; Pargellis, A.; Turok, N., Coarsening dynamics in uniaxial nematic liquid crystals, Phys. Rev. E, 47, 3343, 1993 |
| [310] | Duclos, G.; Adkins, R.; Banerjee, D.; Peterson, M. S.E.; Varghese, M.; Kolvin, I.; Baskaran, A.; Pelcovits, R. A.; Powers, T. R.; Baskaran, A.; Toschi, F.; Hagan, M. F.; Streichan, S. J.; Vitelli, V.; Beller, D. A.; Dogic, Z., Topological structure and dynamics of three-dimensional active nematics, Science, 367, 1120, 2020 |
| [311] | Kralj, N.; Ravnik, M.; Kos, Ž., Defect line coarsening and refinement in active nematics, Phys. Rev. Lett., 130, Article 128101 pp., 2023 |
| [312] | Jänich, K., Topological properties of ordinary nematics in 3-space, Acta Appl. Math., 8, 1, 65-74, 1987 · Zbl 0652.57017 |
| [313] | Čopar, S., Topology and geometry of nematic braids, Phys. Rep., 538, 1, 2014 |
| [314] | Machon, T.; Alexander, G. P., Global defect topology in nematic liquid crystals, Proc. R. Soc. A: Math., Phys. Eng. Sci., 472, 2191, Article 20160265 pp., 2016 |
| [315] | Bouligand, Y., Recherches sur les textures des états mésomorphes: Dislocations coins et signification des cloisons de Grandjean-Cano dans les cholestériques, J. Phys. France, 35, 959, 1974 |
| [316] | Poulin, P.; Stark, H.; Lubensky, T. C.; Weitz, D. A., Novel colloidal interactions in anisotropic fluids, Science, 275, 1770-1773, 1997 |
| [317] | Ruhwandl, R. W.; Terentjev, E. M., Long-range forces and aggregation of colloid particles in a nematic liquid crystal, Phys. Rev. E, 55, 2958-2961, 1997 |
| [318] | Terentjev, E., Disclination loops, standing alone and around solid particles, in nematic liquid crystals, Phys. Rev. E, 51, 2, 1330, 1995 |
| [319] | Stark, H., Physics of colloidal dispersions in nematic liquid crystals, Phys. Rep., 351, 387-474, 2001 |
| [320] | Muševič, I.; Škarabot, M.; Tkalec, U.; Ravnik, M.; Žumer, S., Two-dimensional nematic colloidal crystals self-assembled by topological defects, Science, 313, 954-958, 2006 |
| [321] | Ravnik, M.; Škarabot, M.; Žumer, S.; Tkalec, U.; Poberaj, I.; Babič, D.; Osterman, N.; Muševič, I., Entangled nematic colloidal dimers and wires, Phys. Rev. Lett., 99, Article 247801 pp., 2007 |
| [322] | Senyuk, B.; Liu, Q.; He, S.; Kamien, R. D.; Kusner, R. B.; Lubensky, T. C.; Smalyukh, I. I., Topological colloids, Nature, 493, 200, 2013 |
| [323] | Machon, T.; Alexander, G. P., Knots and nonorientable surfaces in chiral nematics, Proc. Natl. Acad. Sci. USA, 110, 14174-14179, 2013 |
| [324] | Seč, D.; Čopar, S.; Žumer, S., Topological zoo of free-standing knots in confined chiral nematic fluids, Nature Commun., 5, 3057, 2014 |
| [325] | Škarabot, M.; Ravnik, M.; Žumer, S.; Tkalec, U.; Poberaj, I.; Babič, D.; Osterman, N.; Muševič, I., Interactions of quadrupolar nematic colloids, Phys. Rev. E, 77, Article 031705 pp., 2008 |
| [326] | Ognysta, U.; Nych, A.; Nazarenko, V.; Muševič, I.; Škarabot, M.; Ravnik, M.; Žumer, S.; Poberaj, I.; Babič, D., 2D interactions and binary crystals of dipolar and quadrupolar nematic colloids, Phys. Rev. Lett., 100, Article 217803 pp., 2008 |
| [327] | Nych, A.; Ognysta, U.; Škarabot, M.; Ravnik, M.; Žumer, S.; Muševič, I., Assembly and control of 3D nematic dipolar colloidal crystals, Nature Commun., 4, 1489, 2013 |
| [328] | Čopar, S.; Clark, N. A.; Ravnik, M.; Žumer, S., Elementary building blocks of nematic disclination networks in densely packed 3D colloidal lattices, Soft Matter, 9, 8203, 2013 |
| [329] | Čopar, S.; Tkalec, U.; Muševič, I.; Žumer, S., Knot theory realizations in nematic colloids, Proc. Natl. Acad. Sci., 112, 1675, 2015 · Zbl 1355.76009 |
| [330] | Martinez, A.; Ravnik, M.; Lucero, B.; Visvanathan, R.; Žumer, S.; Smalyukh, I. I., Mutually tangled colloidal knots and induced defect loops in nematic fields, Nature Mater., 13, 258, 2014 |
| [331] | Kos, Ž.; Dunkel, J., Nematic bits and universal logic gates, Sci. Adv., 8, 33, eabp8371, 2022 |
| [332] | Machon, T.; Alexander, G. P., Woven nematic defects, skyrmions, and the abelian sandpile model, Phys. Rev. Lett., 121, Article 237801 pp., 2018 |
| [333] | Bouligand, Y.; Derrida, B.; Poenaru, V.; Pomeau, Y.; Toulouse, G., Distortions with double topological character: the case of cholesterics, J. Physique, 39, 8, 863-867, 1978 |
| [334] | Machon, T., Contact topology and the structure and dynamics of cholesterics, New J. Phys., 19, 11, Article 113030 pp., 2017 |
| [335] | Pollard, J.; Posnjak, G.; Čopar, S.; Muševič, I.; Alexander, G. P., Point defects, topological chirality, singularity theory in cholesteric liquid-crystal droplets, Phys. Rev. X, 9, 2, Article 021004 pp., 2019 |
| [336] | Ackerman, P. J.; Smalyukh, I. I., Reversal of helicoidal twist handedness near point defects of confined chiral liquid crystals, Phys. Rev. E, 93, 5, Article 052702 pp., 2016 |
| [337] | Posnjak, G.; Čopar, S.; Muševič, I., Hidden topological constellations and polyvalent charges in chiral nematic droplets, Nat. Commun., 8, 14594, 2017 |
| [338] | Krakhalev, M. N.; Rudyak, V. Y.; Prishchepa, O. O.; Gardymova, A. P.; Emelyanenko, A. V.; Liu, J.-H.; Zyryanov, V. Y., Orientational structures in cholesteric droplets with homeotropic surface anchoring, Soft Matter, 15, 28, 5554-5561, 2019 |
| [339] | Lavrentovich, M. O.; Tran, L., Undulation instabilities in cholesteric liquid crystals induced by anchoring transitions, Phys. Rev. Res., 2, 2, Article 023128 pp., 2020 |
| [340] | Han, Y.; Dalby, J.; Majumdar, A.; Carter, B. M.G. D.; Machon, T., Uniaxial versus biaxial pathways in one-dimensional cholesteric liquid crystals, Phys. Rev. Res., 4, L032018, 2022 |
| [341] | Pollard, J.; Alexander, G. P., Contact topology and the classification of disclination lines in cholesteric liquid crystals, Phys. Rev. Lett., 130, 22, Article 228102 pp., 2023 |
| [342] | Machon, T.; Alexander, G. P., Knotted defects in nematic liquid crystals, Phys. Rev. Lett., 113, 2, Article 027801 pp., 2014 |
| [343] | Tai, J.-S. B.; Smalyukh, I. I., Three-dimensional crystals of adaptive knots, Science, 365, 6460, 1449-1453, 2019 |
| [344] | Nych, A.; Fukuda, J.; Ognysta, U.; Žumer, S.; Muševič, I., Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film, Nat. Phys., 13, 1215, 2017 |
| [345] | Machon, T.; Alexander, G. P., Umbilic lines in orientational order, Phys. Rev. X, 6, Article 011033 pp., 2016 |
| [346] | Foster, D.; Kind, C.; Ackerman, P. J.; Tai, J.-S. B.; Dennis, M. R.; Smalyukh, I. I., Two-dimensional skyrmion bags in liquid crystals and ferromagnets, Nat. Phys., 15, 655, 2019 |
| [347] | Afghah, S.; Selinger, J. V., Theory of helicoids and skyrmions in confined cholesteric liquid crystals, Phys. Rev. E, 96, 1, Article 012708 pp., 2017 |
| [348] | Varanytsia, A.; Chien, L.-C., Photoswitchable and dye-doped bubble domain texture of cholesteric liquid crystals, Opt. Lett., 40, 19, 4392-4395, 2015 |
| [349] | Pišljar, J.; Ghosh, S.; Turlapati, S.; Rao, N. V.S.; Škarabot, M.; Mertelj, A.; Petelin, A.; Nych, A.; Marinčič, M.; Pusovnik, A.; Ravnik, M.; Muševič, I., Blue phase III: Topological fluid of skyrmions, Phys. Rev. X, 12, 1, Article 011003 pp., 2022 |
| [350] | Khesin, B.; Arnold, V. I., Topological Methods in Hydrodynamics, 1992, Springer-Verlag: Springer-Verlag Berlin |
| [351] | Ricca (Ed.), R. L., Lectures on topological fluid mechanics. CIME Lecture Notes in Mathematics 1973, 2009, Springer-Verlag |
| [352] | Enciso, A.; Peralta-Salas, D., Knots and links in steady solutions of the Euler equation, Ann. Math., 175, 345-367, 2012 · Zbl 1238.35092 |
| [353] | Pieranski, P., In search of ideal knots, (Stasiak, A.; Katrich, V.; Kauffmann, L. H., Ideal Knots. Ideal Knots, Series on Knots and Everything, vol. 19, 1998, World Scientific, Singapore), 20-41 · Zbl 0943.57005 |
| [354] | Arnold, V. I., The asymptotic Hopf invariant and its applications, (Proc. Summer School in Diff. Eqs. At Dilizhan, 1974, Armenian Academy of Sciences: Armenian Academy of Sciences Erevan), 229-256, [In Russian.], 1986 Sel. Math. Sov.5, 327-345 [English translation] · Zbl 0623.57016 |
| [355] | Moffatt, H. K., The energy spectrum of knots and links, Nature, 347, 367-369, 1990 |
| [356] | Freedman, M. H.; He, Z.-X., Divergence-free fields: energy and asymptotic crossing number, Ann. Math., 134, 189-229, 1991 · Zbl 0746.57011 |
| [357] | Battye, R.; Sutcliffe, P. M., Knots as stable soliton solutions in a three-dimensional classical field theory, Phys. Rev. Lett., 81, 4798-4801, 1998 · Zbl 0949.58022 |
| [358] | Ashton, T.; Cantarella, J.; Piatek, M.; Rawdon, E. J., Knot tightening by constrained gradient descent, Exp. Math., 20, 57-90, 2011 · Zbl 1261.49007 |
| [359] | Ricca, R. L.; Maggioni, F., On the groundstate energy spectrum of magnetic knots and links, J. Phys. A: Math. Theor., 47, Article 205501 pp., 2014 · Zbl 1303.57010 |
| [360] | Buniy, R. V.; Cantarella, J.; Kephart, T. W.; Rawdon, E. J., Tight knot spectrum in QCD, Phys. Rev. D, 89, Article 054513 pp., 2014 |
| [361] | Berger, M. A., Topological magnetohydrodynamics and astrophysics, (Meyers, R., Encyclopedia of Complexity and Systems Science, 2009, Springer), 9268-9282 |
| [362] | Wilmot-Smith, A. L.; Pontin, D. I.; Hornig, G., Dynamics of braided coronal loops I. Onset of magnetic reconnection, Astron. Astrophys., 516, A5, 2010 · Zbl 1263.85058 |
| [363] | Yeates, A. R.; Hornig, G., Unique topological characterization of braided magnetic fields, Phys. Plasmas, 20, Article 012102 pp., 2013 |
| [364] | Berger, M. A., Energy-crossing number relations for braided magnetic fields, Phys. Rev. Lett., 70, 705-708, 1993 · Zbl 1051.85502 |
| [365] | Wilmot-Smith, A. L.; Pontin, D. I.; Yeates, A. R.; Hornig, G., Heating of braided coronal loops, Astron. Astrophys., 536, 2011 |
| [366] | Aref, H.; Blake, J. R.; Budišić, M.; Cardoso, S. S.S.; Cartwright, J. H.E.; Clercx, H. J.H.; El Omari, K.; Feudel, U.; Golestanian, R.; Gouillart, E.; van Heijst, G. J.F.; Krasnopolskaya, T. S.; Le Guer, Y.; MacKay, R. S.; Meleshko, V. V.; Metcalfe, G.; Mezić, I.; de Moura, A. P.S.; Piro, O.; Speetjens, M. F.M.; Sturman, R.; Thiffeault, J.-L.; Tuval, I., Frontiers of chaotic advection, Rev. Modern Phys., 89, 2, Article 025007 pp., 2017 |
| [367] | Boyland, P. L.; Aref, H.; Stremler, M. A., Topological fluid mechanics of stirring, J. Fluid Mech., 403, 277-304, 2000 · Zbl 0982.76085 |
| [368] | Thiffeault, J.-L., Measuring topological chaos, Phys. Rev. Lett., 94, Article 084502 pp., 2005 |
| [369] | Arrayás, M.; Bouwmeester, D.; Trueba, J. L., Knots in electromagnetism, Phys. Rep., 667, 1-61, 2017 · Zbl 1359.78002 |
| [370] | Kamchatnov, A. M., Topological solitons in magnetohydrodynamics, Sov. Phys.-JETP, 55, 1, 59-73, 1982 |
| [371] | Rañada, A. F., A topological theory of the electromagnetic field, Lett. Math. Phys., 18, 2, 97-106, 1989 · Zbl 0687.57015 |
| [372] | Dennis, M. R.; King, R. P.; Jack, B.; O’Holleran, K.; Padgett, M. J., Isolated optical vortex knots, Nature Phys., 6, 118-121, 2010 |
| [373] | Kedia, H.; Foster, D.; Dennis, M. R.; Irvine, W. T.M., Weaving knotted vector fields with tunable helicity, Phys. Rev. Lett., 117, Article 274501 pp., 2016 |
| [374] | Arrayás, M.; Bouwmeester, D.; Trueba, J. L., Knots in electromagnetism, Phys. Rep., 667, 1-61, 2017 · Zbl 1359.78002 |
| [375] | Bode, B.; Dennis, M. R.; Foster, D.; King, R. P., Knotted fields and explicit fibrations for lemniscate knots, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 473, Article 20160829 pp., 2017 · Zbl 1402.57006 |
| [376] | Kleckner, D.; Irvine, W. T.M., Creation and dynamics of knotted vortices, Nature Phys., 9, 253-258, 2013 |
| [377] | Zuccher, S.; Ricca, R., Creation of quantum knots and links driven by minimal surfaces, J. Fluid Mech., 942, A8, 2022 · Zbl 1504.76112 |
| [378] | Kida, S., A vortex filament moving without change of form, J. Fluid Mech., 112, 397-409, 1981 · Zbl 0484.76030 |
| [379] | Keener, J. P., Knotted vortex filaments in an ideal fluid, J. Fluid Mech., 211, 629-651, 1990 · Zbl 0686.76014 |
| [380] | Ricca, R. L., Torus knots and polynomial invariants for a class of soliton equations, Chaos, 3, 83-91, 1993 · Zbl 0992.53500 |
| [381] | Ricca, R. L.; Samuels, D. C.; Barenghi, C. F., Evolution of vortex knots, J. Fluid Mech., 391, 29-44, 1999 · Zbl 1009.76012 |
| [382] | Aref, H.; Zawadzki, I., Linking of vortex rings, Nature, 354, 50-53, 1991 |
| [383] | Yao, J.; Yang, Y.; Hussain, F., Dynamics of a trefoil knotted vortex, J. Fluid Mech., 923, 2021 · Zbl 07398620 |
| [384] | Zhao, X.; Yu, Z.; J.-B., C.; Scalo, C., Direct numerical and large-eddy simulation of trefoil knotted vortices, J. Fluid Mech., 910, 2021 · Zbl 1461.76315 |
| [385] | Barenghi, C. F.; Ricca, R. L.; Samuels, D. C., How tangled is a tangle?, Physica D, 157, 197-206, 2001 · Zbl 1001.57500 |
| [386] | Kleckner, D.; Kauffman, L. H.; Irvine, W. T.M., How superfluid vortex knots untie, Nat. Phys., 12, 650-655, 2016 |
| [387] | Bai, W.-K.; Yang, T.; Liu, W.-M., Topological transition from superfluid vortex rings to isolated knots and links, Phys. Rev. A, 102, Article 063318 pp., 2020 |
| [388] | Cooper, R. G.; Mesgarnezhad, M.; Baggaley, A. W.; Barenghi, C. F., Knot spectrum of turbulence, Sci. Rep., 9, 10545, 2019 |
| [389] | Everaers, R.; Sukumaran, S. K.; Grest, G. S.; Svaneborg, C.; Sivasubramanian, A.; Kremer, K., Rheology and microscopic topology of entangled polymeric liquids, Science, 303, 5659, 823-826, 2004 |
| [390] | De Gennes, P. G., Reptation of a polymer chain in the presence of fixed obstacles, J. Chem. Phys., 55, 2, 572-579, 1971 |
| [391] | Marrucci, G., Relaxation by reptation and tube enlargement: A model for polydisperse polymers, J. Polym. Sci.: Polym. Phys. Ed., 23, 1, 159-177, 1985 |
| [392] | Viovy, J. L.; Rubinstein, M.; Colby, R. H., Constraint release in polymer melts: tube reorganization versus tube dilation, Macromolecules, 24, 12, 3587-3596, 1991 |
| [393] | Watanabe, H., Viscoelasticity and dynamics of entangled polymers, Prog. Polym. Sci., 24, 9, 1253-1403, 1999 |
| [394] | Likhtman, A. E.; McLeish, T. C.B., Quantitative theory for linear dynamics of linear entangled polymers, Macromolecules, 35, 16, 6332-6343, 2002 |
| [395] | Boudara, V. A.; Read, D. J.; Ramírez, J., REPTATE rheology software: Toolkit for the analysis of theories and experiments, J. Rheol., 64, 3, 709-722, 2020 |
| [396] | Parisi, D.; Ahn, J.; Chang, T.; Vlassopoulos, D.; Rubinstein, M., Stress relaxation in symmetric ring-linear polymer blends at low ring fractions, Macromolecules, 53, 5, 1685-1693, 2020 |
| [397] | Herrmann, A.; Kresse, B.; Wohlfahrt, M.; Bauer, I.; Privalov, A. F.; Kruk, D.; Fatkullin, N.; Fujara, F.; Rössler, E. A., Mean square displacement and reorientational correlation function in entangled polymer melts revealed by field cycling 1H and 2H NMR relaxometry, Macromolecules, 45, 16, 6516-6526, 2012 |
| [398] | Svaneborg, C.; Everaers, R., Characteristic time and length scales in melts of kremer-grest bead-spring polymers with wormlike bending stiffness, Macromolecules, 53, 6, 1917, 2020 |
| [399] | Everaers, R.; Karimi-Varzaneh, H. A.; Fleck, F.; Hojdis, N.; Svaneborg, C., Kremer-grest models for commodity polymer melts: Linking theory, experiment, simulation at the kuhn scale, Macromolecules, 53, 6, 1901-1916, 2020 |
| [400] | McLeish, T. C.B., Tube theory of entangled polymer dynamics, Adv. Phys., 51, 1379-1527, 2002 |
| [401] | Uchida, N.; Grest, G. S.; Everaers, R., Viscoelasticity and primitive path analysis of entangled polymer liquids: From F-actin to polyethylene, J. Chem. Phys., 128, 4, Article 044902 pp., 2008 |
| [402] | Edwards, S. F., The theory of rubber elasticity, Br. Polym. J., 9, 140, 1977 |
| [403] | Rubinstein, M.; Helfand, E., Statistics of the entanglement of polymers: Concentration effects, J. Chem. Phys., 82, 5, 2477-2483, 1985 |
| [404] | Kröger, M., Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems, Comput. Phys. Comm., 168, 209-232, 2005 |
| [405] | Shanbhag, S.; Larson, R. G., Chain retraction potential in a fixed entanglement network, Phys. Rev. Lett., 94, 7, Article 076001 pp., 2005 |
| [406] | Tzoumanekas, C.; Theodorou, D. N., Topological analysis of linear polymer melts: A statistical approach, Macromolecules, 39, 13, 4592-4604, 2006 |
| [407] | Hoy, R. S.; Grest, G. S., Entanglements of an end-grafted polymer brush in a polymeric matrix, Macromolecules, 40, 23, 8389, 2007 |
| [408] | Svaneborg, C.; Everaers, R.; Grest, G. S.; Curro, J. G., Connectivity and entanglement stress contributions in strained polymer networks, Macromolecules, 41, 13, 4920, 2008 |
| [409] | Hoy, R. S.; Foteinopoulou, K.; Kröger, M., Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length, Phys. Rev. E., 80, 3, Article 031803 pp., 2009 |
| [410] | Everaers, R., Topological versus rheological entanglement length in primitive-path analysis protocols, tube models, slip-link models, Phys. Rev. E., 86, 2, Article 022801 pp., 2012 |
| [411] | Hou, J.-X., Note: Determine entanglement length through monomer mean-square displacement, J. Chem. Phys., 146, 2, Article 026101 pp., 2017 |
| [412] | Hsu, H.-P.; Kremer, K., Static and dynamic properties of large polymer melts in equilibrium, J. Chem. Phys., 144, 15, Article 154907 pp., 2016 |
| [413] | Hou, J.-X.; Svaneborg, C.; Everaers, R.; Grest, G. S., Stress relaxation in entangled polymer melts, Phys. Rev. Lett., 105, 6, Article 068301 pp., 2010 |
| [414] | Semenov, A. N., Dynamics of concentrated solutions of rigid-chain polymers. I: Brownian motion of persistent macromolecules in isotropic solution, J. Chem. Soc., Faraday Trans., 82, 317-329, 1986 |
| [415] | Morse, D. C., Tube diameter in tightly entangled solutions of semiflexible polymers, Phys. Rev. E, 63, Article 031502 pp., 2001 |
| [416] | Lin, Y. H., Number of entanglement strands per cubed tube diameter, a fundamental aspect of topological universality in polymer viscoelasticity, Macromolecules, 20, 12, 3080-3083, 1987 |
| [417] | Kavassalis, T. A.; Noolandi, J., New view of entanglements in dense polymer systems, Phys. Rev. Lett., 59, 2674-2677, 1987 |
| [418] | Read, D. J.; Jagannathan, K.; Likhtman, A. E., Entangled polymers: Constraint release, mean paths, tube bending energy, Macromolecules, 41, 18, 6843-6853, 2008 |
| [419] | Likhtman, A. E., The tube axis and entanglements in polymer melts, Soft Matter, 10, 12, 1895, 2014 |
| [420] | Likhtman, A. E.; Ponmurugan, M., Microscopic definition of polymer entanglements, Macromolecules, 47, 4, 1470-1481, 2014 |
| [421] | Michieletto, D.; Sakaue, T., Dynamical entanglement and cooperative dynamics in entangled solutions of ring and linear polymers, ACS Macro Lett., 10, 129, 2020 |
| [422] | Halverson, J. D.; Grest, G. S.; Grosberg, A. Y.; Kremer, K., Rheology of ring polymer melts: From linear contaminants to ring-linear blends, Phys. Rev. Lett., 108, 3, Article 038301 pp., 2012 |
| [423] | Rosa, A.; Everaers, R., Ring polymers in the melt state: The physics of crumpling, Phys. Rev. Lett., 112, Article 118302 pp., 2014 |
| [424] | Schram, R. D.; Rosa, A.; Everaers, R., Local loop opening in untangled ring polymer melts: A detailed “feynman test” of models for the large scale structure, Soft Matter, 15, 2418-2429, 2019 |
| [425] | Wang, J.; Ge, T., Crazing reveals an entanglement network in glassy ring polymers, Macromolecules, 54, 16, 7500-7511, 2021 |
| [426] | Halverson, J. D.; Lee, W. B.; Grest, G. S.; Grosberg, A. Y.; Kremer, K., Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. 1. Statics, J. Chem. Phys., 134, Article 204904 pp., 2011 |
| [427] | Smrek, J.; Kremer, K.; Rosa, A., Threading of unconcatenated ring polymers at high concentrations: double-folded vs time-equilibrated structures, ACS Macro Lett., 8, 2, 155-160, 2019 |
| [428] | Obukhov, S. P.; Rubinstein, M.; Duke, T., Dynamics of a ring polymer in a gel, Phys. Rev. Lett., 73, 1263-1266, 1994 |
| [429] | Chang, T., Polymer characterization by interaction chromatography, J. Polym. Sci. Part B: Polym. Phys., 43, 13, 1591-1607, 2005 |
| [430] | Lee, H. C.; Lee, H.; Lee, W.; Chang, T.; Roovers, J., Fractionation of cyclic polystyrene from linear precursor by HPLC at the chromatographic critical condition, Macromolecules, 33, 22, 8119-8121, 2000 |
| [431] | Doi, Y.; Matsubara, K.; Ohta, Y.; Nakano, T.; Kawaguchi, D.; Takahashi, Y.; Takano, A.; Matsushita, Y., Melt rheology of ring polystyrenes with ultrahigh purity, Macromolecules, 48, 9, 3140-3147, 2015 |
| [432] | Doi, Y.; Matsumoto, A.; Inoue, T.; Iwamoto, T.; Takano, A.; Matsushita, Y.; Takahashi, Y.; Watanabe, H., Re-examination of terminal relaxation behavior of high-molecular-weight ring polystyrene melts, Rheol. Acta, 56, 6, 567-581, 2017 |
| [433] | Tsalikis, D. G.; Mavrantzas, V. G.; Vlassopoulos, D., Analysis of slow modes in ring polymers: Threading of rings controls long-time relaxation, ACS Macro Lett., 5, 6, 755-760, 2016 |
| [434] | Tsalikis, D. G.; Mavrantzas, V. G., Threading of ring poly(ethylene oxide) molecules by linear chains in the melt, ACS Macro Lett., 3, 8, 763-766, 2014 |
| [435] | Michieletto, D.; Marenduzzo, D.; Orlandini, E.; Alexander, G. P.; Turner, M. S., Dynamics of self-threading ring polymers in a gel, Soft Matter, 10, 5936-5944, 2014 |
| [436] | Gooßen, S.; Krutyeva, M.; Sharp, M.; Feoktystov, A.; Allgaier, J.; Pyckhout-Hintzen, W.; Wischnewski, A.; Richter, D., Sensing polymer chain dynamics through ring topology: A neutron spin echo study, Phys. Rev. Lett., 115, 14, Article 148302 pp., 2015 |
| [437] | Obukhov, S. P., Talk at KITP santa barbara, 1997, accessed Apr. 2019 |
| [438] | Lo, W.-C.; Turner, M. S., The topological glass in ring polymers, Europhys. Lett., 102, 5, 58005, 2013 |
| [439] | Borger, A.; Wang, W.; O’Connor, T. C.; Ge, T.; Grest, G. S.; Jensen, G. V.; Ahn, J.; Chang, T.; Hassager, O.; Mortensen, K.; Vlassopoulos, D.; Huang, Q., Threading-unthreading transition of linear-ring polymer blends in extensional flow, ACS Macro Lett., 9, 10, 1452-1457, 2020 |
| [440] | O’Connor, T. C.; Ge, T.; Rubinstein, M.; Grest, G. S., Topological linking drives anomalous thickening of ring polymers in weak extensional flows, Phys. Rev. Lett., 124, Article 027801 pp., 2020 |
| [441] | Huang, Q.; Ahn, J.; Parisi, D.; Chang, T.; Hassager, O.; Panyukov, S.; Rubinstein, M.; Vlassopoulos, D., Unexpected stretching of entangled ring macromolecules, Phys. Rev. Lett., 122, 20, Article 208001 pp., 2019 |
| [442] | Narros, A.; Moreno, A. J.; Likos, C. N., Effective interactions of knotted ring polymers, Biochem. Soc. Trans., 41, 2, 630-634, 2013 |
| [443] | Lang, M.; Fischer, J.; Sommer, J.-U., Effect of topology on the conformations of ring polymers, Macromolecules, 45, 18, 7642-7648, 2012 |
| [444] | Lee, E.; Kim, S.; Jung, Y., Slowing down of ring polymer diffusion caused by inter-ring threading, Macromol. Rapid Commun., 36, 11, 1115-1121, 2015 |
| [445] | Rosa, A.; Smrek, J.; Turner, M. S.; Michieletto, D., Threading-induced dynamical transition in tadpole-shaped polymers, ACS Macro Lett., 9, 5, 743-748, 2020 |
| [446] | Tsalikis, D. G.; Mavrantzas, V. G., Size and diffusivity of polymer rings in linear polymer matrices: The key role of threading events, Macromolecules, 53, 3, 803-820, 2020 |
| [447] | Parks, H. R., Soap-film-like minimal surfaces spanning knots, J. Geom. Anal., 2, 3, 267-290, 1992 · Zbl 0757.49028 |
| [448] | Chubak, I.; Likos, C. N.; Smrek, J., Topological and threading effects in polydisperse ring polymer solutions, Mol. Phys., Article e1883140 pp., 2021 |
| [449] | Parisi, D.; Costanzo, S.; Jeong, Y.; Ahn, J.; Chang, T.; Vlassopoulos, D.; Halverson, J. D.; Kremer, K.; Ge, T.; Rubinstein, M.; Grest, G. S.; Srinin, W.; Grosberg, A. Y., Nonlinear shear rheology of entangled polymer rings, Macromolecules, 54, 6, 2811-2827, 2021 |
| [450] | Nguyen, N.-T.; Wereley, S. T.; Shaegh, S. A.M., Fundamentals and Applications of Microfluidics, 2019, Artech House |
| [451] | Soh, B. W.; Klotz, A. R.; Doyle, P. S., Topological simplification of complex knots untied in elongational flows, Macromolecules, 53, 7389-7398, 2020 |
| [452] | Schroeder, C. M., Single polymer dynamics for molecular rheology, J. Rheol., 62, 371-403, 2018 |
| [453] | Li, Y.; Hsiao, K.-W.; Brockman, C. A.; Yates, D. Y.; Robertson-Anderson, R. M.; Kornfield, J. A.; San Francisco, M. J.; Schroeder, C. M.; McKenna, G. B., When ends meet: Circular DNA stretches differently in elongational flows, Macromolecules, 48, 5997-6001, 2015 |
| [454] | Balducci, A. G.; Tang, J.; Doyle, P. S., Electrophoretic stretching of DNA molecules in cross-slot nanoslit channels, Macromolecules, 41, 24, 9914-9918, 2008 |
| [455] | Dealy, J. M., Weissenberg and deborah numbers - their definition and use, Rheol. Bull., 79, 14-18, 2010 |
| [456] | Tanyeri, M.; Schroeder, C. M., Manipulation and confinement of sinlge particles using fluid flow, Nano Lett., 13, 2357-2364, 2013 |
| [457] | De Gennes, P., Molecular individualism, Science, 276, 5321, 1999-2000, 1997 |
| [458] | Hsiao, K.-W.; Schroeder, C. M.; Sing, C. E., Ring polymer dynamics are governed by a couling between architecture and hydrodynamic interactions, Macromolecules, 49, 1961-1971, 2016 |
| [459] | Liebetreu, M.; Likos, C. N., Hydrodynamic inflation of ring polymers under shear, Commun. Mater., 1, 4, 2020 |
| [460] | Malevanets, A.; Kapral, R., Mesoscopic model for solvent dynamics, J. Chem. Phys., 110, 17, 8605-8613, 1999 |
| [461] | Gompper, G.; Ihle, T.; Kroll, D. M.; Winkler, R. G., Multi-particle collision dynamics - a particle-based mesoscale simulation approach to the hydrodynamics of complex fluids, Adv. Polym. Sci., 221, 1-91, 2008 |
| [462] | Liebetreu, M.; Ripoll, M.; Likos, C. N., Trefoil knot hydrodynamic delocalization on sheared ring polymers, ACS Macro Lett., 7, 447-452, 2018 |
| [463] | Young, C. D.; Qian, J. R.; Marvin, M.; Sing, C. E., Ring polymer dynamics and tumbling-strecth transitions in planar mixed flows, Phys. Rev. E, 99, Article 062502 pp., 2019 |
| [464] | Tu, M. Q.; Lee, M.; Robertson-Anderson, R. M.; Schroeder, C. M., Direct obesrvation of ring polymer dynamics in the flow-gradient plane of shear flow, Macromolecules, 53, 9406-9419, 2020 |
| [465] | Soh, B. W.; Klotz, A. R.; Robertson-Anderson, R. M.; Doyle, P. S., Long-lived self-entanglements in ring polymers, Phys. Rev. Lett., 123, Article 048002 pp., 2019 |
| [466] | Soh, B. W.; Gengaro, I. R.; Klotz, A. R.; Doyle, P. S., Self-entanglement of a tumbled circular chain, Phys. Rev. Res., 1, Article 033194 pp., 2019 |
| [467] | Narsimhan, V.; Renner, C. B.; Doyle, P. S., Jamming of knots along a tensioned chain, ACS Macro Lett., 5, 123-127, 2016 |
| [468] | Dai, L.; Renner, C. B.; Doyle, P. S., Metastable tight knots in semiflexible chains, Macromolecules, 47, 17, 6135-6140, 2014 |
| [469] | Sharma, R. K.; Agrawal, I.; Dai, L.; Doyle, P.; Garaj, S., DNA knot malleability in single-digit nanopores, Nano Lett., 21, 9, 3772-3779, 2021 |
| [470] | Rheaume, S. N.; Klotz, A. R., Nanopore translocation of topologically linked DNA catenanes, Phys. Rev. E, 107, 2, Article 024504 pp., 2023 |
| [471] | Najafi, S.; Tubiana, L.; Podgornik, R.; Potestio, R., Chirality modifies the interaction between knots, Europhys. Lett., 114, 5, 50007, 2016 |
| [472] | Weiss, L. B.; Nikoubashman, A.; Likos, C. N., Topology-sensitive microfluidic filter for polymers of varying stiffness, ACS Macro Lett., 6, 1426-1431, 2017 |
| [473] | Weiss, L. B.; Likos, C. N.; Nikoubashman, A., Spatial demixing of ring and chain polymers in pressure-driven flow, Macromolecules, 52, 7858-7869, 2019 |
| [474] | Marenda, M.; Orlandini, E.; Micheletti, C., Sorting ring polymers by knot type with modulated nanochannels, Soft Matter, 13, 795-802, 2017 |
| [475] | Weiss, L. B.; Marenda, M.; Micheletti, C.; Likos, C. N., Hydrodynamics and filtering of knotted ring polymers in nanochannels, Macromolecules, 52, 4111-4119, 2019 |
| [476] | Boettiger, A. N.; Bintu, B.; Moffitt, J. R.; Wang, S.; Beliveau, B. J.; Fudenberg, G.; Imakaev, M.; Mirny, L. A.; Wu, C.-t.; Zhuang, X., Super-resolution imaging reveals distinct chromatin folding for different epigenetic states, Nature, 529, 7586, 418-422, 2016 |
| [477] | Ou, H. D.; Phan, S.; Deerinck, T. J.; Thor, A.; Ellisman, M. H.; O’Shea, C. C., Chromemt: Visualizing 3D chromatin structure and compaction in interphase and mitotic cells, Science, 357, 6349, 2017 |
| [478] | Lieberman-Aiden, E.; Van Berkum, N. L.; Williams, L.; Imakaev, M.; Ragoczy, T.; Telling, A.; Amit, I.; Lajoie, B. R.; Sabo, P. J.; Dorschner, M. O.; Sandstrom, R.; Bernstein, B.; Bender, M. A.; Groudine, M.; Gnirke, A.; Stamatoyannopoulos, J.; Mirny, L. A.; Lander, E. S.; Dekker, J., Comprehensive mapping of long-range interactions reveals folding principles of the human genome, Science, 326, 5950, 289-293, 2009 |
| [479] | Beagrie, R. A.; Scialdone, A.; Schueler, M.; Kraemer, D. C.A.; Chotalia, M.; Xie, S. Q.; Barbieri, M.; de Santiago, I.; Lavitas, L.-M.; Branco, M. R.; Fraser, J.; Dostie, J.; Game, L.; Dillon, N.; Edwards, P. A.W.; Nicodemi, M.; Pombo, A., Complex multi-enhancer contacts captured by genome architecture mapping, Nature, 543, 7646, 519-524, 2017 |
| [480] | Rao, V. B.; Feiss, M., The bacteriophage DNA packaging motor, Annu. Rev. Genet., 42, 647-681, 2008 |
| [481] | Zandi, R.; Dragnea, B.; Travesset, A.; Podgornik, R., On virus growth and form, Phys. Rep., 847, 1-102, 2020 |
| [482] | Leforestier, A.; Brasiles, S.; de Frutos, M.; Raspaud, E.; Letellier, L.; Tavares, P.; Livolant, F., Bacteriophage T5 DNA ejection under pressure, J. Mol. Biol., 384, 3, 730-739, 2008 |
| [483] | Molineux, I. J.; Panja, D., Popping the cork: Mechanisms of phage genome ejection, Nat. Rev. Microbiol., 11, 194-204, 2013 |
| [484] | Riemer, S. C.; Bloomfield, V. A., Packaging of DNA in bacteriophage heads: Some considerations on energetics, Biopolymers, 17, 785-794, 1978 |
| [485] | Wiggins, P. A.; van der Heijden, T.; Moreno-Herrero, F.; Spakowitz, A.; Phillips, R.; Widom, J.; Dekker, C.; Nelson, P. C., High flexibility of DNA on short length scales probed by atomic force microscopy, Nature Nanotechnol., 1, 137, 2006 |
| [486] | Leforestier, A.; Šiber, A.; Livolant, F.; Podgornik, R., Protein-DNA interactions determine the shapes of DNA toroids condensed in virus capsids, Biophys. J., 100, 9, 2209-2216, 2011 |
| [487] | Hud, N. V.; Downing, K. H.; Balhorn, R., A constant radius of curvature model for the organization of DNA in toroidal condensates, Proc. Natl. Acad. Sci., 92, 8, 3581-3585, 1995 |
| [488] | Leforestier, A.; Livolant, F., Structure of toroidal DNA collapsed inside the phage capsid, Proc. Natl. Acad. Sci. U. S. A., 106, 23, 9157-9162, 2009 |
| [489] | Curk, T.; Farrell, J. D.; Dobnikar, J.; Podgornik, R., Spontaneous domain formation in spherically confined elastic filaments, Phys. Rev. Lett., 123, Article 047801 pp., 2019 |
| [490] | Stoop, N.; Najafi, J.; Wittel, F. K.; Habibi, M.; Herrmann, H. J., Packing of elastic wires in spherical cavities, Phys. Rev. Lett., 106, Article 214102 pp., 2011 |
| [491] | Marenduzzo, D.; Micheletti, C.; Orlandini, E.; Sumners, D. W., Topological friction strongly affects viral DNA ejection, Proc. Natl. Acad. Sci., 110, 50, 20081-20086, 2013 |
| [492] | Mason, D. J.; Powelson, D. M., Nuclear division a s observed in live bacteria by a new technique, J. Bacteriol., 71, 4, 474, 1956 |
| [493] | Azam, T. A.; Ishihama, A., Twelve species of the nucleoid-associated protein from Escherichia coli. Sequence recognition specificity and DNA binding affinity, J. Biol. Chem., 274, 46, 33105-33113, 1999 |
| [494] | Wu, F.; Swain, P.; Kuijpers, L.; Zheng, X.; Felter, K.; Guurink, M.; Solari, J.; Jun, S.; Shimizu, T. S.; Chaudhuri, D.; Mulder, B.; Dekker, C., Cell boundary confinement sets the size and position of the E. coli Chromosome, Curr. Biol., 29, 13, 2131-2144.e4, 2019 |
| [495] | Stuger, R.; Woldringh, C. L.; Van der Weijden, C. C.; Vischer, N. O.; Bakker, B. M.; Van Spanning, R. J.; Snoep, J. L.; Weterhoff, H. V., DNA supercoiling by gyrase is linked to nucleoid compaction, Mol. Biol. Rep., 29, 1-2, 79-82, 2002 |
| [496] | Wang, X.; Llopis, P. M.; Rudner, D. Z., Organization and segregation of bacterial chromosomes, Nature Rev. Genet., 14, 3, 191-203, 2013 |
| [497] | Cairns, J., The bacterial chromosome and its manner of replication as seen by autoradiography, J. Mol. Biol., 6, 3, 208-213, 1963 |
| [498] | Kavenoff, R.; Ryder, O. A., Electron microscopy of membrane-associated folded chromosomes of Escherichia coli, Chromosoma, 55, 1, 13-25, 1976 |
| [499] | Sinden, R. R.; Pettijohn, D. E., Chromosomes in living Escherichia coli cells are segregated into domains of supercoiling, Proc. Natl. Acad. Sci. USA, 78, 1 II, 224-228, 1981 |
| [500] | Noom, M. C.; Navarre, W. W.; Oshima, T.; Wuite, G. J.L.; Dame, R. T., H-NS promotes looped domain formation in the bacterial chromosome, Curr. Biol., 17, 21, 913-914, 2007 |
| [501] | Le, T. B.K.; Imakaev, M. V.; Mirny, L. A.; Laub, M. T., High-resolution mapping of the spatial organization of a bacterial chromosome, Science, 342, 6159, 731-734, 2013 |
| [502] | Benedetti, F.; Dorier, J.; Burnier, Y.; Stasiak, A., Models that include supercoiling of topological domains reproduce several known features of interphase chromosomes, Nucleic Acids Res., 42, 5, 2848-2855, 2014 |
| [503] | Fosado, Y. A.G.; Michieletto, D.; Brackley, C. A.; Marenduzzo, D., Nonequilibrium dynamics and action at a distance in transcriptionally driven DNA supercoiling, Proc. Natl. Acad. Sci. USA, 118, 10, 2021 |
| [504] | Griswold, A., Genome packaging in prokaryotes: the circular chromosome of e. coli, Nature Education, 1, 1, 57, 2008 |
| [505] | Delbrück, M., On the replication of desoxyribonucleic acid (DNA), Proc. Natl. Acad. Sci., 40, 9, 783-788, 1954 |
| [506] | Dingman, C. W., Bidirectional chromosome replication: some topological considerations, J. Theoret. Biol., 43, 1, 187-195, 1974 |
| [507] | Gogou, C.; Japaridze, A.; Dekker, C., Mechanisms for chromosome segregation in bacteria, Front. Microbiol., 12, June, 1-15, 2021 |
| [508] | Brandão, H. B.; Ren, Z.; Karaboja, X.; Mirny, L. A.; Wang, X., DNA-loop-extruding SMC complexes can traverse one another in vivo, Nat. Struct. Mol. Biol., 28, 8, 642-651, 2021 |
| [509] | Jun, S.; Mulder, B., Entropy-driven spatial organization of highly confined polymers: lessons for the bacterial chromosome, Proc. Natl. Acad. Sci. USA, 103, 33, 12388-12393, 2006 |
| [510] | Fosado, Y. A.G.; Howard, J.; Weir, S.; Noy, A.; Leake, M. C.; Michieletto, D., Fluidification of entanglements by a DNA bending protein, Phys. Rev. Lett., 130, 5, 58203, 2023 |
| [511] | Buckle, A.; Brackley, C. A.; Boyle, S.; Marenduzzo, D.; Gilbert, N., Polymer simulations of heteromorphic chromatin predict the 3D folding of complex genomic loci, Mol. Cell, 72, 4, 786-797, 2018 |
| [512] | Grigoryev, S. A.; Arya, G.; Correll, S.; Woodcock, C. L.; Schlick, T., Evidence for heteromorphic chromatin fibers from analysis of nucleosome interactions, Proc. Natl. Acad. Sci. USA, 106, 32, 13317-13322, 2009 |
| [513] | Misteli, T., The self-organizing genome: Principles of genome architecture and function, Cell, 2020 |
| [514] | Prunell, A., A topological approach to nucleosome structure and dynamics: the linking number paradox and other issues, Biophys. J., 74, 5, 2531-2544, 1998 |
| [515] | Lusser, A.; Kadonaga, J. T., Strategies for the reconstitution of chromatin, Nature Methods, 1, 1, 19-26, 2004 |
| [516] | Bertin, A.; Leforestier, A.; Durand, D.; Livolant, F., Role of histone tails in the conformation and interactions of nucleosome core particles, Biochemistry, 43, 16, 4773-4780, 2004 |
| [517] | Schiessel, H., The physics of chromatin, J. Phys. Condens. Matter, 15, R699, 2003 |
| [518] | Dixon, J. R.; Selvaraj, S.; Yue, F.; Kim, A.; Li, Y.; Shen, Y.; Hu, M.; Liu, J. S.; Ren, B., Topological domains in mammalian genomes identified by analysis of chromatin interactions, Nature, 485, 7398, 376-380, 2012 |
| [519] | Rao, S. S.; Huntley, M. H.; Durand, N. C.; Stamenova, E. K.; Bochkov, I. D.; Robinson, J. T.; Sanborn, A. L.; Machol, I.; Omer, A. D.; Lander, E. S.; Lieberman Aiden, E., A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping, Cell, 159, 7, 1665-1680, 2014 |
| [520] | Brackley, C. A.; Liebchen, B.; Michieletto, D.; Mouvet, F.; Cook, P. R.; Marenduzzo, D., Ephemeral protein binding to DNA shapes stable nuclear bodies and chromatin domains, Biophys. J., 112, 6, 1085-1093, 2017 |
| [521] | Michieletto, D.; Orlandini, E.; Marenduzzo, D., Polymer model with epigenetic recoloring reveals a pathway for the de novo establishment and 3D organization of chromatin domains, Phys. Rev. X, 6, 4, Article 041047 pp., 2016 |
| [522] | Fudenberg, G.; Imakaev, M.; Lu, C.; Goloborodko, A.; Abdennur, N.; Mirny, L. A., Formation of chromosomal domains by loop extrusion, Cell Rep., 15, 9, 2038-2049, 2016 |
| [523] | Kim, E.; Kerssemakers, J.; Shaltiel, I. A.; Haering, C. H.; Dekker, C., DNA-loop extruding condensin complexes can traverse one another, Nature, 579, 7799, 438-442, 2020 |
| [524] | Ryu, J.-K.; Bouchoux, C.; Liu, H. W.; Kim, E.; Minamino, M.; de Groot, R.; Katan, A. J.; Bonato, A.; Marenduzzo, D.; Michieletto, D.; Uhlmann, F.; Dekker, C., Bridging-induced phase separation induced by cohesin SMC protein complexes, Sci. Adv., 7, 7, eabe5905, 2021 |
| [525] | Nasmyth, K., Disseminating the genome: joining, resolving, separating sister chromatids during mitosis and meiosis, Annu. Rev. Genet., 35, 1, 673-745, 2001 |
| [526] | Alipour, E.; Marko, J. F., Self-organization of domain structures by DNA-loop-extruding enzymes, Nucleic Acids Res., 40, 22, 11202-11212, 2012 |
| [527] | Sanborn, A. L.; Rao, S. S.; Huang, S.-C.; Durand, N. C.; Huntley, M. H.; Jewett, A. I.; Bochkov, I. D.; Chinnappan, D.; Cutkosky, A.; Li, J.; Geeting, K. P.; Gnirke, A.; Melnikov, A.; McKenna, D.; Stamenova, E. K.; Lander, E. S.; Lieberman Aiden, E., Chromatin extrusion explains key features of loop and domain formation in wild-type and engineered genomes, Proc. Natl. Acad. Sci., 112, 47, E6456-E6465, 2015 |
| [528] | Ganji, M.; Shaltiel, I. A.; Bisht, S.; Kim, E.; Kalichava, A.; Haering, C. H.; Dekker, C., Real-time imaging of DNA loop extrusion by condensin, Science, 360, 6384, 2018 |
| [529] | Davidson, I. F.; Bauer, B.; Goetz, D.; Tang, W.; Wutz, G.; Peters, J. M., DNA loop extrusion by human cohesin, Science, 366, 6471, 1338-1345, 2019 |
| [530] | Nomidis, S. K.; Carlon, E.; Gruber, S.; Marko, J. F., DNA tension-modulated translocation and loop extrusion by SMC complexes revealed by molecular dynamics simulations, Nucleic Acids Res., 50, 9, 4974-4987, 2022 |
| [531] | Shaltiel, I. A.; Datta, S.; Lecomte, L.; Hassler, M.; Kschonsak, M.; Bravo, S.; Stober, C.; Ormanns, J.; Eustermann, S.; Haering, C. H., A hold-and-feed mechanism drives directional DNA loop extrusion by condensin, Science, 376, 6597, 1087-1094, 2022 |
| [532] | Bonato, A.; Michieletto, D., Three-dimensional loop extrusion, Biophys. J., 120, 24, 5544-5552, 2021 |
| [533] | Brackley, C. A.; Taylor, S.; Papantonis, A.; Cook, P. R.; Marenduzzo, D., Nonspecific bridging-induced attraction drives clustering of DNA-binding proteins and genome organization, Proc. Natl. Acad. Sci. USA, 110, 38, E3605-11, 2013 |
| [534] | Rao, S. S.P.; Huang, S.-C.; Hilaire, B. G.S.; Engreitz, J. M.; Perez, E. M.; Kieffer-Kwon, K.-R.; Sanborn, A. L.; Johnstone, S. E.; Bascom, G. D.; Bochkov, I. D.; Huang, X.; Shamim, M. S.; Shin, J.; Turner, D.; Ye, Z.; Omer, A. D.; Robinson, J. T.; Schlick, T.; Bernstein, B. E.; Casellas, R.; Lander, E. S.; Aiden, E. L., Cohesin loss eliminates all loop domains, Cell, 171, 2, 305-320.e24, 2017 |
| [535] | Goloborodko, A.; Imakaev, M. V.; Marko, J. F.; Mirny, L. A., Compaction and segregation of sister chromatids via active loop extrusion, eLife, 1-20, 2016 |
| [536] | Orlandini, E.; Marenduzzo, D.; Michieletto, D., Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology, Proc. Natl. Acad. Sci., 116, 17, 8149-8154, 2019 |
| [537] | Gibcus, J. H.; Samejima, K.; Goloborodko, A.; Samejima, I.; Naumova, N.; Nuebler, J.; Kanemaki, M. T.; Xie, L.; Paulson, J. R.; Earnshaw, W. C.; Mirny, L. A.; Dekker, J., A pathway for mitotic chromosome formation, Science, 359, 6376, 2018 |
| [538] | Marko, J. F.; Siggia, E. D., Polymer models of meiotic and mitotic chromosomes, Mol. Biol. Cell, 8, 11, 2217-2231, 1997 |
| [539] | Racko, D.; Benedetti, F.; Goundaroulis, D.; Stasiak, A., Chromatin loop extrusion and chromatin unknotting, Polymers, 10, 10, 1-11, 2018 |
| [540] | Dyson, S.; Segura, J.; Martínez-García, B.; Valdés, A.; Roca, J., Condensin minimizes topoisomerase II-mediated entanglements of DNA in vivo, EMBO J., 40, 1, 1-14, 2021 |
| [541] | Nir, G.; Farabella, I.; Pérez Estrada, C.; Ebeling, C. G.; Beliveau, B. J.; Sasaki, H. M.; Lee, S. H.; Nguyen, S. C.; McCole, R. B.; Chattoraj, S.; Erceg, J.; AlHaj Abed, J.; Martins, N. M.; Nguyen, H. Q.; Hannan, M. A.; Russell, S.; Durand, N. C.; Rao, S. S.P.; Kishi, J. Y.; Soler-Vila, P.; Di Pierro, M.; Onuchic, J. N.; Callahan, S. P.; Schreiner, J. M.; Stuckey, J. A.; Yin, P.; Aiden, E. L.; Marti-Renom, M. A.; Wu, C. T., Walking along chromosomes with super-resolution imaging, contact maps, integrative modeling, PLoS Genetics, 14, 12, Article e1007872 pp., 2018 |
| [542] | Brangwynne, C. P.; Mitchison, T. J.; Hyman, A. A., Active liquid-like behavior of nucleoli determines their size and shape in xenopus laevis oocytes, Proc. Natl. Acad. Sci., 108, 11, 4334-4339, 2011 |
| [543] | Barbieri, M.; Chotalia, M.; Fraser, J.; Lavitas, L.-M.; Dostie, J.; Pombo, A.; Nicodemi, M., Complexity of chromatin folding is captured by the strings and binders switch model, Proc. Natl. Acad. Sci. USA, 109, 40, 16173-16178, 2012 |
| [544] | Jost, D.; Carrivain, P.; Cavalli, G.; Vaillant, C., Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains, Nucleic Acids Res., 42, 15, 9553-9561, 2014 |
| [545] | Michieletto, D.; Colì, D.; Marenduzzo, D.; Orlandini, E., Nonequilibrium theory of epigenomic microphase separation in the cell nucleus, Phys. Rev. Lett., 123, 22, Article 831396 pp., 2019 |
| [546] | Di Stefano, M.; Nützmann, H.-W.; Marti-Renom, M. A.; Jost, D., Polymer modelling unveils the roles of heterochromatin and nucleolar organizing regions in shaping 3D genome organization in Arabidopsis thaliana, Nucleic Acids Res., 49, 4, 1840-1858, 2021 |
| [547] | Uhler, C.; Shivashankar, G. V., Chromosome intermingling: Mechanical hotspots for genome regulation, Trends Cell Biol., 27, 11, 810-819, 2017 |
| [548] | Michieletto, D.; Lusic, M.; Marenduzzo, D.; Orlandini, E., Physical principles of retroviral integration in the human genome, Nature Commun., 10, 1, 575, 2019 |
| [549] | Bintu, B.; Mateo, L. J.; Su, J.-H.; Sinnott-Armstrong, N. A.; Parker, M.; Kinrot, S.; Yamaya, K.; Boettiger, A. N.; Zhuang, X., Super-resolution chromatin tracing reveals domains and cooperative interactions in single cells, Science, 362, 6413, 2018 |
| [550] | Stevens, T. J.; Lando, D.; Basu, S.; Atkinson, L. P.; Cao, Y.; Lee, S. F.; Leeb, M.; Wohlfahrt, K. J.; Boucher, W.; O’Shaughnessy-Kirwan, A.; Cramard, J.; Faure, A. J.; Ralser, M.; Blanco, E.; Morey, L.; Sansó, M.; Palayret, M. G.S.; Lehner, B.; Di Croce, L.; Wutz, A.; Hendrich, B.; Klenerman, D.; Laue, E. D., 3D structures of individual mammalian genomes studied by single-cell Hi-C, Nature, 544, 7648, 59-64, 2017 |
| [551] | Siebert, J. T.; Kivel, A. N.; Atkinson, L. P.; Stevens, T. J.; Laue, E. D.; Virnau, P., Are there knots in chromosomes?, Polymers, 9, 8, 1-10, 2017 |
| [552] | Virnau, P.; Mirny, L. A.; Kardar, M., Intricate knots in proteins: Function and evolution, PLoS Comput. Biol., 2, 9, Article e122 pp., 2006 |
| [553] | Ko, K.-T.; Hu, I.-C.; Huang, K.-F.; Lyu, P.-C.; Hsu, S.-T. D., Untying a knotted SPOUT RNA methyltransferase by circular permutation results in a domain-swapped dimer, Structure, 27, 8, 1224-1233.e4, 2019 |
| [554] | Potestio, R.; Micheletti, C.; Orland, H., Knotted vs. Unknotted proteins: Evidence of knot-promoting loops, Plos Comput. Biol., 6, 7, Article e1000864 pp., 2010 |
| [555] | Wüst, T.; Reith, D.; Virnau, P., Sequence determines degree of knottedness in a coarse-grained protein model, Phys. Rev. Lett., 114, Article 028102 pp., 2015 |
| [556] | Lua, R. C.; Grosberg, A. Y., Statistics of knots, geometry of conformations, evolution of proteins, PLoS Comput. Biol., 2, 5, 2006 |
| [557] | Mallam, A. L.; Jackson, S. E., Folding studies on a knotted protein, J. Mol. Biol., 346, 5, 1409-1421, 2005 |
| [558] | Wang, I.; Chen, S.-Y.; Hsu, S.-T. D., Folding analysis of the most complex Stevedore’s protein knot, Sci. Rep., 6, 1, 31514, 2016 |
| [559] | Jackson, S., Why are there knots in proteins?, Contemp. Math., 746, 129-153, 2020 · Zbl 1444.57004 |
| [560] | Wang, I.; Chen, S.-Y.; Hsu, S.-T. D., Unraveling the folding mechanism of the smallest knotted protein, MJ0366, J. Phys. Chem. B, 119, 12, 4359-4370, 2015 |
| [561] | Lou, S.-C.; Wetzel, S.; Zhang, H.; Crone, E. W.; Lee, Y.-T.; Jackson, S. E.; Hsu, S.-T. D., The knotted protein UCH-L1 exhibits partially unfolded forms under native conditions that share common structural features with its kinetic folding intermediates, J. Mol. Biol., 428, 11, 2507-2520, 2016 |
| [562] | Hsu, S.-T. D., Protein knotting through concatenation significantly reduces folding stability, Sci. Rep., 6, 1, 39357, 2016 |
| [563] | Zhang, H.; Jackson, S. E., Characterization of the folding of a \(5{}_2\)-knotted protein using engineered single-tryptophan variants, Biophys. J., 111, 12, 2587-2599, 2016 |
| [564] | Mallam, A. L.; Rogers, J. M.; Jackson, S. E., Experimental detection of knotted conformations in denatured proteins, Proc. Natl. Acad. Sci., 107, 18, 8189-8194, 2010 |
| [565] | Burban, D. J.; Haglund, E.; Capraro, D. T.; Jennings, P. A., Heterogeneous side chain conformation highlights a network of interactions implicated in hysteresis of the knotted protein, minimal tied trefoil, J. Phys.: Condens. Matter, 27, 35, Article 354108 pp., 2015 |
| [566] | Capraro, D. T.; Burban, D. J.; Jennings, P. A., Unraveling allostery in a knotted minimal methyltransferase by nmr spectroscopy, J. Mol. Biol., 432, 9, 3018-3032, 2020 |
| [567] | Lee, Y.-T. C.; Chang, C.-Y.; Chen, S.-Y.; Pan, Y.-R.; Ho, M.-R.; Hsu, S.-T. D., Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome, Sci. Rep., 7, 1, 45174, 2017 |
| [568] | Mallam, A. L.; Jackson, S. E., Probing nature’s knots: The folding pathway of a knotted homodimeric protein, J. Mol. Biol., 359, 5, 1420-1436, 2006 |
| [569] | King, N. P.; Jacobitz, A. W.; Sawaya, M. R.; Goldschmidt, L.; Yeates, T. O., Structure and folding of a designed knotted protein, Proc. Natl. Acad. Sci., 107, 48, 20732-20737, 2010 |
| [570] | Wang, L.-W.; Liu, Y.-N.; Lyu, P.-C.; Jackson, S. E.; Hsu, S.-T. D., Comparative analysis of the folding dynamics and kinetics of an engineered knotted protein and its variants derived from HP0242 ofhelicobacter pylori, J. Phys.: Condens. Matter, 27, 35, Article 354106 pp., 2015 |
| [571] | Mallam, A. L.; Onuoha, S. C.; Grossmann, J. G.; Jackson, S. E., Knotted fusion proteins reveal unexpected possibilities in protein folding, Mol. Cell, 30, 5, 642-648, 2008 |
| [572] | Chuang, Y.-C.; Hu, I.-C.; Lyu, P.-C.; Hsu, S.-T. D., Untying a protein knot by circular permutation, J. Mol. Biol., 431, 4, 857-863, 2019 |
| [573] | Žoldák, G.; Rief, M., Force as a single molecule probe of multidimensional protein energy landscapes, Curr. Opin. Struct. Biol., 23, 1, 48-57, 2013 |
| [574] | Schönfelder, J.; Alonso-Caballero, A.; De Sancho, D.; Perez-Jimenez, R., The life of proteins under mechanical force, Chem. Soc. Rev., 47, 3558-3573, 2018 |
| [575] | Bornschlögl, T.; Anstrom, D. M.; Mey, E.; Dzubiella, J.; Rief, M.; Forest, K. T., Tightening the knot in phytochrome by single-molecule atomic force microscopy, Biophys. J., 96, 4, 1508-1514, 2009 |
| [576] | He, C.; Lamour, G.; Xiao, A.; Gsponer, J.; Li, H., Mechanically tightening a protein slipknot into a trefoil knot, J. Am. Chem. Soc., 136, 34, 11946-11955, 2014 |
| [577] | Rivera, M.; Hao, Y.; Maillard, R. A.; Baez, M., Mechanical unfolding of a knotted protein unveils the kinetic and thermodynamic consequences of threading a polypeptide chain, Sci. Rep., 10, 1, 9562, 2020 |
| [578] | Wang, H.; Li, H., Mechanically tightening, untying and retying a protein trefoil knot by single-molecule force spectroscopy, Chem. Sci., 11, 12512-12521, 2020 |
| [579] | Mallam, A. L.; Jackson, S. E., Knot formation in newly translated proteins is spontaneous and accelerated by chaperonins, Nat. Chem. Biol., 8, 2, 147-153, 2012 |
| [580] | He, C.; Genchev, G. Z.; Lu, H.; Li, H., Mechanically untying a protein slipknot: Multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations, J. Am. Chem. Soc., 134, 25, 10428-10435, 2012 |
| [581] | He, C.; Li, S.; Gao, X.; Xiao, A.; Hu, C.; Hu, X.; Hu, X.; Li, H., Direct observation of the fast and robust folding of a slipknotted protein by optical tweezers, Nanoscale, 11, 3945-3951, 2019 |
| [582] | Wang, H.; Gao, X.; Hu, X.; Hu, X.; Hu, C.; Li, H., Mechanical unfolding and folding of a complex slipknot protein probed by using optical tweezers, Biochemistry, 58, 47, 4751-4760, 2019 |
| [583] | Soler, M. A.; Nunes, A.; Faísca, P. F.N., Effects of knot type in the folding of topologically complex lattice proteins, J. Chem. Phys., 141, 2, Article 025101 pp., 2014 |
| [584] | Faísca, P. F., Knotted proteins: A tangled tale of structural biology, Comput. Struct. Biotechnol. J., 13, 459-468, 2015 |
| [585] | Wallin, S.; Zeldovich, K. B.; Shakhnovich, E. I., The folding mechanics of a knotted protein, J. Mol. Biol., 368, 3, 884-893, 2007 |
| [586] | Škrbić, T.; Micheletti, C.; Faccioli, P., The role of non-native interactions in the folding of knotted proteins, PLoS Comput. Biol., 8, 6, Article e1002504 pp., 2012 |
| [587] | Noel, J. K.; Sulkowska, J. I.; Onuchic, J. N., Slipknotting upon native-like loop formation in a trefoil knot protein, Proc. Natl. Acad. Sci., 107, 35, 15403-15408, 2010 |
| [588] | Dabrowski-Tumanski, P.; Jarmolinska, A. I.; Sulkowska, J. I., Prediction of the optimal set of contacts to fold the smallest knotted protein, J. Phys.: Condens. Matter, 27, 35, Article 354109 pp., 2015 |
| [589] | Soler, M. A.; Rey, A.; Faísca, P. F.N., Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding, Phys. Chem. Chem. Phys., 18, 26391-26403, 2016 |
| [590] | Especial, J. N.C.; Faísca, P. F.N., Effects of sequence-dependent non-native interactions in equilibrium and kinetic folding properties of knotted proteins, J. Chem. Phys., 159, 6, Article 065101 pp., 2023 |
| [591] | Sulkowska, J. I.; Sulkowski, P.; Szymczak, P.; Cieplak, M., Stabilizing effect of knots on proteins, Proc. Natl. Acad. Sci. U. S. A., 105, 50, 19714-19719, 2008 |
| [592] | a Beccara, S.; Škrbić, T.; Covino, R.; Micheletti, C.; Faccioli, P., Folding pathways of a knotted protein with a realistic atomistic force field, PLoS Comput. Biol., 9, 3, Article e1003002 pp., 2013 |
| [593] | Najafi, S.; Potestio, R., Folding of small knotted proteins: Insights from a mean field coarse-grained model, J. Chem. Phys., 143, 24, Article 243121 pp., 2015 |
| [594] | Noel, J. K.; Onuchic, J.; Sulkowska, J. I., Knotting a protein in explicit solvent, 4, 21, 3570-3573, 2013 |
| [595] | Covino, R.; Škrbić, T.; a Beccara, S.; Faccioli, P.; Micheletti, C., The role of non-native interactions in the folding of knotted proteins: insights from molecular dynamics simulations, Biomolecules, 4, 1, 1-19, 2014 |
| [596] | Niewieczerzał, S.; Sulkowska, J. I., Supercoiling in a protein increases its stability, Phys. Rev. Lett., 123, Article 138102 pp., 2019 |
| [597] | Dabrowski-Tumanski, P.; Jarmolinska, A. I.; Niemyska, W.; Rawdon, E. J.; Millett, K. C.; Sulkowska, J. I., Linkprot: A database collecting information about biological links, Nucleic Acids Res., 45, D243-D249, 2017 |
| [598] | Lim, N. C.H.; Jackson, S. E., Mechanistic insights into the folding of knotted proteins in vitro and in vivo, J. Mol. Biol., 427, 2, 248-258, 2015 |
| [599] | Stan, G.; Lorimer, G. H.; Thirumalai, D., Friends in need: How chaperonins recognize and remodel proteins that require folding assistance, Front. Mol. Biosci., 9, 2022 |
| [600] | Niewieczerzal, S.; Sulkowska, J. I., Knotting and unknotting proteins in the chaperonin cage: Effects of the excluded volume, PLoS One, 12, 5, 1-23, 2017 |
| [601] | Cassaignau, A. M.; Cabrita, L. D.; Christodoulou, J., How does the ribosome fold the proteome?, Annu. Rev. Biochem., 89, 1, 389-415, 2020 |
| [602] | Chwastyk, M.; Cieplak, M., Cotranslational folding of deeply knotted proteins, J. Phys.: Condens. Matter, 27, 35, Article 354105 pp., 2015 |
| [603] | Bui, P. T.; Hoang, T. X., Protein escape at the ribosomal exit tunnel: Effect of the tunnel shape, J. Chem. Phys., 153, 4, Article 045105 pp., 2020 |
| [604] | Chwastyk, M.; Cieplak, M., Nascent folding of proteins across the three domains of life, Front. Mol. Biosci., 8, 508, 2021 |
| [605] | Dabrowski-Tumanski, P.; Piejko, M.; Niewieczerzal, S.; Stasiak, A.; Sulkowska, J. I., Protein knotting by active threading of nascent polypeptide chain exiting from the ribosome exit channel, J. Phys. Chem. B, 122, 49, 11616-11625, 2018 |
| [606] | Sriramoju, M. K.; Chen, Y.; Hsu, S.-T. D., Protein knots provide mechano-resilience to an AAA+ protease-mediated proteolysis with profound ATP energy expenses, Biochim. Biophys. Acta (BBA)-Proteins Proteomics, 1868, 2, Article 140330 pp., 2020 |
| [607] | Tripathi, P.; Mehrafrooz, B.; Aksimentiev, A.; Jackson, S. E.; Gruebele, M.; Wanunu, M., A marcus-Type Inverted Region in the translocation kinetics of a knotted protein, J. Phys. Chem. Lett., 14, 47, 10719-10726, 2023 |
| [608] | Ohta, S.; Alam, M. T.; Arakawa, H.; Ikai, A., Origin of mechanical strength of bovine carbonic anhydrase studied by molecular dynamics simulation, Biophys. J., 87, 6, 4007-4020, 2004 |
| [609] | Alam, M. T.; Yamada, T.; Carlsson, U.; Ikai, A., The importance of being knotted: effects of the C-terminal knot structure on enzymatic and mechanical properties of bovine carbonic anhydrase II, FEBS Lett., 519, 1-3, 35-40, 2002 |
| [610] | Dzubiella, J., Sequence-specific size, structure, stability of tight protein knots, Biophys. J., 96, 831-839, 2009 |
| [611] | Sulkowska, J. I.; Sułkowski, P.; Szymczak, P.; Cieplak, M., Untying knots in proteins, J. Am. Chem. Soc., 132, 40, 13954-13956, 2010 |
| [612] | Sułkowska, J. I.; Sułkowski, P.; Szymczak, P.; Cieplak, M., Tightening of knots in proteins, Physical review letters, 100, 5, 058106, 2008 |
| [613] | Dzubiella, J., Tightening and untying the knot in human carbonic anhydrase III, J. Phys. Chem. Lett., 4, 11, 1829-1833, 2013 |
| [614] | Xu, Y.; Li, S.; Yan, Z.; Luo, Z.; Ren, H.; Ge, B.; Huang, F.; Yue, T., Stabilizing effect of inherent knots on proteins revealed by molecular dynamics simulations, Biophys. J., 115, 9, 1681-1689, 2018 |
| [615] | Sułkowska, J. I.; Sułkowski, P.; Onuchic, J. N., Jamming proteins with slipknots and their free energy landscape, Physical review letters, 103, 26, 268103, 2009 |
| [616] | Sikora, M.; Sulkowska, J. I.; Cieplak, M., Mechanical strength of 17 134 model proteins and cysteine slipknots, PLoS Comput. Biol., 5, 10, Article e1000547 pp., 2009 |
| [617] | Zhao, Y. I.; Chwastyk, M.; Cieplak, M., Structural entanglements in protein complexes, J. Chem. Phys., 146, 22, Article 225102 pp., 2017 |
| [618] | Huang, L.; Makarov, D. E., Translocation of a knotted polypeptide through a pore, J. Chem. Phys., 129, Article 121107 pp., 2008 |
| [619] | Szymczak, P., Tight knots in proteins: can they block the mitochondrial pores?, Biochem. Soc. Trans., 41, 2, 620-624, 2013 |
| [620] | Szymczak, P., Translocation of knotted proteins through a pore, Eur. Phys. J. Spec. Top., 223, 1805-1821, 2014 |
| [621] | Szymczak, P., Periodic forces trigger knot untying during translocation of knotted proteins, Sci. Rep., 6, 1, 21702, 2016 |
| [622] | Christian, T.; Sakaguchi, R.; Perlinska, A. P.; Lahoud, G.; Ito, T.; Taylor, E. A.; Yokoyama, S.; Sulkowska, J. I.; Hou, Y.-M., Methyl transfer by substrate signaling from a knotted protein fold, Nat. Struct. Mol. Biol., 23, 10, 941-948, 2016 |
| [623] | Perlinska, A. P.; Stasiulewicz, A.; Nawrocka, E. K.; Kazimierczuk, K.; Setny, P.; Sulkowska, J. I., Restriction of S-adenosylmethionine conformational freedom by knotted protein binding sites, PLoS Comput. Biol., 16, 5, Article e1007904 pp., 2020 |
| [624] | Dabrowski-Tumanski, P.; Sulkowska, J. I., Topological knots and links in proteins, Proc. Natl. Acad. Sci., 114, 13, 3415-3420, 2017 |
| [625] | Soler, M. A.; Faísca, P. F., Effects of knots on protein folding properties, PLoS One, 8, 9, Article e74755 pp., 2013 |
| [626] | Sulkowska, J. I.; Cieplak, M., Mechanical stretching of proteins - A theoretical survey of the protein data bank, J. Phys.: Condens. Matt., 19, 28, Article 283201 pp., 2007 |
| [627] | Nureki, O.; Shirouzu, M.; Hashimoto, K.; Ishitani, R.; Terada, T.; Tamakoshi, M.; Oshima, T.; Chijimatsu, M.; Takio, K.; Vassylyev, D. G.; Shibata, T.; Inoue, Y.; Kuramitsu, S.; Yokoyama, S., An enzyme with a deep trefoil knot for the active-site architecture, Acta Crystallogr. D, 58, 7, 1129-1137, 2002 |
| [628] | Hori, H., Transfer RNA methyltransferases with a SpoU-TrmD (SPOUT) fold and their modified nucleosides in tRNA, Biomolecules, 7, 1, 23, 2017 |
| [629] | Tkaczuk, K. L.; Dunin-Horkawicz, S.; Purta, E.; Bujnicki, J. M., Structural and evolutionary bioinformatics of the SPOUT superfamily of methyltransferases, BMC Bioinform., 8, 1, 1-31, 2007 |
| [630] | White, T. A.; Kell, D. B., Comparative genomic assessment of novel broad-spectrum targets for antibacterial drugs, Comp. Funct. Genomics, 5, 4, 304-327, 2004 |
| [631] | Masuda, I.; Matsubara, R.; Christian, T.; Rojas, E. R.; Yadavalli, S. S.; Zhang, L.; Goulian, M.; Foster, L. J.; Huang, K. C.; Hou, Y.-M., tRNA methylation is a global determinant of bacterial multi-drug resistance, Cell Syst., 8, 4, 302-314, 2019 |
| [632] | Ahn, H. J.; Kim, H.-W.; Yoon, H.-J.; Lee, B. I.; Suh, S. W.; Yang, J. K., Crystal structure of tRNA (m1G37) methyltransferase: insights into tRNA recognition, EMBO J., 22, 11, 2593-2603, 2003 |
| [633] | Lahoud, G.; Goto-Ito, S.; Yoshida, K.-i.; Ito, T.; Yokoyama, S.; Hou, Y.-M., Differentiating analogous tRNA methyltransferases by fragments of the methyl donor, RNA, 17, 7, 1236-1246, 2011 |
| [634] | Craik, D. J.; Fairlie, D. P.; Liras, S.; Price, D., The future of peptide-based drugs, Chem. Biol. Drug Des., 81, 1, 136-147, 2013 |
| [635] | Wang, C. K.; Craik, D. J., Designing macrocyclic disulfide-rich peptides for biotechnological applications, Nat. Chem. Biol., 14, 5, 417-427, 2018 |
| [636] | Arnison, P. G.; Bibb, M. J.; Bierbaum, G.; Bowers, A. A.; Bugni, T. S.; Bulaj, G.; Camarero, J. A.; Campopiano, D. J.; Challis, G. L.; Clardy, J.; Cotter, P. D.; Craik, D. J.; Dawson, M.; Dittmann, E.; Donadio, S.; Dorrestein, P. C.; Entian, K.-D.; Fischbach, M. A.; Garavelli, J. S.; Göransson, U.; Gruber, C. W.; Haft, D. H.; Hemscheidt, T. K.; Hertweck, C.; Hill, C.; Horswill, A. R.; Jaspars, M.; Kelly, W. L.; Klinman, J. P.; Kuipers, O. P.; Link, A. J.; Liu, W.; Marahiel, M. A.; Mitchell, D. A.; Moll, G. N.; Moore, B. S.; Müller, R.; Nair, S. K.; Nes, I. F.; Norris, G. E.; Olivera, B. M.; Onaka, H.; Patchett, M. L.; Piel, J.; Reaney, M. J.T.; Rebuffat, S.; Ross, R. P.; Sahl, H.-G.; Schmidt, E. W.; Selsted, M. E.; Severinov, K.; Shen, B.; Sivonen, K.; Smith, L.; Stein, T.; Süssmuth, R. D.; Tagg, J. R.; Tang, G.-L.; Truman, r. W.; Vederas, J. C.; Walsh, C. T.; Walton, J. D.; Wenzel, S. C.; Willey, J. M.; van der Donk, W. A., Ribosomally synthesized and post-translationally modified peptide natural products: overview and recommendations for a universal nomenclature, Nat. Prod. Rep., 30, 108-160, 2013 |
| [637] | Wu, X.; Huang, Y.-H.; Kaas, Q.; Craik, D. J., Cyclisation of disulfide-rich conotoxins in drug design applications, Eur. J. Org. Chem., 2016, 21, 3462-3472, 2016 |
| [638] | Benfield, A. H.; Defaus, S.; Lawrence, N.; Chaousis, S.; Condon, N.; Cheneval, O.; Huang, Y.-H.; Chan, L. Y.; Andreu, D.; Craik, D. J.; Henriques, S. T., Cyclic gomesin, a stable redesigned spider peptide able to enter cancer cells, Biochim. Biophys. Acta (BBA) - Biomembranes, 1863, 1, Article 183480 pp., 2021 |
| [639] | Craik, D. J.; Du, J., Cyclotides as drug design scaffolds, Curr. Opin. Chem. Biol., 38, 8-16, 2017 |
| [640] | Shim, Y. Y.; Song, Z.; Jadhav, P. D.; Reaney, M. J., Orbitides from flaxseed (Linum usitatissimum L.): A comprehensive review, Trends Food Sci. Technol., 93, 197-211, 2019 |
| [641] | Perez, R. H.; Zendo, T.; Sonomoto, K., Circular and leaderless bacteriocins: Biosynthesis, mode of action, applications, prospects, Front. Microbiol., 9, 2085, 2018 |
| [642] | de Veer, S. J.; White, r. M.; Craik, D. J., Sunflower trypsin inhibitor-1 (SFTI-1): Sowing seeds in the fields of chemistry and biology, Angew. Chem. Int. Ed., 60, 15, 8050-8071, 2021 |
| [643] | Clark, R. J.; Jensen, J.; Nevin, S. T.; Callaghan, B. P.; Adams, D. J.; Craik, D. J., The engineering of an orally active conotoxin for the treatment of neuropathic pain, Angew. Chem. Int. Ed., 49, 37, 6545-6548, 2010 |
| [644] | Conibear, A. C.; Craik, D. J., The chemistry and biology of theta defensins, Angew. Chem. Int. Ed., 53, 40, 10612-10623, 2014 |
| [645] | Craik, D. J.; Daly, N. L.; Bond, T.; Waine, C., Plant cyclotides: A unique family of cyclic and knotted proteins that defines the cyclic cystine knot structural motif1 1edited by P. E. Wright, J. Mol. Biol., 294, 5, 1327-1336, 1999 |
| [646] | Wang, C. K.; Gruber, C. W.; Cemazar, M.; Siatskas, C.; Tagore, P.; Payne, N.; Sun, G.; Wang, S.; Bernard, C. C.; Craik, D. J., Molecular grafting onto a stable framework yields novel cyclic peptides for the treatment of multiple sclerosis, ACS Chem. Biol., 9, 1, 156-163, 2014 |
| [647] | Haglund, E.; Sułkowska, J. I.; He, Z.; Feng, G.-S.; Jennings, P. A.; Onuchic, J. N., The unique cysteine knot regulates the pleotropic hormone leptin, PLoS One, 7, 9, 1-13, 2012 |
| [648] | Haglund, E.; Sulkowska, J. I.; Noel, J. K.; Lammert, H.; Onuchic, J. N.; Jennings, P. A., Pierced lasso bundles are a new class of knot-like motifs, PLoS Comput. Biol., 10, 6, 1-11, 2014 |
| [649] | Reith, D.; Cifra, P.; Stasiak, A.; Virnau, P., Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots, Nucleic Acids Res., 40, 11, 5129-5137, 2012 |
| [650] | Haglund, E., Engineering covalent loops in proteins can serve as an on/off switch to regulate threaded topologies, J. Phys.: Condens. Matter, 27, 35, Article 354107 pp., 2015 |
| [651] | Haglund, E.; Pilko, A.; Wollman, R.; Jennings, P. A.; Onuchic, J., Pierced lasso topology controls function in leptin, J. Phys. Chem. B, 121, 4, 706-718, 2017 |
| [652] | Simien, J. M.; Haglund, E., Topological twists in nature, Trends Biochem. Sci., 46, 6, 461-471, 2021 |
| [653] | Dabrowski-Tumanski, P.; Niemyska, W.; Pasznik, P.; Sulkowska, J. I., LassoProt: server to analyze biopolymers with lassos, Nucleic Acids Res., 44, W1, W383-W389, 2016 |
| [654] | Silva, F. B.d.; Lewandowska, I.; Kluza, A.; Niewieczerzal, S.; Augustyniak, R.; Sulkowska, J. I., First crystal structure of double knotted protein trmd-tm1570 - inside from degradation perspective, 2023 |
| [655] | Brems, M. A.; Runkel, R.; Yeates, T. O.; Virnau, P., AlphaFold predicts the most complex protein knot and composite protein knots, Prot. Sci., 31, 8, Article e4380 pp., 2022 |
| [656] | Perlinska, A. P.; Niemyska, W. H.; Gren, B. A.; Bukowicki, M.; Nowakowski, S.; Rubach, P.; Sulkowska, J. I., AlphaFold predicts novel human proteins with knots, Prot. Sci., 32, 5, Article e4631 pp., 2023 |
| [657] | Hsu, M.-F.; Sriramoju, M. K.; Lai, C.-H.; Chen, Y.-R.; Huang, J.-S.; Ko, T.-P.; Huang, K.-F.; Hsu, S.-T. D., Structure, dynamics, and stability of the smallest and most complex 71 protein knot, Journal of Biological Chemistry, 300, 1, 2024 |
| [658] | Doyle, L. A.; Takushi, B.; Kibler, R. D.; Milles, L. F.; Orozco, C. T.; Jones, J. D.; Jackson, S. E.; Stoddard, B. L.; Bradley, P., De novo design of knotted tandem repeat proteins, Nature Commun., 14, 1, 6746, 2023 |
| [659] | Dabrowski-Tumanski, P.; Stasiak, A., Alphafold blindness to topological barriers affects its ability to correctly predict proteins’ topology, Molecules, 28, 22, 2023 |
| [660] | Leigh, D. A.; Danon, J. J.; Fielden, S. D.P.; Lemonnier, J.-F.; Whitehead, G. F.S.; Woltering, S. L., A molecular endless \((7{}_{\text{4}} )\) knot, Nat. Chem., 13, 2, 117-122, 2021 |
| [661] | Ashbridge, Z.; Kreidt, E.; Pirvu, L.; Schaufelberger, F.; Stenlid, J. H.; Abild-Pedersen, F.; Leigh, D. A., Vernier template synthesis of molecular knots, Science, 375, 6584, 1035-1041, 2022 |
| [662] | Polles, G.; Marenduzzo, D.; Orlandini, E.; Micheletti, C., Self-assembling knots of controlled topology by designing the geometry of patchy templates, Nature Commun., 6, 1, 6423, 2015 |
| [663] | Marenda, M.; Orlandini, E.; Micheletti, C., Discovering privileged topologies of molecular knots with self-assembling models, Nature Commun., 9, 1, 3051, 2018 |
| [664] | Coluzza, I.; van Oostrum, P. D.J.; Capone, B.; Reimhult, E.; Dellago, C., Design and folding of colloidal patchy polymers, Soft Matter, 9, 938-944, 2013 |
| [665] | Coluzza, I.; van Oostrum, P. D.J.; Capone, B.; Reimhult, E.; Dellago, C., Sequence controlled self-knotting colloidal patchy polymers, Phys. Rev. Lett., 110, Article 075501 pp., 2013 |
| [666] | Cardelli, C.; Bianco, V.; Rovigatti, L.; Nerattini, F.; Tubiana, L.; Dellago, C.; Coluzza, I., The role of directional interactions in the designability of generalized heteropolymers, Sci. Rep., 7, 1, 4986, 2017 |
| [667] | Kar, P.; Gopal, S. M.; Cheng, Y.-M.; Predeus, A.; Feig, M., PRIMO: A transferable coarse-grained force field for proteins, J. Chem. Theory Comput., 9, 8, 3769-3788, 2013 |
| [668] | Liwo, A.; Baranowski, M.; Czaplewski, C.; Gołaś, E.; He, Y.; Jagieła, D.; Krupa, P.; Maciejczyk, M.; Makowski, M.; Mozolewska, M. A.; Niadzvedtski, A.; Ołdziej, S.; Scheraga, H. A.; Sieradzan, A. K.; Ślusarz, R.; Wirecki, T.; Yin, Y.; Zaborowski, B., A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions, J. Mol. Model., 20, 8, 1-15, 2014 |
| [669] | Noel, J. K.; Levi, M.; Raghunathan, M.; Lammert, H.; Hayes, R. L.; Onuchic, J. N.; Whitford, P. C., SMOG 2: A versatile software package for generating structure-based models, PLoS Comput. Biol., 12, 3, Article e1004794 pp., 2016 |
| [670] | Monticelli, L.; Kandasamy, S. K.; Periole, X.; Larson, R. G.; Tieleman, D. P.; Marrink, S.-J., The MARTINI coarse-grained force field: Extension to proteins, J. Chem. Theory Comput., 4, 5, 819-834, 2008 |
| [671] | Pasi, M.; Lavery, R.; Ceres, N., Palace: A coarse-grain protein model for studying mechanical properties, J. Chem. Theory Comput., 9, 1, 785-793, 2013 |
| [672] | Kolinski, A., Protein modeling and structure prediction with a reduced representation, Acta Biochim. Pol., 51, 2, 349-371, 2004 |
| [673] | Coles, H. J.; Pivnenko, M. N., Liquid crystal ‘blue phases’ with a wide temperature range, Nature, 436, 997-1000, 2005 |
| [674] | Wright, D.; Mermin, N., Crystalline liquids: the blue phases, Rev. Modern Phys., 61, 385, 1989 |
| [675] | Alexander, G. P.; Yeomans, J. M., Stabilizing the blue phases, Phys. Rev. E, 74, Article 061706 pp., 2006 |
| [676] | Yang, D. K.; Crooker, P. P., Chiral-racemic phase diagrams of blue-phase liquid crystals, Phys. Rev. A, 35, 4419, 1987 |
| [677] | Thoen, J., Adiabatic scanning calorimetric results for the blue phases of cholesteryl nonanoate, Phys. Rev. A, 37, 1754, 1988 |
| [678] | Castles, F.; Morris, S.; Coles, H., Flexoelectro-optic properties of chiral nematic liquid crystals in the uniform standing helix configuration, Phys. Rev. E, 80, Article 031709 pp., 2009 |
| [679] | Kikuchi, H.; Yokota, M.; Hisakado, Y.; Yang, H.; Kajiyama, T., Polymer-stabilized liquid crystal blue phases, Nature Mater., 1, 64, 2002 |
| [680] | Huang, Y.; Chen, H.; Tan, G.; Tobata, H.; Yamamoto, S.-I.; Okabe, E.; Lan, Y.-F.; Tsai, C.-Y.; Wu, S.-T., Optimized blue-phase liquid crystal for field-sequential-color displays, Opt. Mater. Express, 7, 641, 2017 |
| [681] | Guo, D.-Y.; Chen, C.-W.; Li, C.-C.; Jau, H.-C.; Lin, K.-H.; Feng, T.-M.; Wang, C.-T.; Bunning, T. J.; Khoo, I. C.; Lin, T.-H., Reconfiguration of three-dimensional liquid-crystalline photonic crystals by electrostriction, Nature Mater., 19, 94, 2020 |
| [682] | Ravnik, M.; Alexander, G. P.; Yeomans, J. M.; Žumer, S., Three-dimensional colloidal crystals in liquid crystalline blue phases, Proc. Natl. Acad. Sci., 108, 5188, 2011 |
| [683] | Pires, D.; Fleury, J.-B.; Galerne, Y., Colloid particles in the interaction field of a disclination line in a nematic phase, Phys. Rev. Lett., 98, Article 247801 pp., 2007 |
| [684] | Škarabot, M.; Ravnik, M.; Žumer, S.; Tkalec, U.; Poberaj, I.; Babič, D.; Muševič, I., Hierarchical self-assembly of nematic colloidal superstructures, Phys. Rev. E, 77, Article 061706 pp., 2008 |
| [685] | Ravnik, M.; Alexander, G. P.; Yeomans, J. M.; Žumer, S., Mesoscopic modelling of colloids in chiral nematics, Faraday Discuss., 144, 159, 2009 |
| [686] | Ravnik, M.; Fukuda, J.; Yeomans, J. M.; Žumer, S., Confining blue phase colloids to thin layers, Soft Matter, 7, 10144, 2011 |
| [687] | Fukuda, J.; Žumer, S., Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal, Nat. Commun., 2, 1, 1-5, 2011 |
| [688] | Lavrič, M.; Cordoyiannis, G.; Tzitzios, V.; Lelidis, I.; Kralj, S.; Nounesis, G.; Žumer, S.; Daniel, M.; Kutnjak, Z., Blue phase stabilization by CoPt-decorated reduced-graphene oxide nanosheets dispersed in a chiral liquid crystal, J. Appl. Phys., 127, Article 095101 pp., 2020 |
| [689] | Muhlbauer, S.; Binz, B.; Jonietz, F.; Pfleiderer, C.; Rosch, A.; Neubauer, A.; Georgii, R.; Boni, P., Skyrmion lattice in a chiral magnet, Science, 323, 915, 2009 |
| [690] | Wang, S.; Ravnik, M.; Žumer, S., Surface-patterning generated half-skyrmion lattices in cholesteric blue phase thin films, Liq. Cryst., 45, 2329, 2018 |
| [691] | Ackerman, P. J.; Trivedi, R. P.; Senyuk, B.; van de Lagemaat, J.; Smalyukh, I. I., Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics, Phys. Rev. E, 90, 1, Article 012505 pp., 2014 |
| [692] | Slussarenko, S.; Murauski, A.; Du, T.; Chigrinov, V.; Marrucci, L.; Santamato, E., Tunable liquid crystal q-plates with arbitrary topological charge, Opt. Express, 19, 4085, 2011 |
| [693] | Loussert, C.; Delabre, U.; Brasselet, E., Manipulating the orbital angular momentum of light at the micron scale with nematic disclinations in a liquid crystal film, Phys. Rev. Lett., 111, Article 037802 pp., 2013 |
| [694] | Humar, M.; Muševič, I., 3D microlasers from self-assembled cholesteric liquid-crystal microdroplets, Opt. Express, 18, 26995, 2010 |
| [695] | Poy, G.; Hess, A. J.; Seracuse, A. J.; Paul, M.; Žumer, S.; Smalyukh, I. I., Interaction and co-assembly of optical and topological solitons, Nature Photon., 16, 454, 2022 |
| [696] | Everts, J. C.; Ravnik, M., Ionically charged topological defects in nematic fluids, Phys. Rev. X, 11, 1, Article 011054 pp., 2021 |
| [697] | Giomi, L.; Kos, Ž.; Ravnik, M.; Sengupta, A., Cross-talk between topological defects in different fields revealed by nematic microfluidics, Proc. Natl. Acad. Sci. USA, 114, E5771, 2017 |
| [698] | Doane, J. W.; Vaz, N. A.; Wu, B. G.; Žumer, S., Field controlled light scattering from nematic microdroplets, Appl. Phys. Lett., 48, 269-271, 1986 |
| [699] | Lavrentovich, O. D., Topological defects in dispersed words and worlds around liquid crystals, or liquid crystal drops, Liq. Cryst., 24, 1, 117-126, 1998 |
| [700] | Martínez-González, J. A.; Zhou, Y.; Rahimi, M.; Bukusoglu, E.; Abbott, N. L.; de Pablo, J. J., Blue-phase liquid crystal droplets, Proc. Natl. Acad. Sci., 112, 13195, 2015 |
| [701] | Lopez-Leon, T.; Fernandez-Nieves, A., Drops and shells of liquid crystal, Colloid Polym. Sci., 289, 4, 345-359, 2011 |
| [702] | Mirantsev, L. V.; de Oliveira, E. J.L.; de Oliveira, I. N.; Lyra, M. L., Defect structures in nematic liquid crystal shells of different shapes, Liquid Cryst. Rev., 4, 1, 35-58, 2016 |
| [703] | Urbanski, M.; Reyes, C. G.; Noh, J.; Sharma, A.; Geng, Y.; Jampani, V. S.R.; Lagerwall, J. P.F., Liquid crystals in micron-scale droplets, shells and fibers, J. Phys.: Condens. Matter, 29, 13, Article 133003 pp., 2017 |
| [704] | Lubensky, T. C.; Prost, J., Orientational order and vesicle shape, J. Phys. II, 2, 3, 371-382, 1992 |
| [705] | Nelson, D. R., Toward a tetravalent chemistry of colloids, Nano Lett., 2, 10, 1125-1129, 2002 |
| [706] | Yi, G. R.; Pine, D. J.; Sacanna, S., Recent progress on patchy colloids and their self-assembly, J. Phys.: Condens. Matter, 25, 19, 2013 |
| [707] | Kim, J. G.; Park, S.-Y., Photonic spring-like shell templated from cholesteric liquid crystal prepared by microfluidics, Adv. Opt. Mater., 5, 13, 1-8, 2017 |
| [708] | Uchida, Y.; Takanishi, Y.; Yamamoto, J., Controlled fabrication and photonic structure of cholesteric liquid crystalline shells, Adv. Mater., 25, 23, 3234-3237, 2013 |
| [709] | Fleischmann, E.-K.; Liang, H.-L.; Kapernaum, N.; Giesselmann, F.; Lagerwall, J.; Zentel, R., One-piece micropumps from liquid crystalline core-shell particles, Nature Commun., 3, 1, 1178, 2012 |
| [710] | Jampani, V. S.R.; Volpe, R. H.; Reguengo de Sousa, K.; Ferreira Machado, J.; Yakacki, C. M.; Lagerwall, J. P.F. F., Liquid crystal elastomer shell actuators with negative order parameter, Sci. Adv., 5, 4, eaaw2476, 2019 |
| [711] | Schwartz, M.; Lenzini, G.; Geng, Y.; Rønne, P. B.; Ryan, P. Y.A.; Lagerwall, J. P.F., Cholesteric liquid crystal shells as enabling material for information-rich design and architecture, Adv. Mater., 1707382, 2018, 1707382-1 |
| [712] | Tran, L.; Bishop, K. J.M., Swelling cholesteric liquid crystal shells to direct the assembly of particles at the interface, ACS Nano, 2020 |
| [713] | Hokmabad, B. V.; Baldwin, K. A.; Krüger, C.; Bahr, C.; Maass, C. C., Topological stabilization and dynamics of self-propelling nematic shells, Phys. Rev. Lett., 123, 17, Article 178003 pp., 2019 |
| [714] | Sheng, M.; Zhang, L.; Jiang, S.; Yang, L.; Zaaboul, F.; Fu, S., Bioinspired electro-responsive multispectral controllable dye-doped liquid crystal yolk-shell microcapsules for advanced textiles, ACS Appl. Mater. Interfaces, 13, 11, 13586-13595, 2021 |
| [715] | Fernandez-Nieves, A.; Vitelli, V.; Utada, A. S.; Link, D. R.; Márquez, M.; Nelson, D. R.; Weitz, D. A., Novel defect structures in nematic liquid crystal shells, Phys. Rev. Lett., 99, 15, Article 157801 pp., 2007 |
| [716] | Utada, A. S.; Lorenceau, E.; Link, D. R.; Kaplan, P. D.; Stone, H. A.; Weitz, D. A., Monodisperse double emulsions generated from a microcapillary device, Science, 308, 5721, 537-541, 2005 |
| [717] | Mermin, N. D., E pluribus boojum: the physicist as neologist, Phys. Today, 34, 4, 46-53, 1981 |
| [718] | Lopez-Leon, T.; Koning, V.; Devaiah, K. B.S.; Vitelli, V.; Fernandez-Nieves, A., Frustrated nematic order in spherical geometries, Nat. Phys., 7, 5, 391-394, 2011 |
| [719] | Vitelli, V.; Nelson, D. R., Nematic textures in spherical shells, Phys. Rev. E, 74, 2, 1-18, 2006 |
| [720] | Shin, H.; Bowick, M. J.; Xing, X., Topological defects in spherical nematics, Phys. Rev. Lett., 101, 3, 1-4, 2008 |
| [721] | Zhou, Y.; Guo, A.; Zhang, R.; Armas-Pérez, J. C.; Martínez-González, J. A.; Rahimi, M.; Sadati, M.; de Pablo, J. J., Mesoscale structure of chiral nematic shells, Soft Matter, 2016 |
| [722] | Carenza, L. N.; Gonnella, G.; Marenduzzo, D.; Negro, G.; Orlandini, E., Cholesteric shells: two-dimensional blue fog and finite quasicrystals, Phys. Rev. Lett., 128, 497, 2022 |
| [723] | Iwai, Y.; Uchida, Y.; Nishiyama, N., Self-assembled magnetic control lever embedded in photonic liquid crystalline microcapsule, Adv. Opt. Mater., 4, 12, 1961-1964, 2016 |
| [724] | Noh, J.; Henx, B.; Lagerwall, J. P.F., Taming liquid crystal self-assembly: The multifaceted response of nematic and smectic shells to polymerization, Adv. Mater., 28, 46, 10170-10174, 2016 |
| [725] | He, K.; Campo-Cortés, F.; Goral, M.; López-León, T.; Gordillo, J. M., Micron-sized double emulsions and nematic shells generated via tip streaming, Phys. Rev. Fluids, 4, 12, Article 124201 pp., 2019 |
| [726] | R.D. Kamien, Colloidal Inclusions in Liquid Crystals, in: Proceedings of the International School of Physics “Enrico Fermi”, Course 193: Soft Matter Assembly, 2015. |
| [727] | Durey, G., Stripes, Fingers and Skyrmions: Taming Cholesteric Liquid Crystal Shells Under Perpendicular Anchoring, 234, 2018, Université PSL, (Ph.D. thesis) |
| [728] | Durey, G.; Sohn, H. R.O.; Ackerman, P. J.; Brasselet, E.; Smalyukh, I. I.; Lopez-Leon, T., Topological solitons, cholesteric fingers and singular defect lines in janus liquid crystal shells, Soft Matter, 16, 11, 2669-2682, 2020 |
| [729] | Lopez-Leon, T.; Fernandez-Nieves, A.; Nobili, M.; Blanc, C., Smectic shells, J. Phys.: Condens. Matter, 24, 28, Article 284122 pp., 2012 |
| [730] | Geng, Y.; Noh, J.; Drevensek-Olenik, I.; Rupp, R.; Lenzini, G.; Lagerwall, J. P.F., High-fidelity spherical cholesteric liquid crystal bragg reflectors generating unclonable patterns for secure authentication, Sci. Rep., 6, 26840, 2016 |
| [731] | Keber, F. C.; Loiseau, E.; Sanchez, T.; DeCamp, S. J.; Giomi, L.; Bowick, M. J.; Marchetti, M. C.; Dogic, Z.; Bausch, A. R., Topology and dynamics of active nematic vesicles, Science, 345, 6201, 1135-1139, 2014 |
| [732] | Blanc, C.; Durey, G.; Kamien, R. D.; Lopez-Leon, T.; Lavrentovich, M. O.; Tran, L., Helfrich-hurault elastic instabilities driven by geometrical frustration, Rev. Modern Phys., 95, 85, 2023 |
| [733] | Sharma, A.; Lagerwall, J. P.F., Influence of head group and chain length of surfactants used for stabilising liquid crystal shells, Liq. Cryst., 1-10, 2018 |
| [734] | Durey, G.; Ishii, Y.; Lopez-Leon, T., Temperature-driven anchoring transitions at liquid crystal/water interfaces, Langmuir, 36, 9368, 2020 |
| [735] | Noh, J.; Jampani, V. S.R.; Haba, O.; Yonetake, K.; Takezoe, H.; Lagerwall, J. P.F., Sub-second dynamic phototuning of alignment in azodendrimer-doped nematic liquid crystal shells, J. Mol. Liq., 267, 197-204, 2018 |
| [736] | Darmon, A.; Benzaquen, M.; Seč, D.; Čopar, S.; Dauchot, O.; Lopez-Leon, T., Waltzing route toward double-helix formation in cholesteric shells, Proc. Natl. Acad. Sci., 113, 34, 9469-9474, 2016 |
| [737] | Tran, L.; Lavrentovich, M. O.; Durey, G.; Darmon, A.; Haase, M. F.; Li, N.; Lee, D.; Stebe, K. J.; Kamien, R. D.; Lopez-Leon, T., Change in stripes for cholesteric shells via anchoring in moderation, Phys. Rev. X, 7, 4, Article 041029 pp., 2017 |
| [738] | Gollapelli, B.; Vallamkondu, J., Electric field-driven structural changes in cholesteric shells for optical applications, Curr. Appl. Phys., 19, 12, 1399-1403, 2019 |
| [739] | Marchetti, M. C.; Joanny, J. F.; Ramaswamy, S.; Liverpool, T. B.; Prost, J.; Rao, M.; Simha, R. A., Hydrodynamics of soft active matter, Rev. Modern Phys., 85, 1143, 2013 |
| [740] | Group, N. P., Nature research collection active matter, 2019 |
| [741] | Doostmohammadi, A.; Ignés-Mullol, J.; Yeomans, J. M.; Sagués, F., Active nematics, Nature Commun., 9, 3246, 2018 |
| [742] | Genkin, M. M.; Sokolov, A.; Lavrentovich, O. D.; Aranson, I. S., Topological defects in a living nematic ensnare swimming bacteria, Phys. Rev. X, 7, Article 011029 pp., 2017 |
| [743] | Lavrentovich, O. D., Active colloids in liquid crystals, Curr. Opin. Colloid Interface Sci., 21, 97, 2016 |
| [744] | Čopar, S.; Aplinc, J.; Kos, Ž.; Žumer, S.; Ravnik, M., Topology of three-dimensional active nematic turbulence confined to droplets, Phys. Rev. X, 9, 3, Article 031051 pp., 2019 |
| [745] | Binysh, J.; Kos, Ž.; Čopar, S.; Ravnik, M.; Alexander, G. P., Three-dimensional active defect loops, Phys. Rev. Lett., 124, 257, 2020 |
| [746] | Ruske, L. J.; Yeomans, J. M., Morphology of active deformable 3D droplets, Phys. Rev. X, 11, Article 021001 pp., 2021 |
| [747] | Ramaswamy, S., The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys., 1, 323-345, 2010 |
| [748] | Narayan, V.; Ramaswamy, S.; Menon, N., Long-lived giant number fluctuations in a swarming granular nematic, Science, 317, 105-108, 2007 |
| [749] | Sanchez, T.; Chen, D.; DeCamp, S.; Heymann, M.; Dogic, Z., Spontaneous motion in hierarchically assembled active matter, Nature, 491, 431, 2012 |
| [750] | Giomi, L.; Bowick, M. J.; Mishra, P.; Sknepnek, R.; Marchetti, M. C., Defect dynamics in active nematics, Phil. Trans. R. Soc. A, 372, Article 20130365 pp., 2014 |
| [751] | Khoromskaia, D.; Alexander, G. P., Vortex formation and dynamics of defects in active nematic shells, New J. Phys., 19, 10, Article 103043 pp., 2017 · Zbl 1516.76005 |
| [752] | Cortese, D.; Eggers, J.; Liverpool, T., Pair creation, motion, annihilation of topological defects in two-dimensional nematic liquid crystals, Phys. Rev. E, 97, Article 022704 pp., 2018 |
| [753] | Shankar, S.; Marchetti, M. C., Hydrodynamics of active defects: From order to chaos to defect ordering, Phys. Rev. X, 9, Article 041047 pp., 2019 |
| [754] | Wensink, H. H.; Dunkel, J.; Heidenreich, S.; Drescher, K.; Goldstein, R. E.; Löwen, H.; Yeomans, J. M., Meso-scale turbulence in living fluids, Proc. Natl. Acad. Sci. USA, 109, 14308, 2012 · Zbl 1355.76026 |
| [755] | Giomi, L., Geometry and topology of turbulence in active nematics, Phys. Rev. X, 5, Article 031003 pp., 2015 |
| [756] | Saw, T. B.; Doostmohammadi, A.; Nier, V.; Kocgozlu, L.; Thampi, S.; Toyama, Y.; Marcq, P.; Lim, C. T.; Yeomans, J. M.; Ladoux, B., Topological defects in epithelia govern cell death and extrusion, Nature, 544, 212, 2017 |
| [757] | Kawaguchi, K.; Kageyama, R.; Sano, M., Topological defects control collective dynamics in neural progenitor cell cultures, Nature, 545, 327, 2017 |
| [758] | Duclos, G.; Erlenkämper, C.; Joanny, J.-F.; Silberzan, P., Topological defects in confined populations of spindle-shaped cells, Nat. Phys., 13, 58, 2017 |
| [759] | Meacock, O. J.; Doostmohammadi, A.; Foster, K. R.; Yeomans, J. M.; Durham, W. M., Bacteria solve the problem of crowding by moving slowly, Nat. Phys., 17, 205, 2021 |
| [760] | Maroudas-Sachs, Y.; Garion, L.; Shani-Zerbib, L.; Livshits, A.; Braun, E.; Keren, K., Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis, Nat. Phys., 17, 251, 2021 |
| [761] | Chandragiri, S.; Doostmohammadi, A.; Yeomans, J. M.; Thampi, S. P., Flow states and transitions of an active nematic in a three-dimensional channel, Phys. Rev. Lett., 125, Article 148002 pp., 2020 |
| [762] | Chandrakar, P.; Varghese, M.; Aghvami, S.; Baskaran, A.; Dogic, Z.; Duclos, G., Confinement controls the bend instability of three-dimensional active liquid crystals, Phys. Rev. Lett., 125, Article 257801 pp., 2020 |
| [763] | Varghese, M.; Baskaran, A.; Hagan, M.; Baskaran, A., Confinement-induced self-pumping in 3D active fluids, Phys. Rev. Lett., 125, Article 268003 pp., 2020 |
| [764] | Friedel, J.; De Gennes, P., Boulces de disclinations dans les cristaux liquides, C. R. Acad. Sc. Paris B, 268, 257-259, 1969 |
| [765] | Binysh, J.; Alexander, G. P., Maxwell’s theory of solid angle and the construction of knotted fields, J. Phys. A, 51, Article 385202 pp., 2018 · Zbl 1498.78014 |
| [766] | Adhyapak, T. C.; Ramaswamy, S.; Toner, J., Live soap: Stability, order, fluctuations in apolar active smectics, Phys. Rev. Lett., 110, Article 118102 pp., 2013 |
| [767] | Chen, L.; Toner, J., Universality for moving stripes: A hydrodynamic theory of polar active smectics, Phys. Rev. Lett., 111, Article 088701 pp., 2013 |
| [768] | Whitfield, C. A.; Adhyapak, T. C.; Tiribocchi, A.; Alexander, G. P.; Marenduzzo, D.; Ramaswamy, S., Hydrodynamic instabilities in active cholesteric liquid crystals, Eur. Phys. J. E, 40, 50, 2017 |
| [769] | Metselaar, L.; Doostmohammadi, A.; Yeomans, J. M., Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions, J. Chem. Phys., 150, Article 064909 pp., 2019 |
| [770] | Carenza, L. N.; Gonella, G.; Marenduzzo, D.; Negro, G., Rotation and propulsion in 3D active chiral droplets, Proc. Natl. Acad. Sci. USA, 116, 22065, 2019 |
| [771] | Bouligand, Y., Twisted fibrous arrangements in biological materials and cholesteric mesophases, Tissue Cell, 4, 2, 189-217, 1972 |
| [772] | Neville, A. C., Biology of Fibrous Composites: Development Beyond the Cell Membrane, 1993, Cambridge University Press |
| [773] | Cartwright, J. H.E.; Checa, A. G., The dynamics of nacre self-assembly, J. R. Soc. Interface, 4, 14, 491-504, 2007 |
| [774] | Cartwright, J. H.E.; Checa, A. G.; Escribano, B.; Sainz-Díaz, C. I., Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal, Proc. Natl. Acad. Sci., 106, 26, 10499-10504, 2009 |
| [775] | Cartwright, J. H.E.; Checa, A. G.; Rousseau, M., Pearls are self-organized natural ratchets, Langmuir, 29, 26, 8370-8376, 2013 |
| [776] | Checa, A. G.; Cartwright, J. H.E.; Sánchez-Almazo, I.; Andrade, J. P.; Ruiz-Raya, F., The cuttlefish sepia officinalis (sepiidae, cephalopoda) constructs cuttlebone from a liquid-crystal precursor, Sci. Rep., 5, 1, 1-13, 2015 |
| [777] | Almagro, I.; Cartwright, J. H.E.; Checa, A. G.; Macías-Sánchez, E.; Sainz-Díaz, C. I., Evidence for a liquid-crystal precursor involved in the formation of the crossed-lamellar microstructure of the mollusc shell, Acta Biomater., 120, 12-19, 2021 |
| [778] | Garnham, C. P.; Roll-Mecak, A., The chemical complexity of cellular microtubules: tubulin post-translational modification enzymes and their roles in tuning microtubule functions, Cytoskeleton, 69, 7, 442-463, 2012 |
| [779] | Welte, M. A., Bidirectional transport along microtubules, Curr. Biol., 14, 13, R525-R537, 2004 |
| [780] | Vicente-Manzanares, M.; Choi, C. K.; Horwitz, A. R., Integrins in cell migration-the actin connection, J. Cell Sci., 122, 2, 199-206, 2009 |
| [781] | Crisp, M.; Liu, Q.; Roux, K.; Rattner, J. B.; Shanahan, C.; Burke, B.; Stahl, P. D.; Hodzic, D., Coupling of the nucleus and cytoplasm: role of the LINC complex, J. Cell Biol., 172, 1, 41-53, 2006 |
| [782] | Bouzid, T.; Kim, E.; Riehl, B. D.; Esfahani, A. M.; Rosenbohm, J.; Yang, R.; Duan, B.; Lim, J. Y., The LINC complex, mechanotransduction, mesenchymal stem cell function and fate, J. Biol. Eng., 13, 1, 1-12, 2019 |
| [783] | Gerardo, H.; Lima, A.; Carvalho, J.; Ramos, J. R.; Couceiro, S.; Travasso, R. D.M.; das Neves, R. P.; Grãos, M., Soft culture substrates favor stem-like cellular phenotype and facilitate reprogramming of human mesenchymal stem/stromal cells (hMSCs) through mechanotransduction, Sci. Rep., 9, 1, 1-18, 2019 |
| [784] | Prost, J.; Jülicher, F.; Joanny, J.-F., Active gel physics, Nat. Phys., 11, 2, 111-117, 2015 |
| [785] | Carenza, L. N.; Gonnella, G.; Lamura, A.; Negro, G.; Tiribocchi, A., Lattice Boltzmann methods and active fluids, Eur. Phys. J. E, 42, 6, 1-38, 2019 |
| [786] | Le Goff, T.; Liebchen, B.; Marenduzzo, D., Actomyosin contraction induces in-bulk motility of cells and droplets, Biophys. J., 119, 5, 1025-1032, 2020 |
| [787] | Camley, B. A.; Zhang, Y.; Zhao, Y.; Li, B.; Ben-Jacob, E.; Levine, H.; Rappel, W.-J., Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns, Proc. Natl. Acad. Sci., 111, 41, 14770-14775, 2014 |
| [788] | Moure, A.; Gomez, H., Three-dimensional simulation of obstacle-mediated chemotaxis, Biomech. Model. Mechanobiol., 17, 5, 1243-1268, 2018 |
| [789] | Moure, A.; Gomez, H., Dual role of the nucleus in cell migration on planar substrates, Biomech. Model. Mechanobiol., 19, 1491-1508, 2020 |
| [790] | Portet, S.; Madzvamuse, A.; Chung, y.; Leube, R. E.; Windoffer, R., Keratin dynamics: modeling the interplay between turnover and transport, PLoS One, 10, 3, Article e0121090 pp., 2015 |
| [791] | Gouveia, M.; Zemljič-Jokhadar, Š.; Vidak, M.; Stojkovič, B.; Derganc, J.; Travasso, R.; Liovic, M., Keratin dynamics and spatial distribution in wild-type and K14 R125P mutant cells—A computational model, Int. J. Mol. Sci., 21, 7, 2596, 2020 |
| [792] | Zemljič Jokhadar, Š.; Stojković, B.; Vidak, M.; Sorčan, T.; Liovic, M.; Gouveia, M.; Travasso, R. D.M.; Derganc, J., Cortical stiffness of keratinocytes measured by lateral indentation with optical tweezers, PLoS One, 15, 12, Article e0231606 pp., 2020 |
| [793] | Antfolk, D.; Sjöqvist, M.; Cheng, F.; Isoniemi, K.; Duran, C. L.; Rivero-Muller, A.; Antila, C.; Niemi, R.; Landor, S.; Bouten, C. V.C.; Bayless, K. J.; Eriksson, J. E.; Sahlgren, C. M., Selective regulation of notch ligands during angiogenesis is mediated by vimentin, Proc. Natl. Acad. Sci., 114, 23, E4574-E4581, 2017 |
| [794] | van Engeland, N. C.A.; Rodriguez, F. S.; Rivero-Müller, A.; Ristori, T.; Duran, C. L.; Stassen, O. M.J. A.; Antfolk, D.; Driessen, R. C.H.; Ruohonen, S.; Ruohonen, S. T.; Nuutinen, S.; Savontaus, E.; Loerakker, S.; Bayless, K. J.; Sjöqvist, M.; Bouten, C. V.C.; Eriksson, J. E.; Sahlgren, C. M., Vimentin regulates notch signaling strength and arterial remodeling in response to hemodynamic stress, Sci. Rep., 9, 1, 1-14, 2019 |
| [795] | Jülicher, F.; Kruse, K.; Prost, J.; Joanny, J.-F., Active behavior of the cytoskeleton, Phys. Rep., 449, 1-3, 3-28, 2007 |
| [796] | Krause, M.; Gautreau, A., Steering cell migration: lamellipodium dynamics and the regulation of directional persistence, Nat. Rev. Mol. Cell Biol., 15, 9, 577-590, 2014 |
| [797] | Kruse, K.; Joanny, J. F.; Jülicher, F.; Prost, J., Contractility and retrograde flow in lamellipodium motion, Phys. Biol., 3, 2, 130, 2006 |
| [798] | Kruse, K.; Joanny, J.-F.; Jülicher, F.; Prost, J.; Sekimoto, K., Generic theory of active polar gels: A paradigm for cytoskeletal dynamics, Eur. Phys. J. E, 16, 1, 5-16, 2005 |
| [799] | Bretschneider, T.; Diez, S.; Anderson, K.; Heuser, J.; Clarke, M.; Müller-Taubenberger, A.; Köhler, J.; Gerisch, G., Dynamic actin patterns and Arp2/3 assembly at the substrate-attached surface of motile cells, Curr. Biol., 14, 1, 1-10, 2004 |
| [800] | Salbreux, G.; Joanny, J.-F.; Prost, J.; Pullarkat, P., Shape oscillations of non-adhering fibroblast cells, Phys. Biol., 4, 4, 268, 2007 |
| [801] | Salbreux, G.; Prost, J.; Joanny, J.-F., Hydrodynamics of cellular cortical flows and the formation of contractile rings, Phys. Rev. Lett., 103, 5, Article 058102 pp., 2009 |
| [802] | Shaebani, M. R.; Wysocki, A.; Winkler, R. G.; Gompper, G.; Rieger, H., Computational models for active matter, Nat. Rev. Phys., 2, 4, 181-199, 2020 |
| [803] | Ramaswamy, R.; Bourantas, G.; Jülicher, F.; Sbalzarini, I. F., A hybrid particle-mesh method for incompressible active polar viscous gels, J. Comput. Phys., 291, 334-361, 2015 · Zbl 1349.76524 |
| [804] | Safran, S., Statistical Thermodynamics of Surfaces, Interfaces, Membranes, 2018, CRC Press |
| [805] | Campelo, F.; Hernandez-Machado, A., Dynamic model and stationary shapes of fluid vesicles, Eur. Phys. J. E, 20, 1, 37-45, 2006 |
| [806] | Shao, D.; Levine, H.; Rappel, W.-J., Coupling actin flow, adhesion, morphology in a computational cell motility model, Proc. Natl. Acad. Sci., 109, 18, 6851-6856, 2012 |
| [807] | Provatas, N.; Elder, K., Phase-Field Methods in Materials Science and Engineering, 2011, John Wiley & Sons |
| [808] | Nonomura, M., Study on multicellular systems using a phase field model, PLoS One, 7, 4, Article e33501 pp., 2012 |
| [809] | Moreira-Soares, M.; Cunha, S. P.; Bordin, J. R.; Travasso, R. D.M., Adhesion modulates cell morphology and migration within dense fibrous networks, J. Phys.: Condens. Matter, 32, 31, Article 314001 pp., 2020 |
| [810] | Santos-Oliveira, P.; Correia, A.; Rodrigues, T.; Ribeiro-Rodrigues, T. M.; Matafome, P.; Rodríguez-Manzaneque, J. C.; Seiça, R.; Girão, H.; Travasso, R. D.M., The force at the tip-modelling tension and proliferation in sprouting angiogenesis, PLoS Comput. Biol., 11, 8, Article e1004436 pp., 2015 |
| [811] | Vilanova, G.; Colominas, I.; Gomez, H., Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis, Int. J. Numer. Methods Biomed. Eng., 29, 10, 1015-1037, 2013 |
| [812] | Moreira-Soares, M.; Coimbra, R.; Rebelo, L.; Carvalho, J.; Travasso, R. D.M., Angiogenic factors produced by hypoxic cells are a leading driver of anastomoses in sprouting angiogenesis-A computational study, Sci. Rep., 8, 1, 1-12, 2018 |
| [813] | Gomez, H.; van der Zee, K. G., Computational phase-field modeling, (Encyclopedia of Computational Mechanics, 2018, Wiley Online Library), 1-35 |
| [814] | Travasso, R. D.; Castro, M.; Oliveira, J. C.R. E., The phase-field model in tumor growth, Phil. Mag., 91, 1, 183-206, 2011 |
| [815] | Lorenzo, G.; Hughes, T. J.; Dominguez-Frojan, P.; Reali, A.; Gomez, H., Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth, Proc. Natl. Acad. Sci., 116, 4, 1152-1161, 2019 |
| [816] | Hohenberg, P. C.; Halperin, B. I., Theory of dynamic critical phenomena, Rev. Modern Phys., 49, 3, 435, 1977 |
| [817] | Wang, Q.; Yang, X.; Adalsteinsson, D.; Elston, T. C.; Jacobson, K.; Kapustina, M.; Forest, M. G., Computational and modeling strategies for cell motility, (Computational Modeling of Biological Systems, 2012, Springer), 257-296 |
| [818] | Camley, B. A.; Zhao, Y.; Li, B.; Levine, H.; Rappel, W.-J., Crawling and turning in a minimal reaction-diffusion cell motility model: coupling cell shape and biochemistry, Phys. Rev. E, 95, 1, Article 012401 pp., 2017 |
| [819] | Kim, J.; Cao, Y.; Eddy, C.; Deng, Y.; Levine, H.; Rappel, W.-J.; Sun, B., The mechanics and dynamics of cancer cells sensing noisy 3D contact guidance, Proc. Natl. Acad. Sci., 118, 10, 2021 |
| [820] | Shankar, S.; Souslov, A.; Bowick, M. J.; Marchetti, M. C.; Vitelli, V., Topological active matter, Nat. Rev. Phys., 4, 380-398, 2022 |
| [821] | Hasan, M. Z.; Kane, C. L., Colloquium: Topological insulators, Rev. Modern Phys., 82, 3045-3067, 2010 |
| [822] | Ozawa, T.; Price, H. M.; Amo, A.; Goldman, N.; Hafezi, M.; Lu, L.; Rechtsman, M. C.; Schuster, D.; Simon, J.; Zilberberg, O.; Carusotto, I., Topological photonics, Rev. Modern Phys., 91, Article 015006 pp., 2019 |
| [823] | Fleury, R.; Sounas, D. L.; Sieck, C. F.; Haberman, M. R.; Alù, A., Sound isolation and giant linear nonreciprocity in a compact acoustic circulator, Science, 343, 516-519, 2014 |
| [824] | Souslov, A.; van Zuiden, B. C.; Bartolo, D.; Vitelli, V., Topological sound in active-liquid metamaterials, Nat. Phys., 13, 1091, 2017 |
| [825] | Sone, K.; Ashida, Y., Anomalous topological active matter, Phys. Rev. Lett., 123, Article 205502 pp., 2019 |
| [826] | Delplace, P.; Marston, J. B.; Venaille, A., Topological origin of equatorial waves, Science, 358, 1075-1077, 2017 · Zbl 1404.86016 |
| [827] | Shankar, S.; Bowick, M. J.; Marchetti, M. C., Topological sound and flocking on curved surfaces, Phys. Rev. X, 7, Article 031039 pp., 2017 |
| [828] | Souslov, A.; Dasbiswas, K.; Fruchart, M.; Vaikuntanathan, S.; Vitelli, V., Topological waves in fluids with odd viscosity, Phys. Rev. Lett., 122, 12, Article 128001 pp., 2019 |
| [829] | Tauber, C.; Delplace, P.; Venaille, A., A bulk-interface correspondence for equatorial waves, J. Fluid Mech., 868, R2, 2019 · Zbl 1415.86022 |
| [830] | Avron, J. E., Odd viscosity, J. Stat. Phys., 92, 543-557, 1998 · Zbl 0939.76005 |
| [831] | Banerjee, D.; Souslov, A.; Abanov, A. G.P.; Vitelli, V., Odd viscosity in chiral active fluids, Nat. Commun., 8, 1, 1-12, 2017 |
| [832] | Brandenbourger, M.; Locsin, X.; Lerner, E.; Coulais, C., Non-reciprocal robotic metamaterials, Nature Commun., 10, 4608, 2019 |
| [833] | Ghatak, A.; Brandenbourger, M.; van Wezel, J.; Coulais, C., Observation of non-hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial, Proc. Natl. Acad. Sci. U.S.A, 117, 29651-29658, 2020 |
| [834] | Scheibner, C.; Souslov, A.; Banerjee, D.; Surówka, P.; Irvine, W. T.M.; Vitelli, V., Odd elasticity, Nat. Phys., 16, 4, 475-480, 2020 |
| [835] | Scheibner, C.; Irvine, W. T.M.; Vitelli, V., Non-hermitian band topology and skin modes in active elastic media, Phys. Rev. Lett., 125, Article 118001 pp., 2020 |
| [836] | Tauber, C.; Delplace, P.; Venaille, A., Anomalous bulk-edge correspondence in continuous media, Phys. Rev. Res., 2, Article 013147 pp., 2020 |
| [837] | Baardink, G.; Cassella, G.; Neville, L.; Milewski, P. A.; Souslov, A., Complete absorption of topologically protected waves, Phys. Rev. E, 104, 1, Article 014603 pp., 2021 |
| [838] | Abbaszadeh, H.; Souslov, A.; Paulose, J.; Schomerus, H.; Vitelli, V., Sonic Landau levels and synthetic gauge fields in mechanical metamaterials, Phys. Rev. Lett., 119, Article 195502 pp., 2017 |
| [839] | Bandres, M. A.; Wittek, S.; Harari, G.; Parto, M.; Ren, J.; Segev, M.; Christodoulides, D. N.; Khajavikhan, M., Topological insulator laser: Experiments, Science, 359, 6381, 2018 |
| [840] | Volovik, G. E., The universe in a helium droplet, (International Series of Monographs on Physics, 2009, OUP Oxford) |
| [841] | Coleman, S., Aspects of Symmetry: Selected Erice Lectures, 1985, Cambridge University Press: Cambridge University Press Cambridge, U.K. |
| [842] | Weinberg, S., The quantum theory of fields. Vol. 2: Modern applications, 2013, Cambridge University Press |
| [843] | Vilenkin, A.; Shellard, E. P.S., Cosmic Strings and Other Topological Defects, 2000, Cambridge University Press |
| [844] | Nechaev, S. K., Statistics of Knots and Entangled Random Walks, 1996, World Scientific · Zbl 0868.57003 |
| [845] | Meluzzi, D.; Smith, D. E.; Arya, G., Biophysics of knotting, Annu. Rev. Biophys., 39, 349-366, 2010 |
| [846] | Pickwell, G. V., Knotting and coiling behavior in the pelagic sea snake pelamis platurus (L.), Copeia, 1971, 2, 348-350, 1971 |
| [847] | Lillywhite, H. B., Unusual shedding behaviors in an aquatic snake, Acrochordus granulatus, Copeia, 1989, 3, 768-770, 1989 |
| [848] | Savidge, J. A.; Seibert, T. F.; Kastner, M.; Jayne, B. C., Lasso locomotion expands the climbing repertoire of snakes, Curr. Biol., 31, 1, R7-R8, 2021 |
| [849] | Miller, T. J., Knotting: A previously undescribed feeding behavior in muraenid eels, Copeia, 1987, 4, 1055-1057, 1987 |
| [850] | Barley, S. C.; Mehta, R. S.; Meeuwig, J. J.; Meekan, M. G., To knot or not? Novel feeding behaviours in moray eels, Mar. Biodivers., 46, 3, 703-705, 2016 |
| [851] | Clark, A. J.; Crawford, C. H.; King, B. D.; Demas, A. M.; Uyeno, T. A., Material properties of hagfish skin, with insights into knotting behaviors, Biol. Bull., 230, 3, 243-256, 2016 |
| [852] | Haney, W. A.; Clark, A. J.; Uyeno, T. A., Characterization of body knotting behavior used for escape in a diversity of hagfishes, J. Zool., 310, 4, 261-272, 2020 |
| [853] | Lambert, P., Sea cucumbers of British Columbia, Southeast Alaska and Puget Sound, 1997, UBC Press |
| [854] | Darwin, C., The Movements and Habits of Climbing Plants, 1875, John Murray |
| [855] | Pieranski, P.; Baranska, J.; Skjeltorp, A., Tendril perversion—A physical implication of the topological conservation law, Eur. J. Phys., 25, 5, 613, 2004 |
| [856] | Feng, J.; Zhang, W.; Liu, C.; Guo, M.; Zhang, C., Homoclinic and heteroclinic orbits in climbing cucumber tendrils, Sci. Rep., 9, 1, 1-14, 2019 |
| [857] | Feng, J.; Zhang, Q.; Wang, W.; Hao, S., Nonlinear dynamics behavior analysis of the spatial configuration of a tendril-bearing plant, Eur. Phys. J. Plus, 132, 3, 1-14, 2017 |
| [858] | Herzfeld, C.; Lestel, D., Knot tying in great apes: etho-ethnology of an unusual tool behavior, Soc. Sci. Inf., 44, 4, 621-653, 2005 |
| [859] | McLennan, M. R., Tie one on: ‘nest tying’ by wild chimpanzees at Bulindi — A variant of a universal great ape behavior?, Primates, 59, 3, 227-233, 2018 |
| [860] | Nesher, N.; Levy, G.; Grasso, F. W.; Hochner, B., Self-recognition mechanism between skin and suckers prevents octopus arms from interfering with each other, Curr. Biol., 24, 11, 1271-1275, 2014 |
| [861] | Wassersug, R. J.; Roberts, L.; Gimian, J.; Hughes, E.; Saunders, R.; Devison, D.; Woodbury, J.; O’Reilly, J. C., The behavioral responses of amphibians and reptiles to microgravity on parabolic flights, Zoology, 108, 2, 107-120, 2005 |
| [862] | Goriely, A., Knotted umbilical cords, (Physical and Numerical Models in Knot Theory: Including Applications To the Life Sciences, 2005, World Scientific), 109-126 · Zbl 1092.92025 |
| [863] | Spellacy, W. N.; Gravem, H.; Fisch, R. O., The umbilical cord complications of true knots, nuchal coils, and cords around the body: report from the collaborative study of cerebral palsy, Am. J. Obstet. Gynecol., 94, 8, 1136-1142, 1966 |
| [864] | Clerici, G.; Koutras, I.; Luzietti, R.; Di Renzo, G. C., Multiple true umbilical knots: A silent risk for intrauterine growth restriction with anomalous hemodynamic pattern, Fetal Diagn. Ther., 22, 6, 440-443, 2007 |
| [865] | López Ramón y. Cajal, C.; Ocampo Martínez, R., Four-dimensional ultrasonography of a true knot of the umbilical cord, Am. J. Obstet. Gynecol., 195, 4, 896-898, 2006 |
| [866] | Barabasi, A.-L.; Oltvai, Z. N., Network biology: understanding the cell’s functional organization, Nat. Rev. Genet., 5, 2, 101-113, 2004 |
| [867] | Mitrea, C.; Taghavi, Z.; Bokanizad, B.; Hanoudi, S.; Tagett, R.; Donato, M.; Voichiţa, C.; Drăghici, S., Methods and approaches in the topology-based analysis of biological pathways, Front. Physiol., 4, 278, 2013 |
| [868] | Winterbach, W.; Mieghem, P. V.; Reinders, M.; Wang, H.; Ridder, D.d., Topology of molecular interaction networks, BMC Syst. Biol., 7, 1-15, 2013 |
| [869] | Gosak, M.; Markovič, R.; Dolenšek, J.; Rupnik, M. S.; Marhl, M.; Stožer, A.; Perc, M., Network science of biological systems at different scales: A review, Phys. Life Rev., 24, 118-135, 2018 |
| [870] | Gan, H. H.; Pasquali, S.; Schlick, T., Exploring the repertoire of RNA secondary motifs using graph theory with implications for RNA design, Nucleic Acids Res., 31, 2926-2943, 2003 |
| [871] | Gan, H. H.; Fera, D.; Zorn, J.; Shiffeldrim, N.; Tang, M.; Laserson, U.; Kim, N.; Schlick, T., RAG: RNA-As-graphs database - concepts, analysis, and features, Bioinformatics, 20, 8, 1285-1291, 2004 |
| [872] | Orland, H.; Zee, A., RNA folding and largenmatrix theory, Nuclear Phys. B, 620, 456-476, 2002 · Zbl 0991.92011 |
| [873] | Vernizzi, G.; Ribeca, P.; Orland, H.; Zee, A., Topology of pseudoknotted homopolymers, Phys. Rev. E, 73, Article 031902 pp., 2016 |
| [874] | Vernizzi, G.; Orland, H.; Zee, A., Classification and predictions of RNA pseudoknots based on topological invariants, Phys. Rev. E, 94, Article 042410 pp., 2016 |
| [875] | Micheletti, C.; Di Stefano, M.; Orland, H., Absence of knots in known RNA structures, Proc. Natl. Acad. Sci., 112, 7, 2052-2057, 2015 |
| [876] | Burton, A.; Di Stefano, M.; Lehman, N.; Orland, H.; Micheletti, C., The elusive quest for RNA knots, RNA Biol., 13, 2, 134-139, 2016 |
| [877] | Ayme, J.-F.; Beves, J. E.; Leigh, D. A.; McBurney, R. T.; Rissanen, K.; Schultz, D., A synthetic molecular pentafoil knot, Nature Chem., 4, 1, 15-20, 2012 |
| [878] | Fielden, S. D.P.; Leigh, D. A.; Woltering, S. L., Molecular knots, Angew. Chem. Int. Ed., 56, 37, 11166-11194, 2017 |
| [879] | Datta, S.; Kato, Y.; Higashiharaguchi, S.; Aratsu, K.; Isobe, A.; Saito, T.; Prabhu, D. D.; Kitamoto, Y.; Hollamby, M. J.; Smith, A. J.; Dalgliesh, R.; Mahmoudi, N.; Pesce, L.; Perego, C.; Pavan, G. M.; Yagai, S., Self-assembled poly-catenanes from supramolecular toroidal building blocks, Nature, 583, 7816, 400-405, 2020 |
| [880] | Sauvage, J.-P.; Collin, J.-P.; Durot, S.; Frey, J.; Heitz, V.; Sour, A.; Tock, C., From chemical topology to molecular machines, C. R. Chim., 13, 3, 315-328, 2010 |
| [881] | Erbas-Cakmak, S.; Fielden, S. D.P.; Karaca, U.; Leigh, D. A.; McTernan, C. T.; Tetlow, D. J.; Wilson, M. R., Rotary and linear molecular motors driven by pulses of a chemical fuel, Science, 358, 6361, 340-343, 2017 |
| [882] | Leigh, D. A.; Wong, J. K.Y.; Dehez, F.; Zerbetto, F., Unidirectional rotation in a mechanically interlocked molecular rotor, Nature, 424, 6945, 174-179, 2003 |
| [883] | Evans, N. H.; Beer, P. D., Progress in the synthesis and exploitation of catenanes since the millennium, Chem. Soc. Rev., 43, 13, 4658-4683, 2014 |
| [884] | Mena-Hernando, S.; Pérez, E. M., Mechanically interlocked materials. Rotaxanes and catenanes beyond the small molecule, Chem. Soc. Rev., 48, 19, 5016-5032, 2019 |
| [885] | Hart, L. F.; Hertzog, J. E.; Rauscher, P. M.; Rawe, B. W.; Tranquilli, M. M.; Rowan, S. J., Material properties and applications of mechanically interlocked polymers, Nat. Rev. Mater., 6, 6, 508-530, 2021 |
| [886] | Neophytou, A.; Chakrabarti, D.; Sciortino, F., Topological nature of the liquid-liquid phase transition in tetrahedral liquids, Nat. Phys., 18, 10, 1248-1253, 2022 |
| [887] | Gladman, A. S.; Matsumoto, E. A.; Nuzzo, R. G.; Mahadevan, L.; Lewis, J. A., Biomimetic 4D printing, Nature Mater., 15, 4, 413-418, 2016 |
| [888] | Schneider, G. F.; Dekker, C., DNA sequencing with nanopores, Nat. Biotechnol., 30, 4, 326-328, 2012 |
| [889] | Senior, A. W.; Evans, R.; Jumper, J.; Kirkpatrick, J.; Sifre, L.; Green, T.; Qin, C.; Zidek, A.; Nelson, A. W.R.; Bridgland, A.; Penedones, H.; Petersen, S.; Simonyan, K.; Crossan, S.; Kohli, P.; Jones, D. T.; Silver, D.; Kavukcuoglu, K.; Hassabis, D., Improved protein structure prediction using potentials from deep learning, Nature, 577, 706-710, 2020 |
| [890] | Hinsen, K.; Hu, S.; Kneller, G. R.; Niemi, A. J., A comparison of reduced coordinate sets for describing protein structure, J. Chem. Phys., 139, Article 124115 pp., 2013 |
| [891] | Chowdhury, R.; Bouatta, N.; Biswas, S.; Floristean, C.; Kharkar, A.; Roy, K.; Rochereau, C.; Ahdritz, G.; Zhang, J.; Church, G. M.; Sorger, P. K.; AlQuraishi, M., Single-sequence protein structure prediction using a language model and deep learning, Nature Biotechnol., 40, 1617-1623, 2022 |
| [892] | Molkenthin, N.; Hu, S.; Niemi, A. J., Discrete nonlinear Schrödinger equation and polygonal solitons with applications to collapsed proteins, Phys. Rev. Lett., 106, Article 078102 pp., 2011 |
| [893] | Dai, J.; Niemi, A. J.; He, J.; Sieradzan, A.; Ilieva, N., Bloch spin waves and emergent structure in protein folding with HIV envelope glycoprotein as an example, Phys. Rev. E, 93, Article 032409 pp., 2016 |
| [894] | Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H., Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092, 1953 · Zbl 1431.65006 |
| [895] | Berman, H. M.; Westbrook, J.; Feng, Z.; Gilliland, G.; Bhat, T.; Weissig, H.; Shindyalov, I. N.; Bourne, P. E., Protein data bank, Nucleic Acids Res., 28, 1, 235-242, 2000 |
| [896] | Schlichting, I.; Berendzen, J.; Phillips, Jr., G. N.; Sweet, R. M., Crystal structure of photolysed carbonmonoxy-myoglobin, Nature, 371, 808-812, 1994 |
| [897] | Lundgren, M.; Krokhotin, A.; Niemi, A. J., Topology and structural self-organization in folded proteins, Phys. Rev. E, 88, Article 042709 pp., 2013 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
