The tangled web of self-tying knots

Belmonte, Andrew

doi:10.1073/pnas.0708150104

Cited by 8 publications

(3 citation statements)

References 19 publications

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“…The study of tight knot characteristics in (bio)polymers has a long history of interest as knots easily self-tie and localize in any long chain [12,13,14,15]. More than 20 years ago de Gennes argued that knots may self-tie in crystallizing or sheared polymer melts changing their macroscopic relaxation behavior [16].…”

Section: Introductionmentioning

confidence: 99%

Sequence-Specific Size, Structure, and Stability of Tight Protein Knots

Dzubiella

2009

Biophysical Journal

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Approximately 1% of known protein structures display knotted configurations in their native fold, but the function of these configurations is not understood. It has been speculated that the entanglement may inhibit mechanical protein unfolding or transport, e.g., as in cellular threading or translocation processes through narrow biological pores. Protein knot manipulation, e.g., knot tightening and localization, has become possible in single-molecule experiments. Here, we investigate tight peptide knot (TPK) characteristics in detail by pulling selected 3(1) and 4(1)-knotted peptides using all-atom molecular dynamics computer simulations. We find that the 3(1)- and 4(1)-TPK lengths are typically Deltal approximately 47+/- 4 A and 69 +/- 4 A, respectively, for a wide range of tensions (0.1 nN less, similarF less, similar 1.5 nN). The 4(1)-knot length is in agreement with recent atomic force microscopy pulling experiments. Calculated TPK radii of gyration point to a pore diameter of approximately 20 A, below which a translocated knotted protein might get stuck. TPK characteristics, however, may be sequence-specific: we find a different size and structural behavior in polyglycines, and, strikingly, a strong hydrogen bonding and water trapping capability of hydrophobic TPKs. Water capture and release is found to be controllable by the tightening force in a few cases. These mechanisms result in a sequence-specific "locking" and metastability of TPKs, which might lead to a blocking of knotted peptide transport at designated sequence positions. We observe that macroscopic tight 4(1)-knot structures are reproduced microscopically ("figure of eight" versus the "pretzel") and can be tuned by sequence, in contrast to mathematical predictions. Our findings may explain a function of knots in native proteins, challenge previous studies on macromolecular knots, and prove useful in bio- and nanotechnology.

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Section: Introductionmentioning

confidence: 99%

Sequence-Specific Size, Structure, and Stability of Tight Protein Knots

Dzubiella

2009

Biophysical Journal

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“…The interweaving of molecular strands in DNA, proteins, and natural and synthetic polymers significantly affects their mechanical, physical, and chemical properties. The presence of knots in proteins can increase stability and improve function and has provided insights into the mechanisms of protein folding. , Knots have been tied in biopolymers with optical tweezers and can also be formed from surfactant nanotubes and chiral nematic colloids . For synthetic chemists the key challenge in the synthesis of entwined and interlocked molecular structures is the generation and linking (with the correct connectivity) of crossing points .…”

Section: Introductionmentioning

confidence: 99%

Pentameric Circular Iron(II) Double Helicates and a Molecular Pentafoil Knot

et al. 2012

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We report on the synthesis of 11 pentameric cyclic helicates formed by imine condensation of alkyl monoamines with a common bis(formylpyridine)bipyridyl-derived building block and iron(II) and chloride ions. The cyclic double-stranded helicates were characterized by NMR spectroscopy, mass spectrometry, and in the case of a 2,4-dimethoxybenzylamine-derived pentameric cyclic helicate, X-ray crystallography. The factors influencing the assembly process (reactant stoichiometry, concentration, solvent, nature and amount of anion) were studied in detail: the role of chloride in the assembly process appears not to be limited to that of a simple template, and larger circular helicates observed with related tris(bipyridine) ligands with different iron salts are not produced with the imine ligands. Using certain chiral amines, pentameric cyclic helices of single handedness could be isolated and the stereochemistry of the helix determined by circular dichroism. By employing a particular diamine, a closed-loop molecular pentafoil knot was prepared. The pentafoil knot was characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography, confirming the topology and providing insights into the reasons for its formation.

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“…Mathematicians and physicists have taken a keen interest in understanding the formation and topology of knots and tangles. To spontaneously form a knot, a long and flexible string with a certain excluded volume and bending stiffness has to be given enough energy to move around and explore its surroundings [31]. For very small strings, like polymer chains, thermal energy is sufficient to reptate and entangle the molecules [7].…”

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confidence: 99%

Tangling of Tethered Swimmers: Interactions between Two Nematodes

et al. 2014

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The tangling of two tethered microswimming worms serving as the ends of "active strings" is investigated experimentally and modeled analytically. C. elegans nematodes of similar size are caught by their tails using micropipettes and left to swim and interact at different separations over long times. The worms are found to tangle in a reproducible and statistically predictable manner, which is modeled based on the relative motion of the worm heads. Our results provide insight into the intricate tangling interactions present in active biological systems.

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The tangled web of self-tying knots

Cited by 8 publications

References 19 publications

Sequence-Specific Size, Structure, and Stability of Tight Protein Knots

Sequence-Specific Size, Structure, and Stability of Tight Protein Knots

Pentameric Circular Iron(II) Double Helicates and a Molecular Pentafoil Knot

Tangling of Tethered Swimmers: Interactions between Two Nematodes

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