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1 tion joins together one end of each overhand knot.
2 ugh not as compact as, e.g., the synchrotron knot.
3 n the medial plantar nerve (MPN) and Henry's knot.
4 ling centers: the initiation knot and enamel knot.
5 s in the dynamics of the loops that form the knot.
6 es probed, the human genome is often free of knots.
7 e composition of fungal communities in olive knots.
8 time, reveal the existence of rare composite knots.
9 r strand enables it to be tied into multiple knots.
10 ance of nanopores in future investigation of knots.
11 ting the shape of biopolymers, including DNA knots.
12 -conjugation and electronic structure of the knots.
13 topologies such as Mobius, ribbon strips and knots.
14 amine the genome in vivo for the presence of knots.
15 f PE, with particular reference to syncytial knots.
16 nslocation of 10-kbp-long DNA rings that are knotted.
17 n unknot (0(1)) macrocycle, a trefoil (3(1)) knot(6-15), and a three-twist (5(2)) knot-were each sele
18 eed with stereoinduction: in the case of one knot, a lanthanide(III)-coordinated crossing pattern for
19 l to understanding the interplay between the knot, activation of the methyltransferase, and the impli
21 ] for the folding of the [Formula: see text]-knotted alpha-haloacid dehalogenase (DehI) protein, we i
27 view of the conformational mechanics of the knot and its relationship to the activation of the ligan
28 if of Celtic interlace, the smallest Chinese knot and one of the eight auspicious symbols of Buddhism
29 ssembly dynamics of an imine-based pentafoil knot and related pentameric circular helicates, each der
31 n on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways co
32 ith large-scale simulations of various nodal knots and an experiment which maps out the topological d
33 gs, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and co
37 ew of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tan
38 synthesis of imine-based pentafoil molecular knots and pentameric circular helicates despite, in prac
39 predict the relative mechanical stability of knots and tangles, in agreement with simulations and exp
40 ure and topology of individual helical field knots and the various hierarchical crystalline organizat
41 ith large statistics, we explore the complex knots and, for the first time, reveal the existence of r
42 ty of the native state with reference to the knotted and unknotted denatured state we find that knott
48 d a (Fe(II))(5)-coordinated pentafoil (5(1)) knot are found to selectively transport anions across ph
55 despite their being open curves in which the knots are not mathematically well defined; knotting can
58 n which the topological properties of framed knots are used in conjunction with prime factorization t
60 rint data from crystal structures of protein knots as evidence that particular protein knots may fold
61 inear regression with 2 linear splines and a knot at January 2015 was used to compare the slope of th
64 lows undistorted propagation of polarization knots at a rate of 28 GHz along a 10 km length of normal
65 he C=C linkages topologically connect pyrene knots at regular intervals into a 2D lattice with pi con
67 esidues, ClpXP tightens and translocates the knot before it reaches GFP, enabling the complete unfold
68 e demonstrate the use of a constructed ssDNA knot both to probe the topological conversion catalysed
69 olecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry
70 rase IV, supercoiled DNA relaxation, and DNA knotting but not intermolecular reactions such as decate
72 ties of the strand: whereas the tighter 5(2) knot can bind two different metal ions simultaneously, t
73 restrictions imposed on molecular strands by knotting can impart significant physical and chemical pr
74 e knots are not mathematically well defined; knotting can only be identified by closing the termini o
81 ot crossing number <m>, a natural measure of knot complexity and, correspondingly, we find E C to be
85 e note a potential source of bias insofar as knotted contours may be more difficult to reliably resol
87 functionals have been related to the average knot crossing number <m>, a natural measure of knot comp
88 different length and stiffness, and minimum knot crossing number values m for a wide class of knot t
89 tic routes to all but the simplest molecular knots currently prevents systematic investigation of the
90 resulted in the discovery of a new class of knotted cyclic peptides from the marine sponge Axinella
91 arboxylase, proteasomal subunit, or cysteine knot (defensin) protein; and the first report of a proka
92 t than the (Fe(II))(5)-coordinated pentafoil knot, derived from a cyclic pentamer of the same buildin
95 rom a functional point of view, most protein knots discovered so far are either enzymes or DNA-bindin
96 th the first of a unique structural class of knotted disulfide-rich peptides and defines a previously
99 a comprises two homologous inhibitor cystine knot domains separated by a short, structurally well-def
100 re, particularly of the glomerular capillary knot, dysregulation of nephrin and collagen IV, and ultr
101 enerated radicals are confined on the pyrene knots, enabling the formation of a paramagnetic carbon s
104 are often misdiagnosed as nematode-mediated knots, even by experts, because the gall symptoms in bot
105 enables two-step assembly of a molecular 819 knot featuring eight nonalternating crossings in a 192-a
106 ments with theory and simulations to analyze knotted fibers that change their color under mechanical
107 represents their complexity in the form of a knotting fingerprint, and presents many biological and g
108 nt strategies for the synthesis of molecular knots focus on twisting, folding and/or threading molecu
109 s confirm Taylor's twisted hairpin theory of knot folding for the [Formula: see text]-knotted protein
110 n, we introduce a topological description of knot folding that could describe pathways for the format
111 We study the percentage of molecules with knots for DNA molecules of up to 166 kilobase pairs in l
115 lding pathway based on the idea that a loose knot forms at a terminus and slides to its native positi
116 physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain mole
117 n the numerical simulation, we find that the knot function can be embedded into the acoustic field by
121 RTX-Preg1a, exhibiting an inhibitory cystine knot (ICK) motif, and N-BUTX-Ptr1a, a short scorpion-CSa
124 This record involved the participant tying a knot in ribbons worn under the clothing each time they h
125 that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 12
141 We introduce a new method for resolving knotting in open curves using virtual knots, which are a
142 ny knot; of opposite handedness for a square knot) in three synthetic steps: first, a CuAAC reaction
145 exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose deg
147 We further investigate the case in which a knot is tied along the chromatin fibre, and find that th
149 effect induced by the tying of the molecular knots is similar to that famously used to rotate a glass
150 easily degrade a protein with a shallow 3(1) knot, it cannot degrade 5(2)-knotted proteins if degrada
151 knotted proteins and the [Formula: see text]-knotted ketol-acid reductoisomerases and present alterna
154 e propose that SHOOT MERISTEMLESS, a class I KNOTTED-LIKE HOMEOBOX gene, is likely to play a role in
158 in knots as evidence that particular protein knots may fold according to specific pathways from our t
160 the evolutionary origin of a novel class of knotted membrane proteins and argue that a novel knotted
162 k reveals several novel structures including knotted mitochondrial proteins and the most deeply embed
163 slocate an entanglement from one region of a knotted molecular structure to another, resulting in an
164 insight into the topology of interlocked and knotted molecules, even when they exist in complex mixtu
165 model, including a previously unappreciated 'knotted' morphology to pathological vascular tufts, abno
166 eir head-to-tail cyclic backbone and cystine knot motif, which render them to be exceptionally stable
168 diverse stresses such as water deficit, root-knot nematode (RKN) infection, and UV exposure, with an
169 anic compounds used by the subterranean root-knot nematode (RKN) Meloidogyne incognita for host locat
172 otypes using root tissue harvested from root-knot nematode infected plants at 0, 3, 7 days after inoc
184 feeding sites induced by both cyst and root-knot nematodes are surrounded by endodermis during early
187 ression analysis provides evidence that root-knot nematodes modulate biological pathways involved in
189 sly reported related cyst nematodes and root-knot nematodes revealed a subset of esophageal gland rel
190 N in a way similar to that reported for root-knot nematodes, but opposite to that suggested for the s
191 lant responses to infection by cyst and root-knot nematodes, with a focus on the functions of microRN
193 6 kilobase pairs in length and find that the knotting occurrence rises with the length of the DNA mol
194 point-chiral centres folds into an overhand knot of single handedness upon coordination to lanthanid
196 ks of defined stereochemistry (here overhand knots of Lambda- or Delta-handed entanglement) is remini
197 ugh the use of lanthanide-complexed overhand knots of specific handedness as three-crossing "entangle
198 is quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing
200 eas topological assays based on Cre-mediated knotting of plasmid DNAs are consistent with a right-han
201 synthons (of the same chirality for a granny knot; of opposite handedness for a square knot) in three
202 ility to tie nanoscale chains into different knots offers opportunities to explore the modification o
204 impair its folding-and about the effect of a knot on the stability and folding kinetics of a protein.
205 n the viewing angle of the observed emitting knots or jet regions have also been suggested as an expl
206 allow the protein to refold from either the knotted or the unknotted denatured state to characterize
207 or both modes the pore obstruction caused by knot passage has a brief duration and typically occurs a
208 engineering and validation of a new cystine knot peptide (knottin) that selectively recognizes human
209 een velvet tarantula is an inhibitor cystine-knot peptide and selective antagonist of the human Nav1.
210 Recently, we demonstrated that the cystine-knot peptide EETI-II is internalized into cells and that
214 lding mechanisms for the [Formula: see text]-knotted phytochromes and the [Formula: see text]- and [F
218 y molecular dynamics simulations to generate knotted polymeric configurations having different length
220 and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric c
222 the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the
225 we characterized the effects of the trefoil-knotted protein MJ0366 from Methanocaldococcus jannaschi
227 uropeptide hormone consisting of two cystine-knot proteins (burs alpha and burs beta), responsible fo
228 of knot folding for the [Formula: see text]-knotted proteins and the [Formula: see text]-knotted ket
229 es of the degradation of both 3(1)- and 5(2)-knotted proteins by ClpXP using numerous constructs wher
232 a shallow 3(1) knot, it cannot degrade 5(2)-knotted proteins if degradation is initiated at the C-te
235 ly published work on the degradation of 5(2)-knotted proteins, our results show that the ClpXP machin
238 turally knotted proteins cannot attain their knot randomly in the unfolded state but must pay the cos
239 show the occurrence of both tight and loose knots, reconciling previous contradictory results from d
240 The primary outcome was change in number of knots (recorded leakage episodes) from recruitment to 24
241 g on the biophysical characterization of the knot region by NMR spectroscopy, we identify the SAM-bin
242 ealed that Myo6 and the transcription factor Knot regulate transient surges of microtubule polymeriza
244 mination of whether genomic trajectories are knotted remains challenging because small errors in the
245 ew scheme, recovering and extending previous knotting results, and identifying topological interest i
246 along the chromatin fibre, and find that the knotted segment enhances local epigenetic order, giving
247 nsistent with mechanisms in which either the knot simply slips along the polypeptide chain and falls
248 opy revealed that roseltide rT7 is a cystine-knotted, six-cysteine hevein-like cysteine-rich peptide.
257 d and unknotted denatured state we find that knotting the polypeptide chain of MJ0366 increase the fo
258 the identification of the so-called cysteine knots, the possibility to analyze all or a non-redundant
259 ynthesis of both molecular granny and square knots through the use of lanthanide-complexed overhand k
260 the unfolded state but must pay the cost of knotting through contacts along their folding landscape.
263 onstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomia
265 t few years that more complex small-molecule knot topologies have been realized through chemical synt
266 umber and complexity of accessible molecular knot topologies increases, it will become increasingly u
269 owever, how a protein substrate containing a knotted topology affects this process remains unknown.
271 m several venoms and characterized a cystine knot toxin called JZTx-27 from the venom of tarantula Ch
272 laborated knottin domains, as well as double-knot toxins, that likely evolved from a single ancestral
274 nce of two quantitatively different modes of knot translocation through the nanopores, involving very
278 rrors and duration on 5 basic robotic tasks (knot tying, continuous suturing, cutting, dissection, an
280 losed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta
281 the formation of all currently known protein knot types and predicts knot types that might be identif
285 perimentally the creation of acoustic vortex knots using metamaterials, with decoupled modulation of
286 e acoustic fields with Hopf link and trefoil knot vortex lines have been observed experimentally.
290 e domain protein harboring a shallow trefoil knot, we allow the protein to refold from either the kno
292 (3(1)) knot(6-15), and a three-twist (5(2)) knot-were each selectively prepared from the same molecu
293 ought to address is as follows: How does the knot, which constricts the backbone as well as forms the
294 t topology corresponds to that of an endless knot, which is a basic motif of Celtic interlace, the sm
295 olving knotting in open curves using virtual knots, which are a wider class of topological objects th
297 interlocked [2]catenane (Solomon link) and a knot with seven crossings in a 258-atom-long closed loop
298 essarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully recipr
299 th free and bound homologs indicate that the knot within the polypeptide backbone plays a significant
301 rs that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding.