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1 es in degrading a 52 knot compared with a 31 knot.
2 erting it from a knot to a different type of knot.
3 knot types formed by subchains of the global knot.
4 ugh not as compact as, e.g., the synchrotron knot.
5 n the medial plantar nerve (MPN) and Henry's knot.
6 uding some not traditionally associated with knots.
7 Long DNA molecules can self-entangle into knots.
8 of non-planar closed folds including several knots.
9 l or pentafoil, or even of more exotic torus knots.
10 ed chromosome structures are largely free of knots.
11 ositions of subknots in the analyzed protein knots.
12 nslocation of 10-kbp-long DNA rings that are knotted.
13 and fold types of proteins with non-trivial knotting.
14 peronin stabilizes interactions that promote knotting.
15 10(10) M(-1) in acetonitrile (for pentafoil knot [2.Cl](PF6)9), making these topologically complex h
17 physical entanglements in polymer networks, knots along polymer chains, and rotaxanes in sliding rin
20 er, our results expand membership of cystine knot alpha-amylase inhibitors in the Apocynaceae family
23 These and the earlier discovery of a trefoil knot also suggest that the number of rigid components in
25 ne--a molecular Solomon link and a pentafoil knot--also self-sort, but up to two of the Solomon-link-
28 ogically active C-C-CC-C-C inhibitor cystine knot and CC-C-C motifs (168 and 44 toxins, respectively)
33 n on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways co
34 planar graph, the topologically non-trivial knots and catenanes represent some of chemistry's most c
36 on factor Foxi3 inhibits formation of enamel knots and cervical loops and thus the differentiation of
37 standing how Topo IV can unknot right-handed knots and decatenate right-handed catenanes without acti
40 constituent particles shaped as freestanding knots and handlebodies of different genus, have been rec
41 ere we show that single-stranded DNA (ssDNA) knots and links can be created by utilizing the inherent
43 ew of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tan
44 s a brief introduction to the mathematics of knots and related topological concepts in the context of
49 ments, we have investigated the mechanism of knotting and folding for two bacterial trefoil-knotted m
50 , including fibers, rings, tubes, catenanes, knots, and cages, have shown that the quaternary structu
53 se of linear molecules, we also observe that knots are able to slide out on application of high drivi
55 despite their being open curves in which the knots are not mathematically well defined; knotting can
59 re, we estimate that the majority of the DNA knots are tight, with remarkably small sizes below 100 n
63 tically to identify, characterise and create knots, as well as to understand and predict their physic
65 inear regression with 2 linear splines and a knot at January 2015 was used to compare the slope of th
66 lows undistorted propagation of polarization knots at a rate of 28 GHz along a 10 km length of normal
68 he C=C linkages topologically connect pyrene knots at regular intervals into a 2D lattice with pi con
70 esidues, ClpXP tightens and translocates the knot before it reaches GFP, enabling the complete unfold
71 e demonstrate the use of a constructed ssDNA knot both to probe the topological conversion catalysed
72 olecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry
73 nt superluminal motions, and the ejection of knots (bright components) from standing shocks in the je
74 rase IV, supercoiled DNA relaxation, and DNA knotting but not intermolecular reactions such as decate
76 restrictions imposed on molecular strands by knotting can impart significant physical and chemical pr
77 e knots are not mathematically well defined; knotting can only be identified by closing the termini o
85 ot crossing number <m>, a natural measure of knot complexity and, correspondingly, we find E C to be
88 croscopy (AFM) image of individual molecular knots, confirmed the formation of the resulting trefoil
90 functionals have been related to the average knot crossing number <m>, a natural measure of knot comp
91 different length and stiffness, and minimum knot crossing number values m for a wide class of knot t
92 tic routes to all but the simplest molecular knots currently prevents systematic investigation of the
98 a comprises two homologous inhibitor cystine knot domains separated by a short, structurally well-def
99 n of the tooth signalling centre, the enamel knot (EK), which maintains dental mesenchymal condensati
100 enerated radicals are confined on the pyrene knots, enabling the formation of a paramagnetic carbon s
104 enables two-step assembly of a molecular 819 knot featuring eight nonalternating crossings in a 192-a
105 The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits user
108 We study the percentage of molecules with knots for DNA molecules of up to 166 kilobase pairs in l
112 selective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer wit
114 physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain mole
119 complicated for incorporation into proteins, knots have been identified in the native fold of a growi
120 number of proteins that contain topological knots have been identified over the past two decades; ho
121 regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from eith
122 n comprises a well-defined inhibitor cystine knot (ICK) backbone region and a flexible C-terminal tai
125 l preformed expanded polytetrafluoroethylene knot implantation device (Harpoon TSD-5) designed to tre
127 that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 12
129 asure a significantly larger size for the 52 knot in the unfolded state that can be further tightened
130 s can be used to directly observe individual knots in both linear and circular single DNA molecules o
137 We introduce a new method for resolving knotting in open curves using virtual knots, which are a
139 e disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by sub
140 es and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associ
142 We further investigate the case in which a knot is tied along the chromatin fibre, and find that th
145 nknotted polypeptide chain thereby promoting knotting is unlikely, and we propose two alternatives: (
146 ynthesize dimers of integrin-binding cystine knot (knottin) miniproteins with low-picomolar binding a
149 class the Pierced Lasso Bundle (PLB) and the knot-like threaded structural motif a Pierced Lasso (PL)
151 ndary genes BLADE-ON-PETIOLE1/2 (BOP1/2) and KNOTTED-LIKE FROM ARABIDOPSIS THALIANA6 (KNAT6) together
152 including transcription factors such as the KNOTTED-LIKE HOMEOBOX (KNOX) genes, the hormone auxin, a
154 e propose that SHOOT MERISTEMLESS, a class I KNOTTED-LIKE HOMEOBOX gene, is likely to play a role in
158 e anterior/posterior boundary, thus blocking KNOT-mediated repression of EGFR activity and preventing
165 diverse stresses such as water deficit, root-knot nematode (RKN) infection, and UV exposure, with an
166 anic compounds used by the subterranean root-knot nematode (RKN) Meloidogyne incognita for host locat
168 otypes using root tissue harvested from root-knot nematode infected plants at 0, 3, 7 days after inoc
170 nction increases resistance against the root-knot nematode Meloidogyne javanica and suggests a potent
176 ression analysis provides evidence that root-knot nematodes modulate biological pathways involved in
178 N in a way similar to that reported for root-knot nematodes, but opposite to that suggested for the s
183 6 kilobase pairs in length and find that the knotting occurrence rises with the length of the DNA mol
184 that the threading event that creates the 52 knot occurs during these steps, suggesting that there is
186 se of only (R,R)-1 leads solely to a trefoil knot of Lambda-handedness, whereas (S,S)-1 forms the Del
187 t stages of a collision with a slower-moving knot of speed (1.8 +/- 0.5)c just downstream, resulting
188 tions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned f
191 We introduce disk matrices which encode the knotting of all subchains in circular knot configuration
194 , we experimentally reveal the impact of the knot on the landscape, the origin of the bistable nature
195 impair its folding-and about the effect of a knot on the stability and folding kinetics of a protein.
197 n the viewing angle of the observed emitting knots or jet regions have also been suggested as an expl
198 itions in the interwound portions and in the knotted or catenated portions of the studied molecules.
200 nd to adopt the so-called "inhibitor cystine knot" or "knottin" fold stabilized by three disulfide bo
201 sociated with formation of either a 31 or 52 knot, or a step closely associated with it, significantl
202 l and electrical properties and can be bent, knotted, or woven into flexible electronic textiles.
203 elf-assembled topological superstructures of knotted particles linked by nematic fields, in topologic
204 or both modes the pore obstruction caused by knot passage has a brief duration and typically occurs a
206 he expected changes in the properties of the knotted polymer compared to a linear analogue, for examp
207 is reported for the production of a trefoil knotted polymer from a copper(I)-templated helical knot
210 y molecular dynamics simulations to generate knotted polymeric configurations having different length
212 and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric c
216 perimental techniques for observing such DNA knots (primarily gel electrophoresis) are limited to bul
218 of electrons into topologically non-trivial knots-producing protected surface states with anomalous
219 egy could be used to design folding of other knotted programmable polymers such as RNA or proteins.
221 we characterized the effects of the trefoil-knotted protein MJ0366 from Methanocaldococcus jannaschi
222 ing topology of the unfolded state of the 52-knotted protein ubiquitin C-terminal hydrolase isoenzyme
223 pe, the origin of the bistable nature of the knotted protein, and broaden the view of knot formation
224 uropeptide hormone consisting of two cystine-knot proteins (burs alpha and burs beta), responsible fo
225 ide mechanistic insights into the folding of knotted proteins both in vitro and in vivo, thus elucida
227 -terminus, C-terminus or both termini of the knotted proteins clearly demonstrate that threading of t
232 turally knotted proteins cannot attain their knot randomly in the unfolded state but must pay the cos
233 terestingly, for most of these proteins, the knotted region appears critical both in folding and func
234 mine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a kno
236 ew scheme, recovering and extending previous knotting results, and identifying topological interest i
237 tterned differentiation of cells into enamel knots, root-forming cervical loops and enamel-forming am
238 , the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many
239 along the chromatin fibre, and find that the knotted segment enhances local epigenetic order, giving
240 be principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated
244 nds can be accommodated within the pentafoil knot structure and are either incorporated or omitted de
245 y modified peptides (RiPPs), with a threaded knot structure that is formed by an isopeptide bond atta
246 GVIIJ[C24S] adopts an inhibitor cystine knot structure, with two antiparallel beta-strands stabi
248 aneous folding of a polypeptide chain into a knotted structure remains one of the most puzzling and f
249 becomes short on the confinement scale, the knotted structures change to practically unperturbed cho
252 lding block may translate into corresponding knot symmetry and could set the basis of a new strategy
253 the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot co
255 we report on a synthetic molecular pentafoil knot that allosterically initiates or regulates catalyze
257 al parameters to the conventional results of knot theory, which couple with the knot topology and int
259 the unfolded state but must pay the cost of knotting through contacts along their folding landscape.
262 t few years that more complex small-molecule knot topologies have been realized through chemical synt
263 umber and complexity of accessible molecular knot topologies increases, it will become increasingly u
266 esults of knot theory, which couple with the knot topology and introduce order into the phase diagram
268 owever, how a protein substrate containing a knotted topology affects this process remains unknown.
270 ion of pulling directions, we controlled the knotting topology of the unfolded state of the 52-knotte
271 m several venoms and characterized a cystine knot toxin called JZTx-27 from the venom of tarantula Ch
272 size parallel evolution of inhibitor cystine knot toxins from Araneomorphae and Mygalomorphae suborde
275 sed on the study of linear chains in which a knot type is associated to the chain by means of a spati
276 orm of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of
280 We compare the sets of observed subknots to knot types obtained by changing crossings in the classic
291 e curvature and torsion, double-stranded DNA knots were accessed by hybridizing and ligating the comp
292 s that are normally restricted to the enamel knots were expanded in the epithelium, and Sostdc1, a ma
293 olving knotting in open curves using virtual knots, which are a wider class of topological objects th
295 e design of new ways to synthesize molecular knots, which may prove, for instance, to be efficient ca
298 he sets of subknots observed in open protein knots with the subknots observed in the ideal configurat
299 res and colloidal particles, such as trefoil knots, with 'frozen' orientational order of flakes.
300 sts that G-quadruplex structures may act as 'knots' within genomic DNA, and it has been hypothesized
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