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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
16 ail suggests that ClpXP tightens the trefoil knot against GFP, which prevents GFP unfolding.
17  physical entanglements in polymer networks, knots along polymer chains, and rotaxanes in sliding rin
18                                      Cystine knot alpha-amylase inhibitors are cysteine-rich, proline
19           Similar to other knottins, cystine knot alpha-amylase inhibitors are highly resistant to de
20 er, our results expand membership of cystine knot alpha-amylase inhibitors in the Apocynaceae family
21                   Here, we show that cystine knot alpha-amylase inhibitors named alstotides discovere
22 nds, characteristics shared by other cystine knot alpha-amylase inhibitors.
23 These and the earlier discovery of a trefoil knot also suggest that the number of rigid components in
24                    Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the
25 ne--a molecular Solomon link and a pentafoil knot--also self-sort, but up to two of the Solomon-link-
26  native (homologous) FRT sites are a 3-noded knot and a 4-noded catenane, respectively.
27  "non-homologous" FRT partners are a 4-noded knot and a 5-noded knot, respectively.
28 ogically active C-C-CC-C-C inhibitor cystine knot and CC-C-C motifs (168 and 44 toxins, respectively)
29 btain different RT-PCR patterns for an ssRNA knot and circle of the same sequence.
30                        A molecular pentafoil knot and doubly and triply entwined [2]catenanes based o
31 ever, the mechanism as to how these proteins knot and fold efficiently remains unclear.
32 d to define the relationship between Henry's knot and the plantar nerves.
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
35 and its expression was reduced in the enamel knots and cervical loops and in ameloblasts.
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
38              Bmp4, a known inducer of enamel knots and dental epithelial differentiation, downregulat
39                            The importance of knots and entanglements in biological systems is increas
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
42            Nematic braids are reconfigurable knots and links formed by the disclination loops that en
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
45                                          The knots and their isomeric unknot macrocycles were charact
46 ed, with data modeled with the use of spline knots and visualized via spaghetti plots.
47                                              Knotted and solitonic fields and defects were also obtai
48                                       Though knotting and entanglement have been observed in DNA and
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
51                                              Knots appear in chemistry, not only in synthetic molecul
52                                          The knot architecture is crucial to this function because it
53 se of linear molecules, we also observe that knots are able to slide out on application of high drivi
54                                              Knots are natural topologies of chains.
55 despite their being open curves in which the knots are not mathematically well defined; knotting can
56                                      The DNA knots are observed as short spikes in the nanopore curre
57                                       Enamel knots are signaling centers that define the positions of
58                                              Knots are some of the most remarkable topological featur
59 re, we estimate that the majority of the DNA knots are tight, with remarkably small sizes below 100 n
60               Despite the common belief that knots are too complicated for incorporation into protein
61 an potentially arise from tying molecules in knots are, for the most part, unclear.
62                 By using a constructed ssRNA knot as a highly sensitive topological probe, we find th
63 tically to identify, characterise and create knots, as well as to understand and predict their physic
64 downstream, resulting in brightening of both knots--as seen in the most recent epoch of imaging.
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
67                          Linear splines with knots at each policy change were used in survey-weighted
68 he C=C linkages topologically connect pyrene knots at regular intervals into a 2D lattice with pi con
69 systematic investigation of the influence of knotting at the molecular level.
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
75 were not expressed in this mislocated enamel knot, but remained at the tip of the enamel organ.
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
78  tensioning and sliding of the translocating knotted chains.
79               Despite possessing the trefoil knot characteristic of SPOUT enzymes, Trm10 does not sha
80                       The C-terminal cystine knot (CK) (CTCK) domain in von Willebrand factor (VWF) m
81 ulfide bonds between the C-terminal cysteine knot (CK) domains of 2 monomers.
82 aired nucleoside that stacks onto the pseudo-knot-closing Watson-Crick base pair.
83 the potential difficulties in degrading a 52 knot compared with a 31 knot.
84 round the lanthanide ion to form an overhand knot complex of single handedness.
85 ot crossing number <m>, a natural measure of knot complexity and, correspondingly, we find E C to be
86                                          The knotting complexity of the cataloged proteins is present
87 de the knotting of all subchains in circular knot configurations.
88 croscopy (AFM) image of individual molecular knots, confirmed the formation of the resulting trefoil
89     Interestingly, if the linker between the knot core of MJ0366 and GFP is longer than 36 residues,
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
93 ally important plant parasites, such as root-knot, cyst, and lesion nematodes.
94        Here we show that the mobility of DNA knots depends crucially and subtly on the physical prope
95 a regime of open curves in which the virtual knotting description is likely to be important.
96 by changing crossings in the classical prime knot diagrams.
97 we find E C to be directly related to <m> of knotted DNA.
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
101                  The resolved metal-free 819 knot enantiomers have pronounced features in their circu
102           Subsequent joining of the overhand knot end groups by ring-closing olefin metathesis afford
103                             CAP-D3 represses KNOT expression in cells immediately adjacent to the ant
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
106 protein or polymer chains and generate their knotting fingerprints.
107 ke structure, including the typical cysteine-knot fold, as evidenced by CD spectroscopy.
108    We study the percentage of molecules with knots for DNA molecules of up to 166 kilobase pairs in l
109 the knotted protein, and broaden the view of knot formation as uniquely decoupled from folding.
110       Yet, little is known about spontaneous knot formation in a polypeptide chain-an event that can
111 lue, indicating that the free energy cost of knot formation is of entropic origin.
112 selective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer wit
113 ncrease with its length, and a wide gamut of knots from standard tabulations occur.
114 physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain mole
115           Tangles of string typically become knotted, from macroscopic twine down to long-chain macro
116                 Given the intricacies of the knotted geometry, the interplay between a protein's fold
117 s the buried chromophore through distinctive knot, hairpin, and helical spine features.
118                                              Knotting has been previously identified in protein backb
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
123 roscopy revealed a classic inhibitor cystine knot (ICK) motif.
124 d to adopt a well-defined inhibitory cystine knot (ICK) scaffold structure.
125 l preformed expanded polytetrafluoroethylene knot implantation device (Harpoon TSD-5) designed to tre
126 s affords a single enantiomer of the trefoil knot in 90% yield.
127  that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 12
128  of Bmp4, p21, and Shh in the primary enamel knot in the Osr2(-/-)Runx2(-/-) compound mutants.
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
131  walls in the form of localized polarization knots in conventional optical fibres.
132                    The statistics of virtual knots in protein chains are compared with those of open
133          Twenty years after their discovery, knots in proteins are now quite well understood.
134 r understanding the possible implications of knots in proteins for cellular degradation.
135 port observations of a collision between two knots in the jet of nearby radio galaxy 3C 264.
136                             The existence of knotting in a filament naturally affects its configurati
137      We introduce a new method for resolving knotting in open curves using virtual knots, which are a
138            These observations suggest that a knot-induced stall during degradation of multidomain pro
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
141 robed by computing the distribution of their knot invariants.
142   We further investigate the case in which a knot is tied along the chromatin fibre, and find that th
143                                   Folding of knots is encoded by the arrangement of modules of differ
144        The probability that a vortex loop is knotted is found to increase with its length, and a wide
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
147 Norrin (Norrie Disease Protein) is a cystine-knot like growth factor.
148  that reinforce existing structure or induce knot-like conformations.
149 class the Pierced Lasso Bundle (PLB) and the knot-like threaded structural motif a Pierced Lasso (PL)
150  including multiple orthologs of Arabidopsis KNOTTED-like Arabidopsis 2/6.
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
153                                      Class I KNOTTED-LIKE HOMEOBOX (KNOX) proteins regulate developme
154 e propose that SHOOT MERISTEMLESS, a class I KNOTTED-LIKE HOMEOBOX gene, is likely to play a role in
155 hat threading of the nascent chain through a knotting loop occurs via the C-terminus.
156                                              Knots may ultimately prove just as versatile and useful
157 ovides the first experimental evidence for a knotting mechanism.
158 e anterior/posterior boundary, thus blocking KNOT-mediated repression of EGFR activity and preventing
159 otting and folding for two bacterial trefoil-knotted methyltransferases.
160                                  The cystine-knot miniproteins present in tomato fruit (TCMPs) have b
161                     Our results suggest that knotting molecules may be a useful strategy for reducing
162 und in plant caleosins, along with a proline knot motif defined by only two proline residues.
163 de was consistent with an inhibitory cystine knot motif.
164  prolines and three disulfides arranged in a knotted motif.
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
167 de (BCN), Heterodera schachtii, and the root-knot nematode (RKN), Meloidogyne incognita.
168 otypes using root tissue harvested from root-knot nematode infected plants at 0, 3, 7 days after inoc
169 ibility to H. schachtii, but not to the root-knot nematode Meloidogyne incognita.
170 nction increases resistance against the root-knot nematode Meloidogyne javanica and suggests a potent
171                           Resistance to root-knot nematode was introgressed into cultivated peanut Ar
172 dditional phloem-feeding insects and to root-knot nematodes (Meloidogyne spp.).
173                                         Root knot nematodes (RKNs) penetrate into the root vascular c
174                                         Root-knot nematodes (RKNs; Meloidogyne spp.) are plant parasi
175                                Cyst and root-knot nematodes are obligate parasites of economic import
176 ression analysis provides evidence that root-knot nematodes modulate biological pathways involved in
177                Plant-parasitic cyst and root-knot nematodes synthesize and secrete a suite of effecto
178 N in a way similar to that reported for root-knot nematodes, but opposite to that suggested for the s
179 on in roots infected by plant-parasitic root-knot nematodes.
180                             Entanglement and knots occur across all aspects of the physical world.
181              In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at
182                                    Molecular knots occur in DNA, proteins, and other macromolecules.
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
185 ve the threading of the chain to form the 52-knot occurs late on the folding pathway.
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
189  form topologically chiral molecular trefoil knots of single handedness.
190          MukB is known to be able to mediate knotting of a DNA ring, an intramolecular reaction.
191  We introduce disk matrices which encode the knotting of all subchains in circular knot configuration
192 experiments aimed at probing the spontaneous knotting of biopolymers.
193 ctivity towards cancer cells and distinctive knotting of DNA.
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.
196 efore been able to quantify the influence of knotting on its folding rate.
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.
199 of supercoiled DNA molecules that are either knotted or catenated.
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
205      Although the potential of such cyclized/knot polymer architectures is far from being fulfilled,
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
208 DRP has led to the formation of new cyclized/knotted polymer structures.
209 irmed the formation of the resulting trefoil knotted polymer.
210 y molecular dynamics simulations to generate knotted polymeric configurations having different length
211 se ratios should be useful in characterizing knotted polymers experimentally.
212 and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric c
213            We then compute E C for all these knotted polymers using the program ZENO and find that th
214                             Self-assembly of knotted polymers without breaking or forming covalent bo
215 d polymer from a copper(I)-templated helical knot precursor through ring expansion.
216 perimental techniques for observing such DNA knots (primarily gel electrophoresis) are limited to bul
217 the DNA molecule, consistent with a constant knotting probability per unit length.
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.
220 neration of a carbocation formed through the knot-promoted cleavage of a carbon-halogen bond.
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
226        Therefore, we conclude that naturally knotted proteins cannot attain their knot randomly in th
227 -terminus, C-terminus or both termini of the knotted proteins clearly demonstrate that threading of t
228 indicating that even the folding pathways of knotted proteins have some plasticity.
229                     Mechanical stretching of knotted proteins is also of importance for understanding
230                               The folding of knotted proteins is on the timescale of minutes and thus
231 he polypeptide chain is threaded (as seen in knotted proteins).
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
235 RT partners are a 4-noded knot and a 5-noded knot, respectively.
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
241  by the knot translocation velocity than the knot size.
242 d into topologically complex shapes, such as knots, slipknots or complex lassos.
243  ligating the complementary strands with the knotted ssDNA templates.
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
247 15% of its amino acids and a deletion of the knot structure.
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
250 umber of proteins with topologically complex knotted structures has risen.
251 rality that results from the topology of the knots studied by circular dichroism.
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
254 ncreasingly useful for chemists to adopt the knot terminology employed by other disciplines.
255 we report on a synthetic molecular pentafoil knot that allosterically initiates or regulates catalyze
256                                              Knot theory is a branch of pure mathematics, but it is i
257 al parameters to the conventional results of knot theory, which couple with the knot topology and int
258           From the translocation time of the knot through the nanopore, we estimate that the majority
259  the unfolded state but must pay the cost of knotting through contacts along their folding landscape.
260 rotein structure before converting it from a knot to a different type of knot.
261 bles the transfer of helicity from links and knots to helical coils.
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
264                            The eight cystine knot topologies that are characterized by exclusively in
265                                          The knot topology and handedness were confirmed by NMR spect
266 esults of knot theory, which couple with the knot topology and introduce order into the phase diagram
267                It contains a complex Gordian knot topology formed by the polypeptide chain alone.
268 owever, how a protein substrate containing a knotted topology affects this process remains unknown.
269                              UCH-L1 has a 52-knotted topology.
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
273  obstruction event is more controlled by the knot translocation velocity than the knot size.
274  rather two qualitatively different modes of knot translocation.
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
277 he ideal configurations of the corresponding knot type.
278  of random configurations of the same global knot type.
279 ect circular knots into their subknots, i.e. knot types formed by subchains of the global knot.
280  We compare the sets of observed subknots to knot types obtained by changing crossings in the classic
281 -stabilized alpha/beta and inhibitor cystine knot types of fold.
282 crossing number values m for a wide class of knot types relevant to the real DNA.
283                               In many of the knot types we analyzed, the sets of subknots from the id
284 ts in random configurations of corresponding knot types.
285                     The results suggest that knotted vortex structures are generic in complex three-d
286 between the medial plantar nerve and Henry's knot was 5.96 mm (range, 3.34 to 7.84, SD = 1.12).
287 regions, whereas the spline model with 1 age knot was a better fit for 40 regions.
288                      The pseudo-D3-symmetric knot was employed as an asymmetric catalyst in Mukaiyama
289        The first synthetic molecular trefoil knot was prepared in the late 1980s.
290                    Compared with a simple 31 knot, we measure a significantly larger size for the 52
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
294 inks-entangled structures, more complex than knots, which consist of several components.
295 e design of new ways to synthesize molecular knots, which may prove, for instance, to be efficient ca
296                                     A bright knot with an apparent speed of (7.0 +/- 0.8)c, where c i
297 ess, whereas (S,S)-1 forms the Delta-trefoil knot with complete stereoselectivity.
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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