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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
20 ail suggests that ClpXP tightens the trefoil knot against GFP, which prevents GFP unfolding.
21 ] for the folding of the [Formula: see text]-knotted alpha-haloacid dehalogenase (DehI) protein, we i
22 btain different RT-PCR patterns for an ssRNA knot and circle of the same sequence.
23                                    Both root-knot and cyst nematodes are endoparasites that have co-e
24      Sedentary endoparasitic nematodes, root-knot and cyst nematodes in particular, as well as gall-i
25 hytoplasma, rust fungi, Ustilago smuts, root knot and cyst nematodes, and gall midges.
26 t with two signaling centers: the initiation knot and enamel knot.
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
30 d to define the relationship between Henry's knot and the plantar nerves.
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
34                                              Knots and links have been conjectured to play a fundamen
35                                Although both knots and open circular helicates self-assemble under th
36 llects information about proteins which form knots and other entangled structures.
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
43           In achiral liquid crystals, dopant knotted and unknotted strands induce supramolecular heli
44                                       Though knotting and entanglement have been observed in DNA and
45 dynamic switching achievable through in situ knotting and unknotting events.
46                 Here we demonstrate that the knotting and unknotting of a molecular strand can be use
47 to six Hopf and two Solomon links, a trefoil knot, and a [3]catenate.
48 d a (Fe(II))(5)-coordinated pentafoil (5(1)) knot are found to selectively transport anions across ph
49                                The composite knots are assembled by combining two entanglement syntho
50                                  Equilibrium knots are common in biological polymers-their prevalence
51                            The properties of knots are exploited in a range of applications, from sho
52                                     Although knots are found in DNA and proteins(2), and form randoml
53                                              Knots are intricate structures that cannot be unambiguou
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                                              Knots are remarkable topological features in nature.
57                                        These knots are robust and topologically distinct from the hos
58 n which the topological properties of framed knots are used in conjunction with prime factorization t
59                 By using a constructed ssRNA knot as a highly sensitive topological probe, we find th
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
62 l loops and basal constriction around enamel knot at the center of the cap.
63           Linear spline models with a single knot at time of switch accounted for nonlinear trends.
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
66 systematic investigation of the influence of knotting at the molecular level.
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
71         These results support that a protein knot can be formed during a single cooperative step of f
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
75  tensioning and sliding of the translocating knotted chains.
76               Despite possessing the trefoil knot characteristic of SPOUT enzymes, Trm10 does not sha
77                                    Our nodal knot circuits can be characterized with impedance measur
78                                    The MXene-knotted CNT composite electrodes achieve high capacitanc
79       The large, knot-like structures in the knotted CNTs prevent the usual restacking of the Ti(3)C(
80  MXene Ti(3)C(2) by using specially designed knotted CNTs.
81 ot crossing number <m>, a natural measure of knot complexity and, correspondingly, we find E C to be
82 atural product which possess a unique lariat knot conformation.
83 se in writhe (topological strain) in the new knotted conformation.
84                                              Knots contain both at once a stable core as well as movi
85 e note a potential source of bias insofar as knotted contours may be more difficult to reliably resol
86     Interestingly, if the linker between the knot core of MJ0366 and GFP is longer than 36 residues,
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
93 a regime of open curves in which the virtual knotting description is likely to be important.
94 roteins and the most deeply embedded protein knot discovered so far.
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
97 ted membrane proteins and argue that a novel knotted DNA-binding protein constitutes a new fold.
98 we find E C to be directly related to <m> of knotted DNA.
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
102                  The resolved metal-free 819 knot enantiomers have pronounced features in their circu
103 free terminus, or one in which the tightened knot enters the translocation pore of ClpXP.
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
112       Yet, little is known about spontaneous knot formation in a polypeptide chain-an event that can
113 lue, indicating that the free energy cost of knot formation is of entropic origin.
114 oaches have been used to investigate protein knot formation.
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
118 ower for the analogous closed-loop pentafoil knot (&gt;60 days).
119                                              Knotting has been previously identified in protein backb
120 y been associated with the inhibitor cystine knot (ICK) fold.
121 RTX-Preg1a, exhibiting an inhibitory cystine knot (ICK) motif, and N-BUTX-Ptr1a, a short scorpion-CSa
122 d to adopt a well-defined inhibitory cystine knot (ICK) scaffold structure.
123           Finally, we have also discovered a knot in an artificially designed protein structure.
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
126 ,4), methods for tying(5) different sorts of knots in a synthetic nanoscale strand are lacking.
127  walls in the form of localized polarization knots in conventional optical fibres.
128                              The presence of knots in crystallographic structures of proteins have st
129              Starting with Gauss and Kelvin, knots in fields were postulated to behave like particles
130 oduce energetically stable, micrometer-sized knots in helical fields of chiral liquid crystals.
131                    The statistics of virtual knots in protein chains are compared with those of open
132                                              Knots in proteins are hypothesized to make them resistan
133                                              Knots in proteins are increasingly being recognized as a
134          Twenty years after their discovery, knots in proteins are now quite well understood.
135 r understanding the possible implications of knots in proteins for cellular degradation.
136              Recently, tying isolated vortex knots in the complex optical field has been realized.
137                                              Knots in the human genome would greatly impact diverse c
138 long to the SpoU-TrmD family contain trefoil knots in their backbone fold.
139 ysis to determine if a genomic trajectory is knotted in the setting of experimental noise.
140                             The existence of knotting in a filament naturally affects its configurati
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
143                               Momentum space knots, in particular, have been elusive due to their req
144            These observations suggest that a knot-induced stall during degradation of multidomain pro
145 exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose deg
146 owever, how to construct the acoustic vortex knot is still an unknown problem.
147   We further investigate the case in which a knot is tied along the chromatin fibre, and find that th
148  topology, which means that only one type of knot is usually possible.
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
152                                   The large, knot-like structures in the knotted CNTs prevent the usu
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 inuation of PrEP, with age included as a one-knot linear spline.
156 etathesis (RCM) then affords the closed-loop knot, locking the topology.
157                                          The knot loops form the S-adenosyl-methionine (SAM)-binding
158 in knots as evidence that particular protein knots may fold according to specific pathways from our t
159                                              Knots may ultimately prove just as versatile and useful
160  the evolutionary origin of a novel class of knotted membrane proteins and argue that a novel knotted
161                                  The cystine-knot miniproteins present in tomato fruit (TCMPs) have b
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
167 mino acid-long cyclic backbone and a cystine knot motif.
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
170                Here, we report that the root-knot nematode (RKN) Meloidogyne incognita induces the sy
171 de (BCN), Heterodera schachtii, and the root-knot nematode (RKN), Meloidogyne incognita.
172 otypes using root tissue harvested from root-knot nematode infected plants at 0, 3, 7 days after inoc
173                                         Root-knot nematode is a very destructive pathogen, to which m
174 t nematode Heterodera schachtii and the root-knot nematode Meloidogyne incognita.
175 ibility to H. schachtii, but not to the root-knot nematode Meloidogyne incognita.
176           In this study, a total of 244 root-knot nematode populations from various hosts from 39 cou
177                           Resistance to root-knot nematode was introgressed into cultivated peanut Ar
178                                         Root-knot nematodes (Meloidogyne spp.) are the most common ma
179                                         Root-knot nematodes (RKN) such as Meloidogyne spp. are among
180 sm by which plants defend against plant root-knot nematodes (RKNs) is largely unknown.
181                                         Root knot nematodes (RKNs) penetrate into the root vascular c
182 ided and evolutionary trends within the root-knot nematodes are discussed.
183                                Cyst and root-knot nematodes are obligate parasites of economic import
184  feeding sites induced by both cyst and root-knot nematodes are surrounded by endodermis during early
185 stainable management strategies against root-knot nematodes in Arkansas.
186                           Both cyst and root-knot nematodes induce specialized long-term feeding stru
187 ression analysis provides evidence that root-knot nematodes modulate biological pathways involved in
188                                     The root-knot nematodes of the genus Meloidogyne are highly adapt
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
192 ry endoparasites that includes cyst and root-knot nematodes.
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
195                                    Molecular knots of high symmetry have previously been synthesized
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
199 experiments aimed at probing the spontaneous knotting of biopolymers.
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
203           In this study, the impact of olive knot (OK) disease caused by the bacteria Pseudomonas sav
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
211                                      Cystine-knot peptides are attractive templates in drug discovery
212 to enhance the cytosolic delivery of cystine-knot peptides.
213      Our results indicate that these cystine knot PET tracers may have potential utility in multiple
214 lding mechanisms for the [Formula: see text]-knotted phytochromes and the [Formula: see text]- and [F
215                                              Knots play a fundamental role in the dynamics of biologi
216      Although the potential of such cyclized/knot polymer architectures is far from being fulfilled,
217 DRP has led to the formation of new cyclized/knotted polymer structures.
218 y molecular dynamics simulations to generate knotted polymeric configurations having different length
219 se ratios should be useful in characterizing knotted polymers experimentally.
220 and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric c
221            We then compute E C for all these knotted polymers using the program ZENO and find that th
222 the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the
223 the DNA molecule, consistent with a constant knotting probability per unit length.
224                    Results of experiments on knotted protein fusions with a highly stable domain show
225  we characterized the effects of the trefoil-knotted protein MJ0366 from Methanocaldococcus jannaschi
226  that ClpXP can easily degrade a deeply 3(1)-knotted protein.
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
230        Therefore, we conclude that naturally knotted proteins cannot attain their knot randomly in th
231                                          How knotted proteins fold has remained controversial since t
232  a shallow 3(1) knot, it cannot degrade 5(2)-knotted proteins if degradation is initiated at the C-te
233                     Mechanical stretching of knotted proteins is also of importance for understanding
234 roversial since the identification of deeply knotted proteins nearly two decades ago.
235 ly published work on the degradation of 5(2)-knotted proteins, our results show that the ClpXP machin
236 [Formula: see text]- and [Formula: see text]-knotted proteins.
237 nitude close to the energy cost of forming a knot randomly in the denatured state.
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
243 ay between topology and mechanics in elastic knots remains poorly understood.
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.
249  by the knot translocation velocity than the knot size.
250 d into topologically complex shapes, such as knots, slipknots or complex lassos.
251                                 Paradigmatic knotted solitons, Hopfions, that are characterized by to
252 f topologies which we quantify in terms of a knot spectrum and its scaling law.
253 d mass spectrometry and the chirality of the knot stereoisomers compared by circular dichroism.
254 sion scores, error scores, leak volumes, and knot tensile strengths.
255 ncreasingly useful for chemists to adopt the knot terminology employed by other disciplines.
256                  Links are generalization of knots, that consist of several components.
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.
261 ium structure of DNA knots, without spurious knot tightening and sliding.
262 nding/unwinding in helical propensity as the knot tightens to secure the SAM cofactor.
263 onstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomia
264 the way for the synthesis of other molecular knot topologies and to woven polymer materials.
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
267                                          The knot topology affects the chemical properties of the str
268                                    This 7(4) knot topology corresponds to that of an endless knot, wh
269 owever, how a protein substrate containing a knotted topology affects this process remains unknown.
270 derstand allosteric effects modulated by the knotted topology.
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
273 nsform an unknotted trajectory into a highly knotted trajectory and vice versa.
274 nce of two quantitatively different modes of knot translocation through the nanopores, involving very
275  obstruction event is more controlled by the knot translocation velocity than the knot size.
276  rather two qualitatively different modes of knot translocation.
277                          Tying the molecular knot transmits information regarding asymmetry across le
278 rrors and duration on 5 basic robotic tasks (knot tying, continuous suturing, cutting, dissection, an
279                     Participants completed a knot-tying task within a collective reward ("cooperation
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
282 crossing number values m for a wide class of knot types relevant to the real DNA.
283 rently known protein knot types and predicts knot types that might be identified in the future.
284 range of applications, from shoelaces to the knots used for climbing, fishing and sailing(1).
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.
287                     The results suggest that knotted vortex structures are generic in complex three-d
288 between the medial plantar nerve and Henry's knot was 5.96 mm (range, 3.34 to 7.84, SD = 1.12).
289        The first synthetic molecular trefoil knot was prepared in the late 1980s.
290 e domain protein harboring a shallow trefoil knot, we allow the protein to refold from either the kno
291                                The composite knots were characterized by (1)H and (13)C NMR spectrosc
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
296 inks-entangled structures, more complex than knots, which consist of several components.
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
300 al realization of structures known as framed knots within optical polarization fields.
301 rs that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding.

 
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