Статистические свойства трехмерных полиэдров Клейна

2020 ◽  
Vol 211 (5) ◽  
pp. 78-97
Author(s):  
Андрей Анатольевич Илларионов ◽  
Andrei Anatol'evich Illarionov
Keyword(s):  
Gamma S

Пусть $\Gamma$ - $s$-мерная решетка из $\mathbb R^s$. Выпуклые оболочки ненулевых узлов из $\Gamma$, содержащихся в каждом ортанте, называются полиэдрами Клейна решетки $\Gamma$. Эта конструкция была введена Ф. Клейном (1895 г.) в связи с обобщением классического алгоритма непрерывных дробей на многомерный случай. В. И. Арнольд сформулировал ряд задач о статистических и геометрических свойствах полиэдров Клейна. В двумерном случае соответствующие результаты вытекают из теории непрерывных дробей. В работе выводится асимптотическая формула для среднего значения $f$-вектора (количество граней, ребер и вершин) трехмерных полиэдров Клейна. Усреднение проводится по полиэдрам Клейна трехмерных целочисленных решеток с определителем из отрезка $[1,R]$, где $R$ - растущий параметр. Библиография: 27 названий.

scholarly journals The role of ATP in in vitro vaccinia virus RNA synthesis effects of AMP-PNP and ATP gamma S.

1980 ◽  
Vol 255 (11) ◽  
pp. 5396-5403
Author(s):  
S. Shuman ◽  
E. Spencer ◽  
H. Furneaux ◽  
J. Hurwitz
Keyword(s):  
Vaccinia Virus ◽  
Rna Synthesis ◽  
Virus Rna ◽  
Gamma S

The neuropeptide FMRFa both inhibits and enhances the Ca2+ current in dissociated Helix neurons via independent mechanisms

1991 ◽  
Vol 65 (6) ◽  
pp. 1517-1527 ◽  
Author(s):  
J. L. Yakel
Keyword(s):  
G Protein ◽  
Cell Voltage ◽  
Inhibitory Response ◽  
Central Neurons ◽  
S 100 ◽  
Helix Neurons ◽  
20 Nm ◽  
Gamma S ◽  
Ca2 Channels ◽  
Rate Of Activation

1. The modulation of the voltage-activated Ca2+ current by the neuropeptide Phe-Met-Arg-Phe-NH2 (FMRFa) was investigated in dissociated central neurons from Helix aspersa using whole-cell voltage-clamp recording techniques. External Ba2+ was always used as the charge carrier in this study, and the intracellular Ca2+ concentration was buffered to 20 nM with ethylene glycol-bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA). 2. Run-down of the Ca2+ currents was not a problem as long as the neurons were dialyzed with a patch electrode filling solution containing ATP (1 or 2 mM). In ATP-dialyzed neurons, the rate of inactivation of the calcium current increased with time without any significant change in the rate of activation. However, when neurons were dialyzed with guanosine 5'-O-(3-thiotriphosphate) (GTP gamma S; 100 microM; with ATP), the rate of inactivation decreased with time. There was no effect of GTP gamma S on the rate of activation of the Ca2+ current. This suggests that guanosine 5'-triphosphate (GTP)-binding proteins (G proteins) are able to modulate the rate of inactivation of the Ca2+ current in Helix neurons. 3. FMRFa both decreased and enhanced the amplitude of the Ca2+ current in these neurons. This inhibition was observed in most neurons, while the enhancement was observed in 20% of the neurons. Although the enhancement usually was preceded by the inhibitory response, sometimes the enhancement was observed separately. 4. The FMRFa-induced inhibition of the Ca2+ current usually consisted of a decrease in both the amplitude and the rate of inactivation of this current, effects that were reduced as the membrane potential was stepped to more depolarized potentials. A pertussis toxin (PTX)-sensitive G protein mediated this response, whereas no evidence was found to suggest the involvement of any known intracellular messenger. Therefore this inhibition may have resulted from a direct coupling between the FMRFa receptor and the Ca2+ channels via a PTX-sensitive G protein. 5. Arachidonic acid (100 microM) irreversibly reduced the amplitude of the Ca2+ current, but it did not alter the relative inhibition of this current by FMRFa. 6. The FMRFa-induced enhancement of the Ca2+ current was difficult to study because it was observed infrequently, and was rarely observed independently of the FMRFa-induced inhibitory response. In addition, the ability of FMRFa to enhance this current usually disappeared with time.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Epidermal growth factor-induced phosphoinositide hydrolysis in permeabilized 3T3 cells: lack of guanosine triphosphate dependence and inhibition by tyrosine-containing peptides.

1990 ◽  
Vol 1 (9) ◽  
pp. 615-620 ◽  
Author(s):  
G F Verheijden ◽  
I Verlaan ◽  
J Schlessinger ◽  
W H Moolenaar
Keyword(s):  
Growth Factor ◽  
Epidermal Growth Factor ◽  
G Protein ◽  
Egf Receptor ◽  
Phosphoinositide Hydrolysis ◽  
3T3 Cells ◽  
Guanosine Triphosphate ◽  
Intact Cells ◽  
Epidermal Growth ◽  
Gamma S

The possible involvement of a stimulatory guanosine triphosphate (GTP)-binding (G) protein in epidermal growth factor (EGF)-induced phosphoinositide hydrolysis has been investigated in permeabilized NIH-3T3 cells expressing the human EGF receptor. The mitogenic phospholipid lysophosphatidate (LPA), a potent inducer of phosphoinositide hydrolysis, was used as a control stimulus. In intact cells, pertussis toxin partially inhibits the LPA-induced formation of inositol phosphates, but has no effect on the response to EGF. In cells permeabilized with streptolysin-O, guanosine 5'-O-(3-thiotriphosphate) (GTP gamma S) dramatically increases the initial rate of inositol phosphate formation induced by LPA. In contrast, activation of phospholipase C (PLC) by EGF occurs in a GTP-independent manner. Guanine 5'-O-(2-thiodiphosphate) (GDP beta S) which keeps G proteins in their inactive state, blocks the stimulation by LPA and GTP gamma S, but fails to affect the EGF-induced response. Tyrosine-containing substrate peptides, when added to permeabilized cells, inhibit EGF-induced phosphoinositide hydrolysis without interfering with the response to LPA and GTP gamma S. These data suggest that the EGF receptor does not utilize an intermediary G protein to activate PLC and that receptor-mediated activation of effector systems can be inhibited by exogenous substrate peptides.

scholarly journals A GTPase controls cell-substrate adhesion in Xenopus XTC fibroblasts.

1992 ◽  
Vol 118 (5) ◽  
pp. 1235-1244 ◽  
Author(s):  
M H Symons ◽  
T J Mitchison
Keyword(s):  
Control Cell ◽  
Response To Treatment ◽  
Nucleotide Analogs ◽  
Cell Contractility ◽  
Cell Rounding ◽  
Substrate Adhesion ◽  
Cell Substrate ◽  
Adhesive Interactions ◽  
Cell Substrate Adhesion ◽  
Gamma S

Cell-substrate adhesion is crucial at various stages of development and for the maintenance of normal tissues. Little is known about the regulation of these adhesive interactions. To investigate the role of GTPases in the control of cell morphology and cell-substrate adhesion we have injected guanine nucleotide analogs into Xenopus XTC fibroblasts. Injection of GTP gamma S inhibited ruffling and increased spreading, suggesting an increase in adhesion. To further investigate this, we made use of GRGDSP, a peptide which inhibits binding of integrins to vitronectin and fibronectin. XTC fibroblasts injected with non-hydrolyzable analogs of GTP took much more time to round up than mock-injected cells in response to treatment with GRGDSP, while GDP beta S-injected cells rounded up in less time than controls. Injection with GTP gamma S did not inhibit cell rounding induced by trypsin however, showing that cell contractility is not significantly affected by the activation of GTPases. These data provide evidence for the existence of a GTPase which can control cell-substrate adhesion from the cytoplasm. Treatment of XTC fibroblasts with the phorbol ester 12-o-tetradecanoylphorbol-13-acetate reduced cell spreading and accelerated cell rounding in response to GRGDSP, which is essentially opposite to the effect exerted by non-hydrolyzable GTP analogs. These results suggest the existence of at least two distinct pathways controlling cell-substrate adhesion in XTC fibroblasts, one depending on a GTPase and another one involving protein kinase C.

scholarly journals Two ATP-activated conductances in bullfrog atrial cells.

1988 ◽  
Vol 91 (1) ◽  
pp. 1-27 ◽  
Author(s):  
D D Friel ◽  
B P Bean
Keyword(s):  
Ionic Channels ◽  
Extracellular Atp ◽  
Fluctuation Analysis ◽  
Current Fluctuation ◽  
Atrial Cells ◽  
Atp Analogues ◽  
Alpha Beta ◽  
Gamma S ◽  
Inwardly Rectifying ◽  
Current Fluctuation Analysis

Currents activated by extracellular ATP were studied in single voltage-clamped bullfrog atrial cells. Rapid application of ATP elicited currents carried through two different conductance pathways: a rapidly desensitizing conductance reversing near -10 mV, and a maintained, inwardly rectifying conductance reversing near -85 mV. ATP activated the desensitizing component of current with a K 1/2 of approximately 50 microM and the maintained component with a K 1/2 of approximately 10 microM. Both types of current were activated by ATP but not by adenosine, AMP, or ADP. The desensitizing current was selectively inhibited by alpha, beta-methylene ATP, and the maintained, inwardly rectifying current was selectively suppressed by extracellular Cs. The desensitizing component of current was greatly reduced when extracellular Na was replaced by N-methylglucamine, but was slightly augmented when Na was replaced by Cs. GTP, ITP, and UTP were all ineffective in activating the desensitizing current, and of a variety of ATP analogues, only ATP-gamma-S was effective. Addition of EGTA or BAPTA to the intracellular solution did not obviously affect the desensitizing current. Fluctuation analysis of currents through the desensitizing conductance suggested that current is carried through ionic channels with a small (less than pS) unitary conductance.

scholarly journals Identification of a novel, N-ethylmaleimide-sensitive cytosolic factor required for vesicular transport from endosomes to the trans-Golgi network in vitro.

1991 ◽  
Vol 112 (5) ◽  
pp. 823-831 ◽  
Author(s):  
Y Goda ◽  
S R Pfeffer
Keyword(s):  
Early Stage ◽  
Gradient Centrifugation ◽  
Vesicular Transport ◽  
Free System ◽  
Transport Reaction ◽  
Trans Golgi Network ◽  
Transport Vesicles ◽  
Golgi Network ◽  
Gamma S

We have recently described a cell-free system that reconstitutes the vesicular transport of 300-kD mannose 6-phosphate receptors from late endosomes to the trans-Golgi network (TGN). We report here that the endosome----TGN transport reaction was significantly inhibited by low concentrations of the alkylating agent, N-ethylmaleimide (NEM). Addition of fresh cytosol to NEM-inactivated reaction mixtures restored transport to at least 80% of control levels. Restorative activity was only present in cytosol fractions, and was sensitive to trypsin treatment or incubation at 100 degrees C. A variety of criteria demonstrated that the restorative activity was distinct from NSF, an NEM-sensitive protein that facilitates the transport of proteins from the ER to the Golgi complex and between Golgi cisternae. Cytosol fractions immunodepleted of greater than or equal to 90% of NSF protein, or heated to 37 degrees C to inactivate greater than or equal to 93% of NSF activity, were fully able to restore transport to NEM-treated reaction mixtures. The majority of restorative activity sedimented as a uniform species of 50-100 kD upon glycerol gradient centrifugation. We have termed this activity ETF-1, for endosome----TGN transport factor-1. Kinetic experiments showed that ETF-1 acts at a very early stage in vesicular transport, which may reflect a role for this factor in the formation of nascent transport vesicles. GTP hydrolysis appears to be required throughout the transport reaction. The ability of GTP gamma S to inhibit endosome----TGN transport required the presence of donor, endosome membranes, and cytosol, which may reflect a role for guanine nucleotides in vesicle budding. Finally, ETF-1 appears to act before a step that is blocked by GTP gamma S, during the process by which proteins are transported from endosomes to the TGN in vitro.

scholarly journals Essential synergy between Ca2+ and guanine nucleotides in exocytotic secretion from permeabilized rat mast cells.

1987 ◽  
Vol 105 (1) ◽  
pp. 191-197 ◽  
Author(s):  
T W Howell ◽  
S Cockcroft ◽  
B D Gomperts
Keyword(s):  
Mast Cells ◽  
Rank Order ◽  
Regulatory Protein ◽  
Metabolic Inhibitors ◽  
Pyrimidine Nucleotides ◽  
Permeabilized Cells ◽  
Streptolysin O ◽  
Gamma S ◽  
Sufficient Stimulus ◽  
Rat Mast Cells

Rat mast cells, pretreated with metabolic inhibitors and permeabilized by streptolysin-O, secrete histamine when provided with Ca2+ (buffered in the micromolar range) and nucleoside triphosphates. We have surveyed the ability of various exogenous nucleotides to support or inhibit secretion. The preferred rank order in support of secretion is ITP greater than XTP greater than GTP much greater than ATP. Pyrimidine nucleotides (UTP and CTP) are without effect. Nucleoside diphosphates included alongside Ca2+ plus ITP inhibit secretion in the order 2'-deoxyGDP greater than GDP greater than o-GDP greater than ADP approximately equal to 2'deoxyADP approximately equal to IDP. Secretion from the metabolically inhibited and permeabilized cells can also be induced by stable analogues of GTP (GTP-gamma-S greater than GppNHp greater than GppCH2p) which synergize with Ca2+ to trigger secretion in the absence of phosphorylating nucleotides. ATP enhances the effective affinity for Ca2+ and GTP analogues in the exocytotic process but does not alter the maximum extent of secretion. The results suggest that the presence of Ca2+ combined with activation of events controlled by a GTP regulatory protein provide a sufficient stimulus to exocytotic secretion from mast cells.

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