Enzymic activities and galactomannan mobilisation in germinating seeds of fenugreek (Trigonella fœnum-graecum L. Leguminosae)

Summary The activities of -galactosidase, -mannosidase and -mannosidase were determined in extracts from the endosperm and from the embryo of fenugreek seeds at different stages of germination. Endosperm homogenates contained little or no activity of the above enzymes in the early stages of germination, before the reserve galactomannan began to be mobilised. The onset of galactomannan breakdown coincided with the appearance of -galactosidase and -mannosidase activities, which increased throughout the period of galactomannan degradation and then remained constant. A similar rise in -galactosidase and -mannosidase activities occurred during galactomannan breakdown in dry-isolated endosperms incubated under germination conditions. The increase could be suppressed by metabolic inhibitors which also inhibit galactomannan breakdown. Embryo homogenates contained high -galactosidase, high -mannosidase and some -mannosidase activity at all stages of germination.No oligomannosyl -1,4 phosphorylase activity could be detected either in the endosperm or in the embryo.It is concluded that the galactomannan of fenugreek is broken down by a series of hydrolases secreted by the aleurone layer of the endosperm. They include -galactosidase, -mannosidase and probably also endo--mannanase.This is part four in a series of papers dealing with galactomannan metabolism. Part three: Planta (Berl.) 106, 44–60 (1972).     

The β-1,3-glucan-binding protein from the crayfish Pacifastacus leniusculus,when reacted with a β-1,3-glucan,induces spreading and degranulation of crayfish granular cells

Summary A -1,3-glucan-binding protein (GBP) was purified from crayfish plasma, and incubated with laminarin (L), a -1,3-glucan. The GBP reacted with laminarin (GBP-L) induced strong spreading and partial degranulation of isolated and separated crayfish granular haemocytes. However, neither the GBP nor laminarin alone induced any changes in the crayfish granular cells. When monolayers of granular haemocytes were incubated with 20 g of GBP-L, more than 82% of the haemocytes were affected. The activity of GBP-L on granular cells was dose-dependent and a plateau was reached at 10 g of GBP-L. The degranulation of crayfish haemocytes induced by GBP-L seemed to occur by a regulated exocytosis, since it was strongly inhibited by specific blockers of this process such as SITS or calmidazolium. Monospecific anti-GBP antibodies also totally blocked the effect of GBP-L on crayfish granular cells. Indirect immunofluoresence staining demonstrated that the GBP-L could bind to the surface of granular cells, whereas GBP did not bind or bound very weakly to the haemocyte surface.     

Binding of benzo(α)pyrene, ellipticine, and cis-parinaric acid to β-lactoglobulin: Influence of protein modifications

The binding of benzo()pyrene, ellipticine, and cis-parinaric acid to native, esterified, and alkylated -lactoglobulin was followed by enhancement of the ligand fluorescence. Three studied ligands bind to native or modified -lactoglobulin in apparent molar ratios varying between 1/8 and 2/1, with apparent dissociation constants in the range of 10^–8 M for ligand/-lactoglobulin complexes. The studied, chemically modified -lactoglobulin derivatives display higher binding affinities for all studied ligands, cis-parinaric acid excluded. The reductive alkylation of -NH₂ lysyl residues of -lactoglobulin increases the apparent molar ratios of benzo()pyrene and cis-parinaric acid, and decreases it for ellipticine. The esterified and native -lactoglobulin complexed to the investigated ligands display similar stoichiometries. Dynamic light scattering study of ligand--lactoglobulin complexes in solution shows the formation of aggregates: the apparent hydrodynamic radius value of -lactoglobulin dimer (3.4 nm) reaches 49, 46, and 74 nm upon addition and binding of benzo()pyrene, ellipticine, and cis-parinaric acid, respectively.     

Enzymic synthesis of the trisaccharide core region of the carbohydrate chain ofN-glycoprotein

Transmannosylation from mannotriose (Man1-4Man1-4Man) to the 4-position at the nonreducing end N-acetylglucosaminyl residue ofN,N-diacetylchitobiose was regioselectively induced through the use of -d-mannanase fromAspergillus niger. The enzyme formed the trisaccharide Man1-4GlcNAc1-4GlcNAc (3.7% of the enzyme-catalysed net decrease ofN,N-diacetylchitobiose) from mannotriose as a donor andN,N-diacetylchitobiose as an acceptor. Mannobiose (Man1-4Man) was also shown to be useful as a donor substrate for the desired trisaccharide synthesis.Abbreviations Man d-mannose - (M _n) (n=1–5) -linkedn-mer of mannose - GlcNAc₂ 2-acetamido-2-deoxy--d-glucopyranosyl-(1–4)-2-acetamido-2-deoxy-d-glucose     

Identification of a cDNA encoding a plant Lewis-type alpha1,4-fucosyltransferase

Recently, it has been found that plants, including tomato (Lycopersicon esculentum), express the Lewis-a epitope, Gal1,3(Fuc1,4)GlcNAc, on some N-glycans. By searching the EST database, it was possible to identify a tomato cDNA encoding a protein, designated FucTC, of 413 amino acids with homology to plant and mammalian 1,3/4-fucosyltransferases. The cDNA was expressed in Pichia pastoris and the recombinant enzyme was found to transfer fucose from GDP-Fuc (K_m 16 M) to lacto-N-tetraose (Gal1,3GlcNAc1,3Gal1,4Glc; K_m 80 M) as well as to 1,3- and 1,4-galactosylated N-glycans. It is concluded that FucTC is responsible for the biosynthesis of Lewis-a on N-glycans in tomato.     

Differences in N-acetyllactosamine synthesis between β-1,4-galactosyltransferases I and V

Unlike classical -1,4-galactosyltransferase (-1,4-GalT I), -1,4-GalT V (formerly IV*) has little activity towards 1 mM N-acetylglucosamine [Sato et al. (1998) Proc Natl Acad Sci USA 95: 472-477]. The human -1,4-GalTs I and V were expressed individually in Sf-9 cells by transfection of the full coding sequences, and their N-acetyllactosamine synthetase activities were determined towards different N-acetylglucosamine concentrations. Kinetic studies using the cell homogenates as an enzyme source revealed that -1,4-GalTs I and V possess Km values of 0.6 mM and 33 mM towards N-acetylglucosamine, and of 48 µM and 41 µM towards UDPGal, respectively. No significant inhibition of N-acetyllactosamine synthesis with -lactalbumin was observed for -1,4-GalT V but the significant inhibition with -lactalbumin was observed for -1,4-GalT I.     

Evidence of β-carotene 7,8(7′,8′) oxygenase (β-cyclocitral,crocetindial generating) in Microcystis

A -carotene oxygenase is described which occurs in the Cyanobacterium Microcystis. It cleaves -carotene and zeaxanthin specifically at the positions 7,8 and 7,8, while echinenone and myxoxanthophyll are not affected. The oxidative cleavage of -carotene leads to the formation of -cyclocitral and crocetindial and that of zeaxanthin to hydroxy--cyclocitral and crocetindial in nearly stoichiometric amounts. Oxidant is dioxygen as has been demonstrated by high incroporation (86%) of ¹⁸O₂ into -cyclocitral. -Carotene oxygenase is membrane bound, sensitive to sulfhydryl reagents, antioxidants and chelating agents. Iron seems to be an essential part of the enzyme activity. Cofactors necessary for the reaction could not be detected.Abbreviations TLC thin layer-chromatography - PIPES piperazine-N,N-bis-(2-ethanesulfonate) Na - TES 2{[tris-(hydroxymethyl)-methyl]-amino} ethanesulfonic acid Dedicated to Professor G. Drews on occasion of his 60th birthday     

Highly efficient transformation and regeneration of aspen plants through shoot-bud formation in root culture

The natural capacity of aspen (Populus tremula L.) roots for direct shoot-bud regeneration was harnessed to establish a highly efficient transformation and regeneration procedure that does not require a pre-selection stage on antibiotics. Aspen stem segments were transformed using wildtype Agrobacterium rhizogenes (LBA9402) with the binary p35SGUSINT plasmid carrying the genes coding for -glucuronidase (GUS) and neomycin phosphotransferase II. High levels of transient GUS expression were found in the basal cut surface of 87% of the segments, and 98% of these formed well-developed adventitious roots. Proliferating root cultures were established in liquid culture, and GUS expression was found in 75% of the roots. Shoot-bud regeneration in root cultures was very high: 99% of the roots yielded shoot-buds (4.3 buds per root), of which 91% expressed GUS. Southern blot analysis and polymerase chain reaction confirmed the transgenic nature of the plants expressing GUS. Kanamycin resistance of transformants was tested with respect to callus growth and bud regeneration. Callus from transgenic plants exhibited a high growth rate in the presence of up to 100 g/l kanamycin, and bud regeneration from transformed roots occurred in the presence of up to 30 g/l kanamycin. Callus and buds from control (non-transformed) plants failed to proliferate or regenerate, respectively, in the presence of kanamycin at concentrations above 10 g/l. Ninety-four independent clones from different transformation events were established, of which 52 were phenotypically true-to-type.Abbreviations NAA -naphthaleneacetic acid - BA 6-benzylaminopurine - GUS -glucuronidase - NPTII neomycin phosphotransferase II - PCR polymerase chain reaction - EtOH ethanol - CTAB cetyltrimethylammonium bromide - SDS sodium dodecyl sulfate - NOS nopaline synthase - CaMV cauliflower mosaic virus     

Mode of uptake of sterol by Arthrobacter simplex

The mechanism of uptake of water-insoluble -sitosterol by a newly isolated strain of Arthrobacter simplex SS-7 was studied. The production of an extracellular sterol-pseudosolubilizing protein during growth of A. simplex on -sitosterol was demonstrated by isolating the factor from the cell-free supernatant and its subsequent purification by Sephadex G-150 column chromatography. The M _r of the purified sterol-pseudosolubilizing protein determined by SDS–PAGE was 19kDa. The rate of sterol pseudosolubilization (5.2×10^–3g l^–1h^–1) could not adequately account for the rate of sterol uptake (72×10^–3g l^–1h^–1) and the specific growth rate (56×10^–3 h^–1). However in the unfavourable growth condition, when the cells were treated with sodium azide at the level of 30–60% of MIC, the sterol pseudosolubilization accounted for nearly 74% of the total growth containing 96% free cells. Cellular adherence to substrate particles was found to play an active role in the normal growth of the strain on -sitosterol. Unlike sodium acetate-grown cells, whose surface activity was negligible (60mNm^–1), the sterol-grown cells had strong surface activity (40mNm^–1). The high lipid content and long chain fatty acids in the cell-wall of -sitosterol-grown cells probably contribute to the high sterol adherence activity of the cells.     

Action of rat liver Galβ1-4GlcNAc α(2-6)-sialyltransferase on Manβ1-4GlcNAcβ-OMe,GalNAcβ1-4GlcNAcβ-OMe,Glcβ1-4GlcNAcβ-OMe and GlcNAcβ1-4GlcNAcβ-OMe as synthetic substrates

Incubation of synthetic Man\1-4GlcNAc-OMe, GalNAc1-4GlcNAc-OMe, Glc1-4GlcNAc-OMe, and GlcNAc1-4GlcNac-OMe with CMP-Neu5Ac and rat liver Gal1-4GlcNAc (2-6)-sialyltransferase resulted in the formation of Neu5Ac2-6Man1-4GlcNAc-OMe, Neu5Ac2-6GalNAc1-4GlcNAc-OMe, Neu5Ac2-6Glc1-4GlcNAc-OMe and Neu5Ac2-6GlcNAc1-4GlcNAc-OMe, respectively. Under conditions which led to quantitative conversion of Gal1-4GlcNAc-OEt into Neu5Ac2-6Gal1-4GlcNAc-OEt, the aforementioned products were obtained in yields of 4%, 48%, 16% and 8%, respectively. HPLC on Partisil 10 SAX was used to isolate the various sialyltrisaccharides, and identification was carried out using 1- and 2-dimensional 500-MHz¹H-NMR spectroscopy.Abbreviations 2D 2-dimensional - CMP cytidine 5-monophosphate - CMP-Neu5Ac cytidine 5-monophospho--N-acetylneuraminic acid - COSY correlation spectroscopy - DQF double quantum filtered - HOHAHA homonuclear Hartmann-Hahn - MLEV composite pulse devised by M. Levitt - Neu5Ac N-acetylneuraminic acid - Neu5Ac2en 2-deoxy-2,3-didehydro-N-acetylneuraminic acid     

Mapping of β-glucan content and β-glucanase activity loci in barley grain and malt

Genetic study of -glucan content and -glucanase activity has been facilitated by recent developments in quantitative trait loci (QTL) analysis. QTL for barley and malt -glucan content and for green and finished malt -glucanase activity were mapped using a 123-point molecular marker linkage map from the cross of Steptoe/Morex. Three QTL for barley -glucan, 6 QTL for malt -glucan, 3 QTL for -glucanase in green malt and 5 QTL for -glucanase in finished malt were detected by interval mapping procedures. The QTL with the largest effects on barley -glucan, malt glucan, green malt -glucanase and finished malt glucanase were identified on chromosomes 2,1,4 and 7, respectively. A genome map-based approach allows for dissection of relationships among barley and malt glucan content, green and finished malt -glucanase activity, and other malting quality parameters.     

Intron III-Specific Markers for Screening of β-amylase Alleles in Barley Cultivars

In modern malting barley breeding it is important to increase the level of -amylase activity level in barley. The aim of this study was to investigate if a PCR method for screening -amy1 alleles can be used as an indicator for -amylase activity level in barley. Activity was assayed from 24 cultivars, 7 lines, and a Hordeum spontaneum PI 296897 strain grown in the same field. The -amy1 alleles were identified by amplifying the intron III-specific region of the gene using PCR. No new alleles were detected in addition to the three alleles found earlier: cv Adorra-like, cv Haruna Nijo-like and PI 296897-like -amy1 allele. Samples were grouped according to the nature of their -amy1 locus and enzyme activities were compared between the groups. Cultivars carrying a cv Haruna Nijo-like -amy1 allele had 1.3 times and lines carrying a PI 296897-like -amy1 allele had 2.1 times higher -amylase activity than cultivars carrying a cv Adorra-like -amy1 allele. The mean activities are significantly different in the allele groups (Kruskal–Wallis: for protein H= 11.54, P< 0.01; for meal H= 12.74, P< 0.01). PCR fragments can be used as allele specific markers to predict the level of -amylase activity in breeding when such variation of the intron III is concerned.     

Immobilized Lotus tetragonolobus agglutinin binds oligosaccharides containing the Lex determinant

A defined set of oligosaccharides and glycopeptides containing -linked fucose were used to examine the specificity of the immobilized fucose-binding lectin Lotus tetragonolobus agglutinin (LTA1), also known as lotus lectin. Glycans containing the Lewis x determinant (Lex) Gal1-4[Fuc1-3]GlcNAc1-3-R were significantly retarded in elution from high density LTA-Emphaze columns. The lectin also bound the fucosylated lacdiNAc trisaccharide GalNAc1-4[Fuc1-3]GlcNAc. The lectin did not bind glycans containing either sialylLex or VIM-2 determinants, nor did it bind the isomeric Lea, Gal1-3[Fuc1-4]GlcNAc-R. Although 2-fucosyllactose Fuc1-2Gal1-4Glc) was retarded in elution from the columns, larger glycans containing the H-antigen Fuc1-2Gal1-3(4)GlcNAc-R interacted poorly with immobilized LTA. Our results demonstrate that immobilized LTA is effective in isolating glycans containing the Lex antigen and is useful in analyzing specific fucosylation of glycoconjugates. Abbreviations: LTA, Lotus tetragonolobus agglutinin; UEA-1, Ulex europaeus agglutinin-I; LNT, AAL, Aleuria aurantia agglutinin; Gal1-3GlcNAc1-3Gal1-3Glc; LNnT, Gal1-4GlcNAc1-3Gal1-3Glc; Lex, Lewis x antigen; Lea, Lewis a antigen; GDPFuc, guanosine 5-diphosphate--L-fucose     

Elimination of the disulphide bond alters the conformation of mature lipo-β-lactamase in yeast

Summary When expressed in Saccharomyces cerevisiae the precursor of the hybrid prokaryotic protein lipo--lactamase is accumulated in reduced form whereas the majority of the mature form contains an intra molecular disulphide bond (oxidized form). We have previously shown that mature mutant lipo--lactamases in which the cysteine residue 131 was changed to either tyrosine or threonine lack the capacity to form a disulphide bond but are nevertheless processed and secreted efficiently in yeast. Here we show that these mutant mature lipo--lactamases, in yeast cell extracts, exhibit a tenfold lower -lactamase-specific activity than the wild-type protein and that the mature mutant proteins are more susceptible to trypsin digestion. Thus, elimination of the disulphide bond alters the conformation of mature lipo--lactamase in yeast.Correspondence to: O. Pines     

Immunohistological analyses of neutral glycosphingolipids and gangliosides in normal mouse skeletal muscle and in mice with neuromuscular diseases

The expression of neutral glycosphingolipids (GSLs) and gangliosides was investigated in cryosections of normal mouse skeletal muscle and in muscle of mice with neuromuscular diseases using indirect immunofluorescence microscopy. Transversal and longitudinal sections were immunostained with specific polyclonal antibodies against lactosylceramide, lacto-N-neotetraosylceramide, globoside, G_M3(Neu5Ac), G_M3(Neu5Gc) and G_M1(Neu5Ac) as well as monoclonal anti-Forssman GSL antibody. In normal CBA/J mouse muscle (control) the main immunohistochemically detected ganglioside was G_M3(Neu5Ac) followed by moderately expressed G_M3(Neu5Gc) and G_M1. The neutral GSLs lactosylceramide and globoside were stained with almost identical, high fluorescence intensity. Low amounts of lacto-N-neotetraosylceramide and trace quantities of Forssman GSL were immunostained. All GSLs were detected in the sarcolemma, but also in considerable amounts at the intracellular level. Mice with neuromuscular diseases were the A2G-adr mouse mutant (a model for human recessive myotonia of Becker type), the BL6-wr mutant (a model for motor neuron disease) and the BL10-mdx mouse mutant (a model for human Duchenne muscular dystrophy). No changes in GSL expression were found in the A2G-adr mouse, while muscle of the BL6-wr mouse showed increased intensity of immunofluorescence in stainings with anti-lactosylceramide and anti-G_M3(Neu5Ac) antibodies. Muscle of BL10-mdx mice showed the most prominent changes in GSL expression with reduced fluorescence intensity for all antibodies. Major differences were not observed in the intensities of GSLs, but there were significant differences in the patterns of distribution on plasma membrane and at the subcellular level. The exact nature and pathogenesis of these changes should be elucidated since such investigations could furnish advances in understanding the functional role of neutral GSLs and gangliosides in normal as well as in diseased muscle. Abbreviations: BSA, bovine serum albumin; DAPI, 4, 6-diamidine-2-phenylindole-dihydrochloride; DTAF, dichlorotriazinylamino-fluorescein; GSL(s), glycosphingolipid(s); Neu5Ac,N-acetylneuraminic acid; Neu5Gc,N-glycolylneuraminic acid [53]; PBS, phosphate buffered saline. The designation of the following glycosphingolipids follows the IUPAC-IUB recommendations [54] and the nomenclature of Svennerholm [55]. Lactosylceramide or LacCer, Gal1-4Glc1-1Cer; gangliotriaosylceramide or GgOse₃Cer, GalNAc1-4Gal1-4Glc1-1Cer; globotriaosylceramide or GbOse₃Cer, Gal1-4Gal1-4Glc1-1Cer; gangliotetraosylceramide or GgOse₃Cer, Gal1-3GalNAc1-4Gal1-4Glc1-1Cer; globotetraosylceramide or GbOse₄Cer, GalNAc1-3Gal1-4Gal1-4Glc1-1Cer; lacto-N-neotetraosylceramide or nLcOse₄Cer, Gal1-4GlcNAc1-3Gal1-4Glc1-1Cer; Forssman GSL or GbOse₅Cer, GalNAc1-3GalNAc1-3GAl1-4Gal1-4Glc1-1Cer; G_M3, II³Neu5Ac-LacCer; G_M1, II³Neu5Ac-GgOse₄Cer.     

Organization of α-chain genes among Hb G-Philadelphia heterozygotes in association with Hb S, β-thalassemia,and α-thalassemia-2

The percentages of the -chain variant Hb G-Philadelphia (Hb G) or ₂ 68 AsnLys₂ were evaluated in 84 adult and 18 newborn heterozygotes. These included members of three families who were studied in more detail by nucleic acid hybridization techniques. The adult heterozygotes fell in two categories, one with a higher proportion of Hb G [46.5±1.0% (SD), N=21] and another with lower values (33.9±3.4%, N=63). Among the newborn heterozygotes, two babies fell in the category with the higher proportion of Hb G while 16 babies gave values between 25 and 34%. Studies of -chain gene organization on the parents of one neonate with a Hb G level of 27% at birth and 37% at 8 months excluded the presence of chromosomes with triplicated -chain genes which could lead to the ^0G/ genotype. Rather, these studies on five Hb G heterozygotes from three families confirmed the linkage between Hb G and a specific type of -thalassemia-2 associated with the presence of a 16-kbp Bgl II fragment which most probably carries the ^G locus since it has been found in 19 Hb G heterozygotes studied to date. The presence of an -thal-2 heterozygosity and three -chain genes (^0G/) was confirmed among Hb G heterozygotes with lower proportions of this variant. It is likely that the even lower values found in some newborn could arise through defective assembly of ^G- dimers. The presence of an -thal-2 homozygosity and two active -chain genes, one on each chromosome (^0G/⁰), was confirmed among heterozygotes with the higher proportion of Hb G. One of each of these categories was present in each of the three families investigated. This type of variability in the number of active -chain genes due to a heterozygosity or a homozygosity for -thalassemia-2 explains the trimodality of Hb S percentages among heterozygotes and the atypical hematological or biosynthetic features among patients with -thalassemia and sickle-cell syndromes.This research was supported by USPHS Research Grants HLB-05168 and HLB-15158 and by designated research funds of the Veterans Administration. This is Contribution No. 0693 of the Department of Cell and Molecular Biology, Medical College of Georgia, Augusta.     

Ganglioside-cholera toxin interactions: a binding and lipid monolayer study

Summary On t.l.c. plates ¹²⁵I-cholera toxin binds to a disialoganglioside tentatively identified as GD_lb with about 10 times less capacity than to ganglioside GM₁. Binding of labeled toxin to both gangliosides was abolished in presence of excess amounts of unlabeled B subunit. Ganglioside extracts from human or pig intestinal mucosa showed toxin binding to gangliosides GM₁ and GD_1b. In ganglioside-containing lipid monolayers the penetration of the toxin was independent of the ganglioside binding capacity.Abbreviations GM₂ Gal-NAc14Gal(3-2NeuAc)14G1c1Cer - GM₁ Gal3Ga1-NAc14Gal(32NeuAc)14G1c11Cer - GD_1a NeuAc23Ga113Gal-NAc14Gal(32NeuAc)14G1c11Cer - GD1b Gall3Gal-NAcl4Gal(32NeuAc82NeuAc)14Glc11Cer - GT_1b NeuAc23Ga113Ga1-NAcal4Gal(3-2NeuAc82NeuAc)14G1c11Cer - dpPC 1,2-hexadecanoyl-sn-glycero-3-phosphocholine - dpPE 1,2-hexadecanoyl-sn-glycero-3-phosphoethanolamine     

Constant-time NOESY: An aid in the analysis of protein NMR spectra

Summary A constant-time version of the homonuclear NOESY experiment (CT-NOESY) is described. The experiment yields simplified protein spectra, in which cross peaks arising from protons with zero or small couplings are differentiated from other cross peaks, thus partially overcoming the problem of signal overlap. In addition, the CT-NOESY spectrum provides information on the magnitude of³J_NH- and³J coupling' constants, and is thus useful to determine torsion angle constraints and to perform stereospecific assignments of CHH protons in the case of³J constants.     

Average phase difference theory and 1∶1 phase entrainment in interlimb coordination

The dynamics of coupled biological oscillators can be modeled by averaging the effects of coupling over each oscillatory cycle so that the coupling depends on the phase difference between the two oscillators and not on their specific states. Average phase difference theory claims that mode locking phenomena can be predicted by the average effects of the coupling influences. As a starting point for both empirical and theoretical investigations, Rand et al. (1988) have proposed d/dt= — K sin ), with phase-locked solutions =arcsin( /K), where is the difference between the uncoupled frequencies and K is the coupling strength. Phase-locking was evaluated in three experiments using an interlimb coordination paradigm in which a person oscillates hand-held pendulums. was controlled through length differences in the left and right pendulums. The coupled frequency _c was varied by a metronome, and scaled to the eigenfrequency _v of the coupled system K was assumed to vary inversely with _c. The results indicate that: (1) and K contribute multiplicatively to (2) =0 or = regardless of K when =0; (3) 0 or regardless of when K is large (relative to ); (4) results (1) to (3) hold identically for both in phase and antiphase coordination. The results also indicate that the relevant frequency is _c/_v rather than _c. Discussion high-lighted the significance of confirming =arcsin(/K) for more general treatments of phase-locking, such as circle map dynamics, and for the 11 phase-entrainment which characterizes biological movement systems.