Four fluorochromes for the demonstration and microfluorometric estimation of RNA

Summary Microfluorometric estimates of total RNA were made in selected test material stained with berberine sulfate, acridine orange, and Hoechst 33258. These measurements were compared with those obtained with propidium iodide, which is known to interact only with double-stranded nucleic acids. It was observed that all of the fluorochromes, including propidium iodide, yielded very similar patterns of fluorescence in the various types of material tested. In isolated thymocyte and hepatocyte nuclei stained with either propidium iodide or Hoechst 33258 at pH 2, it was evident that RNA could be estimated only indirectly by measuring the amount of fluorescence before and after extraction with RNase. It was apparent that the total fluorescence of small thymocyte nuclei was affected much less by RNase extraction than that of 2c hepatocyte nuclei. Attempts to obtain direct estimates of RNA by exposing the preparations to DNase were not successful: the fluorescence of thymocyte nuclei dropped almost to zero, and hepatocyte nuclei could no longer be assigned to distinct ploidy classes. In addition, since the highly condensed chromatin of thymocyte nuclei was stained much more prominently than the looser chromatin of hepatocyte nuclei with Hoechst 33258, it was apparent that this fluorochrome — when used at pH 2 — has potential usefulness as a probe of organizational differences in chromatin.     

Cellular fatty acid composition of six fastidious,gramnegative, xylem-limited bacteria from plants

Composition of cellular fatty acids was determined for strains of fastidious, Gramnegative, xylem-limited bacteria causing or associated with Pierce's disease of grapevine, phony disease of peach, plum leaf scorch, stunt of ragweed, elm leaf scorch, and periwinkle wilt. The most abundant fatty acids were straight-chain 150, 160, 170, and 180, unsaturated 161, 181, and unsaturated 17-and 19=carbon homologs. Minor fatty acids included straightchain 120, 140, 190, and 200; an unsaturated 15-carbon homolog; hydroxy-substituted 2-OH 120, 3-OH 120, and 3-OH 140; and branched chain iso-140 and iso-200. Cyclopropane acids were not detected. Physiological age had no effect on fatty acid composition. Class analysis of data indicated relative uniformity within the group. Saturated even-carbon chains comprised 31%–42%, unsaturated acids 41%–52%, saturated odd-carbon chains 10%–18%, hydroxysubstituted chains 2%–7%, and branched-chains 1%–4% of total fatty acids. The ratio of saturated-unsaturated acids ranged from 0.8 to 1.2.     

Synthesis of aspartame precursor by solid thermolysin in organic solvent

Summary The enzymatic synthesis of a peptide compound was carried out successfully in homogeneous organic solvent.Solid Thermolysin was found to catalyze the synthetic reaction of N-benzyloxycarbonyl-L-aspartyl-L-phenylalanine methyl ester (Z-APM; a precursor of sweetner Aspartame) from N-benzyloxycarbonyl-L-aspartic acid (Z-L-Asp) and L-phenylalanine methyl ester (L-PheOMe) in a 98 percent organic medium (ethylacetatebenzenemethanolwater=5029192). The dissolution of enzyme was not observed. The optimal pH shifted to acidic side by 1.0 pH unit, compared with that in aqueous medium. The enzymatic activity of solid thermolysin with an average size of 3.4×9.5 m was determined to be 0.18 moles-product/(mg-solid)·h under the initial concentrations of L-PheOMe of 0.1M and Z-L-Asp of 0.05M, and at pH 6.0 and 40°C.     

Modification of the properties of a translocation in the German cockroach by selection

Summary A stock of Blattella germanica bearing the interchange T(3; 12)/3;12 was subjected to close inbreeding with selection for random disjunction at metaphase I. After 3–4 generations of selection, interchange quadrivalent chiasma frequency decreased, variability in free bivalent chiasma frequency increased sharply, and individuals with either random or directed disjunction were present in the stock. Random disjunction was modified from a ratio of 2112 (adj.-1; alt.-1; adj.-2; alt.-2) to a ratio of 1111. After 7–8 generations of selection, chiasma frequency appeared to stabilize at lower than normal levels and variability decreased for both quadrivalents and free bivalents. Directed disjunction was modified from a ratio of 2114 to 1112, and no individuals with the original high level of directed disjunction were detected. Chains-of-four tended to orient randomly, especially in individuals where the ring quadrivalents showed directed disjunction. Relaxation of inbreeding, but not selection, produced an increase in chiasma frequency and variability in both free bivalents and quadrivalents, but the modified ratios for both random and directed disjunction were retained. These results are discussed with respect to inbreeding effects and genetic control of chiasma frequency and metaphase I disjunction in interchange quadrivalents.     

Sex determination in Sarotherodon (tilapia)

Summary The simplest possible model of the sex determination process adding autosomal influence to a minimal number of sex chromosomes was developed to explain matings of Tilapia (Sarotherodon) species. Eighteen different genotypes, each having two autosomes (AA, Aa, or aa) and two sex chromosomes (WX, WY, WW, XY, XX or YY) involved in sex determination, are predicted by the theory. Their sex (10 males and 8 females) were determined using a series of directed graphs, showing the relative strength of the chromosome pairs, developed on the basis of Chen's sex ratio results (Chen 1969). This theoretical model predicts eight different sex ratios (01, 13, 35, 11, 97, 53, 31, 10 ); three of them are not predicted by the WXYZ theory. The greatest part of these sex ratios have been obtained experimentally in extensive series of crosses between related species of Tilapia and their hybrids, carried out by several authors. The theory succeeds in explaining all of Chen's results, including those ratios 53 and 01 seen in certain crosses but not predicted by the WXYZ theory. The importance of the autosomes is seen in comparisons of the genotype pairs (AaWY, aaWY), (AaXY, aaXY) and (AAWW, AaWW) in which the first genotype in each case is male while the second is female as proven by the sex ratio results. The members of the pair differ only in the substitution of one autosome for the other. To test the theory, experiments consisting of hormonal sex reversion and a series of crosses are proposed. Finally, theoretical and practical implications of the theory are discussed.     

Nutrient proportions in foliage of semi-mature loblolly pine

Summary Nitrogen and phosphorus limitations to growth are common in many loblolly pine (Pinus taeda) stands. Interactions of these nutrients may complicate interpretation of foliar nutrient analysis for predicting response to forest fertilization. Proportions of foliar nutrient concentrations (and the changes in these proportions following fertilization) were examined in 36 semi-mature loblolly pine plantations in the southeastern United States. Mean proportions of nutrient concentrations (NPKCaMg) for non-fertilized stands were 1009.336.517.29.2. Potassium and phosphorus were higher. Nitrogen fertilization generally decreased the PN ratio and enhanced growth, indicating a nitrogen deficiency in most stands under study. Additions of nitrogen and phosphorus together yielded a significant increase in the PN ratio. Effects of fertilization effects on other nutrient concentration ratios were also examined.Paper No. 9401 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, NC 27695.     

Comparative mapping in F2∶3 and F6∶7 generations of quantitative trait loci for grain yield and yield components in maize

This study was conducted to compare maize quantitative trait loci (QTL) detection for grain yield and yield components in F₂₃ and F₆₇ recombinant inbred (RI) lines from the same population. One hundred and eighty-six F₆₇ RIs from a Mo17×H99 population were grown in a replicated field experiment and analyzed at 101 loci detected by restriction fragment length polymorphisms (RFLPs). Single-factor analysis of variance was conducted for each locus-trait combination to identify QTL. For grain yield, 6 QTL were detected accounting for 22% of the phenotypic variation. A total of 63 QTL were identified for the seven grain yield components with alleles from both parents contributing to increased trait values. Several genetic regions were associated with more than one trait, indicating possible linked and/or pleiotropic effects. In a comparison with 150 F₂₃ lines from the same population, the same genetic regions and parental effects were detected across generations despite being evaluated under diverse environmental conditions. Some of the QTL detected in the F₂₃ seem to be dissected into multiple, linked QTL in the F₆₇ generation, indicating better genetic resolution for QTL detection with RIs. Also, genetic effects at QTL are smaller in the F₆₇ generation for all traits.Abbreviations RFLPs Restriction fragment length polymorphisms - QTL quantitative trait loci - RIs recombinant inbreds Journal Paper no. J-16261 of the Iowa Agric and Home Economics Exp Stn Project no. 3134     

Glycerolipid-fatty-acid desaturase deficiencies in chloroplasts from fruits of Capsicum annuum L.

Chloroplasts from fruits and leaves of Capsicum annuum cv. Bell Tower were purified on sucrose gradients, and the lipids were separated by column and thin-layer chromatography. The glycerolipids mono- and digalactosyldiacylglycerol (MGDG, DGDG), sulfoquinovosyldiacylglycerol (SQDG), and phosphatidylglycerol (PG) were quantified, and the fatty-acid composition at the 1 and 2 positions of the glycerol moiety (sn-1 and sn-2) was determined after hydrolysis with position-specific lipases. In fruit chloroplasts, ³-trans hexadecenoate (trans-3-161) was absent and replaced by palmitate (160) at sn-2 of PG, and ^7,10,13-hexadecatrienoate (163) at sn-2 of MGDG was greatly reduced and largely replaced by linoleate (182). The ratio of 182 to linolenate (183) was consistently greater in glycerolipids from fruit compared with leaf chloroplasts. The lower percentage of C-16 fatty acids at sn-2 indicated that prokaryotic molecular species were reduced by 15% in DGDG, 40% in SQDG, and 90% in MGDG, in fruit compared with leaf chloroplasts. The MGDGDGDG ratios in fruit and leaf chloroplasts were 1.21 and 2.21, respectively. Taken together, the data indicate that chloroplasts in Capsicum fruit are deficient in three desaturases: those that convert 1) 160 to ³-trans-161 at sn-2 of PG, 2) 160 to ⁷–cis-161 at sn-2 of MGDG, and 3) 182 to 183 at both sn-1 and sn-2 of various chloroplast glycerolipids.Abbreviations Chl chlorophyll - DGDG digalactosyldiacylglycerol - FS free sterol - GL galactolipid - MGDG monogalactosyldiacylglycerol - PE phosphatidyl ethanolamine - PG phosphatidylglycerol - PL phospholipid - SQDG sulfoquinovosyldiacylglycerol We are grateful to Dr. Roger Calza for providing us with the tobacco gt11 cDNA expression library and to Dr. Eric Huttner for his advice throughout the screening procedure. We also wish to thank M. Gosse for his assistance in growing and maintaining our plants. T.W.B. was supported by a BAP research grant from the Commission of the European Communities.     

Mechanisms for controlling balance between light input and utilisation in the salt tolerant alga Dunaliella C9AA

The yield of photosynthetic O₂ evolution was measured in cultures of Dunaliella C9AA over a range of light intensities, and a range of low temperatures at constant light intensity. Changes in the rate of charge separation at Photosystem I (PS I) and Photosystem II (PS II) were estimated by the parameters _{PS I} and _{PS II} . _{PS I} is calculated on the basis of the proportion of centres in the correct redox state for charge separation to occur, as measured spectrophotometrically. _{PS II} is calculated using chlorophyll fluorescence to estimate the proportion of centres in the correct redox state, and also to estimate limitations in excitation delivery to reaction centres. With both increasing light intensity and decreasing temperature it was found that O₂ evolution decreased more than predicted by either _{PS I} or _{PS II}. The results are interpreted as evidence of non-assimilatory electron flow; either linear whole chain, or cyclic around each photosystem.Abbreviations F₀ dark level of chlorophyll fluorescence yield (PS II centres open) - F_m maximum level of chlorophyll fluorescence yield (PS II centres closed) - F_v variable fluorescence (F_m-F₀) - PS I Photosystem I - PS II Photosystem II - P₇₀₀ reaction centre chlorophyll(s) of PS I - q_N coefficient of non-photochemical quenching of chlorophyll fluorescence - q_P coefficient of photochemical quenching of fluorescence yield - q_E high-energy-state quenching coefficient - _{PS I} yield of PS I - _{PS II} yield of PS II - _S yield of photosynthetic O₂ evolution - _P intrinsic yield of open PS II centres     

Osmotropotaxis inDrosophila melanogaster

Summary Drosophila melanogaster is able to perform osmotropotaxis under open-loop conditions. With an optimal stimulus the average turning tendency to the side of higher concentration corresponds to a circular track with radiusr=0.8 cm. The response amplitude does not decrease within 1 or 2 h. Unilaterally antennectomized flies in an homogeneous odor field show a permanent turning tendency towards their intact side.The smallest concentration ratio to elicit osmotropotaxis in normal flies ranges between 610 and 910 at high and between 210 and 510 at an about 50 times lower odor intensity. No negative tropotaxis (i.e. turning to the side of lower concentration) is observed, even with strong repellents.     

Bioassembly of acyl lipids in microspore-derived embryos of Brassica campestris L.

The native lipid composition and the capacity of cell-free extracts to biosynthesize acyl lipids in vitro were determined for the first time using the recently reported microspore-derived (MD) embryo system from the Brassica campestris low erucic acid line BC-2 (Baillie et al. 1992). The total lipid fraction isolated from midcotyledonary stage MD embryos (21 days in culture) was composed primarily of triacylglycerol (76%) with an acyl composition quite similar to that of mature BC-2 seed. When incubated in the presence of glycerol-3-phosphate, ¹⁴C 181-CoA, and reducing equivalents, homogenates prepared from 21-day cultured MD embryos were able to biosynthesize glycerolipids via the Kennedy pathway. The maximum in vitro rate of triacylglycerol biosynthesis could more than account for the known rate of lipid accumulation in vivo. The homogenate catalyzed the desaturation of 181 to 182 and to a lesser extent, 183. The newly-synthesized polyunsaturated fatty acids initially accumulated in the polar lipid fraction (primarily phosphatidic acid and phosphatidylcholine) but began to appear in the triacylglycerol fraction after longer incubation periods. As expected for a low erucic acid cultivar, homogenates of MD embryos from the BC-2 line were incapable of biosynthesizing very long chain monounsaturated fatty acyl moieties (201 and 221) from 181-CoA in vitro. Nonetheless, embryo extracts were still capable of incorporating these fatty acyl moieties into triacylglycerols when supplied with ¹⁴C 201-CoA or ¹⁴C 221-CoA. Collectively, the data suggest that developing BC-2 MD embryos constitute an excellent experimental system for studying pathways for glycerolipid bioassembly and the manipulation of this process in B. campestris.Abbreviations CPT sn-1,2-diacylglycerol cholinephosphotransferase - DAG diacylglycerol - DGAT diacylglycerol acyltransferase - DGDG digalactosyldiacylglycerol - G-3-P glycerol-3-phosphate - G-3-PAT glycerol-3-phosphate acyltransferase - LPA lyso-phosphatidic acid - LPAT lyso-phosphatidic acid acyltransferase - LPC lyso-phosphatidylcholine - LPCAT acyl-CoA: lyso-phosphatidylcholine acyltransferase - LPE lyso-phosphatidylethanolamine - MGDG monogalactosyldiacylglycerol - PA phosphatidic acid - PA Phosphatase, phosphatidic acid phosphatase - PC phosphatidylcholine - PE phosphatidylethanolamine - PG phosphatidylglycerol - TAG triacylglycerol - 181-CoA oleoyl-Coenzyme A - 181 oleic acid, cis-9-octadecenoic acid - 182 linoleic acid, cis-9,12-octadecadienoic acid - 183 -linolenic acid, cis-9,12,15-octadecatrienoic acid - 201 cis-11-eicosenoic acid - 221 erucic acid, cis-13-docosenoic acid; all other fatty acids are designated by number of carbon atoms: number of double bonds National Research Council of Canada Publication No. 35896     

Inhibition by n-3 fatty acids of arachidonic acid metabolism in a primary culture of astroglial cells

Docosahexaenoic acid (226 n-3) was present in low concentrations in a primary culture of rat brain astroglial cells, when compared to brain cortex. We have thus supplemented these cells with this fatty acid and investigated the effects of its incorporation in cell phospholipids on the conversion of arachidonic acid, 204 n-6, through the cyclo and lipoxygenase pathways, after cell stimulation. Docosahexaenoic acid-enriched cells produced less thromboxane B₂ and 6-keto-Prostaglandin F₁ and markedly less 12-hydroxyeicosatetraenoic acid than unsupplemented cells, after stimulation with the Ca²⁺-ionophore A23187. The production of 15-hydroxyeicosatetraenoic acid from arachidonic acid was slightly increased in docosahexaenoic acid-supplemented cells. We have also supplemented these cells with eicosapentaenoic acid (205 n-3) and, in addition to accumulation of this fatty acid in cell phospholipids, we found elevation of 225 n-3 and some increment of 226, confirming that glial cells are able to convert eicosapentaenoic acid to the long chain, more unsaturated derivatives. In conclusion, n-3 fatty acids, when supplemented to glial cells, appear to modulate the arachidonic acid cascade and to be converted through the elongation and desaturation pathways.     

Developmental changes in the fatty acids of synaptic membrane phospholipids: Effect of protein malnutrition

The acyl-linked fatty acid composition of the major phospholipid species in rat cortical synaptic membranes was determined at various stages of development. For most species there was a decrease during development in the short chain saturated fatty acids, 140 and 160, an increase in 180 and 226 (n-3) and an increase in the ratio of 226 (n-3)/225 (n-6). Pups were protein deprived by feeding the dams a 12% casein diet as compared to the 24% casein control diet. Protein malnutrition markedly affected the composition of acyl-linked fatty acids in the synaptic membranes. The increases in the ratio of 226 (n-3)/225 (n-6) fatty acids were especially compromised.Abbreviations used (PC) Phosphatidylcholine - (PE) phosphatidylethanolamine - (EP) ethanolamine plasmalogen - (PS) phosphatidylserine - (PI) phosphatidylinositol - (SP) sphingomyelin - (t.l.c.) thin layer chromatography - (BHT) butylated-hydroxytoluene     

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     

A quantitative study of synaptic ribbons in pinealocytes of adult Chinese hamsters (Cricetulus griseus) under different photoperiodic conditions

Summary Synaptic ribbons (SR) in pinealocytes of adult (120–130 day-old) male Chinese hamsters (Cricetulus griseus) were classified into types 1, 2 and 3; these have a central dense structure showing rod-like, various and ringlike profiles, respectively. The central structure of the type-2 SR usually appeared as round, oval or comma-like bodies, and occasionally as plates showing various profiles or clubshaped bodies. The quantity of each type of SR, expressed as the SR index, was determined over a 24-h period under a light/dark regime (LD) 1212 or LD 1410. On comparing the results obtained from adults with previously published data from young (60–70-days-old) animals under LD 1212, it was found that, in both young and adult animals, the type-1 and type-3 SR indices exhibited different 24-h variations, whereas the type-2 SR index remained constant over a 24-h period. In addition, the indices of the type-2 SR, but not those of the other SR types, were found to be significantly larger in adult than in young animals. In adult animals, the effects of the photoperiod were different between the three types of SR. A nocturnal increase in the type-1 SR index was observed under both LD 1212 and LD 1410, its time course being different for each of these photoperiods. Under LD 1410, the type-2 SR index showed a significant 24-h rhythm with larger values during the dark period; this was not observed under LD 1212. The type-3 SR index was almost the same under LD 1212 and LD 1410. The results suggest that pinealocyte SR of the Chinese hamster may be composed of three types of SR, each with a different functional role.     

Resolution of components of non-photochemical chlorophyll fluorescence quenching in barley leaves

Non-photochemical chlorophyll fluorescence quenching (qN) in barley leaves has been analysed by monitoring its relaxation in the dark, by applying saturating pulses of light. At least three kinetically distinct phases to qN recovery are observed, which have previously been identified (Quick and Stitt 1989) as being due to high-energy state quenching (fast), excitation energy redistribution due to a state transition (medium) and photoinhibition (slow). However, measurements of chlorophyll fluorescence at 77 K from leaf extracts show that state transitions only occur in low light conditions, whereas the medium component of qN is very large in high light. The source of that part of the medium component not accounted for by a state transition is discussed.Abbreviations ATP adenosine 5-triphosphate - DCMU 3[3,4-dichlorophenyl]-1,1 dimethylurea - pH trans-thylakoid pH gradient - F_o, F_m room-temperature chlorophyll fluorescence yield with all reaction centres open, closed - F_v variable fluorescence = F_m–F_o - LHC II Light harvesting complex II - PS I, PS II Photosystem I, II - P700, P680 primary donor in photosystem I, II - qP photochemical quenching of variable fluorescence - qN non-photochemical quenching of variable fluorescence - qN_e, qN_t, qN_i non-photochemical quenching due to high energy state, state transition, photoinhibition - qN_f, qN_m, qN_s components of qN relaxing fast, medium, slow - q_r quenching of r relative to the dark state - tricine N-tris[hydroxymethyl]methylglycine - r ratio of fluorescence maximum from photosystem II to that from photosystem I at 77 K     

Endosperm Balance Number and the polar-nuclei activation hypotheses for endosperm development in interspecific crosses of Solanaceae and Gramineae,respectively

The Endosperm Balance Number (EBN) and the polar-nuclei activation (PNA) hypotheses have been developed to interpret, explain and predict interspecific and interploidy crossabilities in the Solanums and the Gramineae, respectively. Although these two hypotheses evolved independently, they share a number of common features. Assignment of EBNs and activation/response values (AVs/RVs) depend on plumpness, size, and germinability of hybrid seeds. Also, both hypotheses emphasize the importance of a balanced parental genic contribution for the normal development of endosperm. However, in the EBN hypothesis a 2 maternal1 paternal EBN ratio is a prerequisite for successful interspecific crossability, while the PNA hypothesis is based on the stimulative strength of the male nuclei to initiate mitotic divisions in the primary endosperm nucleus and is idependent on a 21 ratio between the RV of the polar nuclei and the AV of the male gamete. Differences and similarities betweeen the EBN and PNA hypotheses are summarized and contrasted. It is proposed that EBN and PNA be considered as the same concept.     

A new type of phosphoglycolipid fromPseudomonas cepacia

A new type of phosphoglycolipid was found inPseudomonas cepacia. A ratio of glucosamine/phosphoric acid/polar fatty acid/nonpolar fatty acid was resolved to be 1 1 1 1, and the molecular weight of the phosphoglycolipid was determined to be 777 by mass spectrometry. An amino group of the glucosamine was free, and both a phosphoric acid and two kinds of fatty acids were bound directly to the glucosamine.     

Genetics of fertility restoration in hybrid rice

Summary The cross combination involving 14 male-sterile lines in rice, when crossed with different maintainers, showed fertility restoration in certain combinations. When F₂ segregating populations were classified based on spikelet fertility, fertility restoration was shown to be governed by 31, 9331, and 1231, due to allelic differences. This indicated that the cytosterility of the same group showed monogenic fertility restoration, whereas crossing plants belonging to different cystosterile groups showed a digenic pattern of segregation.     

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.