Localization and synthesis of an insulin-binding region on human insulin receptor

Seven regions of the subunit of human insulin receptor (HIR) were synthesized and examined for their ability to bind radioiodinated insulin. A peptide representing one of these regions (namely, residues 655–670) exhibited a specific binding activity for insulin. In quantitative radiometric titrations, the binding curves of¹²⁵I-labeled insulin to adsorbents of peptide 655–670 and of purified placental membrane were similar or superimposable. The binding of radioiodinated insulin to peptide or to membrane adsorbents was completely inhibited by unlabeled insulin, and the inhibition curves indicated that the peptide and the membrane on the adsorbents had similar affinities. Synthetic peptides that were shorter (peptide 661–670) or longer (peptide 651–670) than the region 655–670 exhibited lower insulin-binding activity. It was concluded that an insulin-binding region in the HIR subunit resides within residues 655–670. The results do not rule out the possibility that other regions of the subunit may also participate in binding of HIR to insulin, with the region described here forming a face within a larger binding site.     

Structure-function relationships of β- D-glucan endo- and exohydrolases from higher plants

(13),(14)--d-Glucans represent an important component of cell walls in the Poaceae family of higher plants. A number of glycoside endo- and exohydrolases is required for the depolymerization of (13),(14)--d-glucans in germinated grain or for the partial hydrolysis of the polysaccharide in elongating vegetative tissues. The enzymes include (13),(14)--d-glucan endohydrolases (EC 3.2.1.73), which are classified as family 17 glycoside hydrolases, (14)--d-glucan glucohydrolases (family 1) and -d-glucan exohydrolases (family 3). Kinetic analyses of hydrolytic reactions enable the definition of action patterns, the thermodynamics of substrate binding, and the construction of subsite maps. Mechanism-based inhibitors and substrate analogues have been used to study the spatial orientation of the substrate in the active sites of the enzymes, at the atomic level. The inhibitors and substrate analogues also allow us to define the catalytic mechanisms of the enzymes and to identify catalytic amino acid residues. Three-dimensional structures of (13),(14)--d-glucan endohydrolases, (14)--d-glucan glucohydrolases and -d-glucan exohydrolases are available or can be reliably modelled from the crystal structures of related enzymes. Substrate analogues have been diffused into crystals for solving of the three-dimensional structures of enzyme-substrate complexes. This information provides valuable insights into potential biological roles of the enzymes in the degradation of the barley (13),(14)--d-glucans during endosperm mobilization and in cell elongation.     

Photoreversion und Photoprotektion bei UV-induzierten Mutationen des nichtphotoreaktivierbaren Bacteriums E.coli phr?

Summary Stationary phase cells of strain phr^–/MC 2 ofE. coli are not photoreactivable but the frequency of UV-induced mutations to low Streptomycine-resistance (S 3, 3/ml) is decreased strongly by illumination with light of fluorescence tubes (310 to 500 nm) after UV-irradiation. Also dark-reversion (DRM) of these mutations due to keeping UV-irradiated cells in saline is observed. Illumination before UV-irradiation decreases the frequency of the mutations (photoprotection against mutation=PPM) to the same extent as the combined action of photoreversion (PRM) and DRM. The lag-phase of cell division is prolonged strongly by illumination from 80 min without light to 150 min by the light-dose of highest activity. The additional lag is nearly the same if the illumination is done before, after or without UV-irradiation; this lag is about additive to the small lag caused by UV. Pre-illumination of the stationary-phase cells does not cause photoprotection against killing (PP), it even decreases the survival after high UV-doses. The observations support the hypothesis that PRM in this strain may be indirect, i.e. caused by the light-induced additional division lag which enhances the dark repair of UV-premutations. Also spontaneous premutations which are apparently present in the stationary-phase cells seem to be influenced by the light in this way.     

Purification and properties of gammagamma-enolase from pig brain

Isoelectric focusing revealed three enolase isoforms in pig brain, which were designated as - (pI = 6.5), - (pI = 5.6), and -enolase (pI = 5.2). The pI of purified -enolase was also 5.2. The -enolase isoform of enolase was purified from pig brain by a purification protocol involving heating to 55°C for 3 min, acetone precipitation, ammonium sulfate precipitation (40%–80%), DEAE Sephadex ion-exchange chromatography (pH 6.2), and Sephadex G200 gel filtration. The final specific activity was 82 units/mg protein. As with other vertebrate enolases, -enolase from pig proved to be a dimer with a native mass of 85 kDa and a subunit mass of 45 kDa. The pH optimum for the reaction in the glycolytic direction is 7.2. The K _m values for 2-PGA, PEP, and Mg²⁺ were determined to be 0.05, 0.25, and 0.50 mM, respectively, similar to K _m values of other vertebrate enolases. The amino acid composition of pig -enolase, as determined by amino acid analysis, shows strong similarity to the compositions of -enolases from rat, human, and mouse, as determined from their amino acid sequences. Despite the differences seen with some residues, and considering the ways that the compositions were obtained, it is assumed that pig -enolase is more similar than the composition data would indicate. Moreover, it is likely that the sequences of pig -enolase and the other -enolases are almost identical. Li⁺ proved to be a noncompetitive inhibitor with either 2-PGA or Mg²⁺ as the variable substrate. This enolase crystallized in the monoclinic space group P2, or P2₁. An R _symm <5% was obtained for data between 50 and 3.65 Å, but was a disappointing 30% for data between 3.65 and 3.10 Å, indicating crystal disorder.     

Inhibitory Effects of Bombusae concretio Salicea on Neuronal Secretion of Alzheimer's β-Amyloid Peptides, a Neurodegenerative Peptide

Alzheimer's disease (AD) is characterized by the age-related deposition of -amyloid (A) 40/42 peptide aggregates in vulnerable brain regions. Multiple levels of evidence implicate a central role for A in the pathophysiology of AD. A is generated by the regulated cleavage of a = 700 amino acid A precursor protein (APP). Full-length APP can undergo proteolytic cleavage either within the A domain to generate secreted sAPP or at the N-terminal and C-terminal domain(s) of A to generate amyloidogenic A peptides. Several epidemiological studies have reported that estrogen replacement therapy protects against the development of AD in postmenopausal women. The aim of this study was to elucidate the antioxidant neuroprotective mechanism of Bombusae concretio Salicea (BC). BC was effective protectants against oxidative glutamate toxicity in the murine neuroblastoma cells (N2a) and human neuroblastoma cells (SK-N-MC). BC exhibited similar protective properties against oxidative glutamate toxicity and H₂O₂ toxicity. BC exhibited an antioxidant activity at approximately 20 g/ml. BC of 5 g/ml was ineffective in preventing the oxidative modification of LDL. The half-maximal effective concentration for BC was 16 g/ml. These results suggested that BC supplementation in elderly men may be protective in the treatment of Alzheimer's disease (AD). We report here that treatment with BC increases the secretion of the nonamyloidogenic APP fragment, sAPP and decreases the secretion of A peptides from N2a cells and rat primary cerebrocortical neurons. These results raise the possibility that BC supplementation in elderly men may be protective in the treatment of AD.     

Simultaneous removal of chemical oxygen demand and nitrate in aerobic treatment of sewage wastewater using an immobilized photosynthetic bacterium of porous ceramic plates

A denitrifying photosynthetic bacterium (PSB), Rhodobacter sphaeroides S was immobilized on a porous ceramic plate (10×10×0.5cm) using a small amount of agar. In the bioreactor (3.5 l liquid) using this plate, repeated batch treatments of sewage wastewater (acetic acid as a carbon source) were carried out under aerobic conditions (DO 5mg/l) for two weeks. The simultaneous and effective removal of chemical oxygen demand (COD), ammonium, and nitrate was observed. In continuous treatment at a relatively high dilution rate of 0.20 h^–1 (retention time, five hours), the same simultaneous treatments were observed for about one month.     

Expression of a chimeric stilbene synthase gene in transgenic wheat lines

A chimeric stilbene synthase (sts)gene was transferred into wheat. Stilbene synthases play a role in the defence against fungal diseases in some plant species (e.g. groundnut or grapevine) by producing stilbenetype phytoalexins like resveratrol. Resveratrol is also claimed to have positive effects to human health. Embryogenic scutellar calli derived from immature embryos of the two commercial German spring wheat cultivars Combi and Hanno were used as target tissue for cotransformation by microprojectile delivery. The selectable marker/reporter gene constructs contained the bargene either driven by the ubiquitinpromoter from maize (pAHC 25, also containing the uidAgene driven by the ubiquitinpromoter), or by the actinpromoter (pDM 302) from rice. The cotransferred plasmid pStil 2 consisted of a grapevine stscoding region driven by the ubiquitin promoter. Eight transgenic Combi and one Hanno T_Oplant were obtained and, except one Combi T_Oplant, found to be cotransformants due to the integration of both the stsgene and the selectable marker or reporter genes. Expression of the stsgene was proven by RTPCR, and, for the first time, by detection of the stilbene synthase product resveratrol by HPLC and mass spectrometry. The stsgene was expressed in four of the seven transgenic Combi T_{_o}plants. Two of the respective T₁progenies segregated in a Mendelian manner were still expressing the gene. Investigations into methylation of the stsgene showed that in three nonexpressing progenies inactivation was paralleled by methylation.     

Expression of the human milk protein β-casein in transgenic potato plants

A 1177 bp cDNA fragment encoding the human milk protein -casein was introduced into Solanum tuberosum cells under control of the auxin-inducible, bidirectional mannopine synthase mas12) promoters using Agrobacterium tumefaciens-mediated leaf disc transformation methods. Antibiotic-resistant plants were regenerated and transformants selected based on luciferase activity carried by the expression vector containing the human -casein cDNA. The presence of human -casein cDNA in the plant genome was detected by PCR and DNA hybridization experiments. Human -casein mRNA was identified in leaf tissues of transgenic plants by RT-PCR analysis. Human - casein was identified in auxin-induced leaf and tuber tissues of transformed potato plants by immunoprecipitation and immunoblot analysis. Human -casein produced in transgenic plants migrated in polyacrylamide gels as a single band with an approximate molecular mass of 30 kDa. Immunoblot experiments identified approximately 0.01% of the total soluble protein of transgenic potato leaf tissue as -casein. The above experiments demonstrate the expression of human milk - casein as part of an edible food plant. These findings open the way for reconstitution of human milk inedible plants for replacement of bovine milk in baby foods for general improvement of infant nutrition, and for prevention of gastric and intestinal diseases in children     

Die Hypokotylfarbe als Markierungsfaktor von Genomstufen der Zuckerrübe

Zusammenfassung In zunehmendem Maße werden anisoploideBeta-Rübensorten angebaut, deren zytologische Kontrolle zwecks Feststellung der Genomstufenprozentanteile recht arbeitszeitaufwendig ist. Übereinstimmend mit polnischen Autoren wurde festgestellt, daß die Hypokotylfarbe ein geeigneter Markierungsfaktor für die einzelnen Genomstufen darstellt. Kreuzt man tetraploide Pflanzen, die ein grünes Hypokotyl besitzen, mit diploiden Pflanzen, die ein rosa Hypokotyl aufweisen, so erhält man von dem tetraploiden Partner tetraploide grüne und triploide hellbraune, von dem diploiden Partner diploide rosa und triploide hellbraune Nachkommenschaften. Die in bezug auf die Hypokotylfarbe heterozygoten Pflanzen kann man demnach von den homozygot grünen und homozygot rosa Individuen unterscheiden. Die Kreuzung diploid grünxtetraploid rosa ist für diese Zwecke nicht brauchbar, da sich die triploiden Heterozygoten mit einem grünen und zwei rosa Allelen in der Hypokotylfarbe nicht deutlich von den homozygoten rosa Pflanzen abheben. Auf die Bedeutung dieser Markierungsmöglichkeit für bestimmte Forschungsprobleme, die Züchtung und die Saatgutkontrolle wird hingewiesen.     

Conformation of the circular dumbbell d〈pCGC-TT-GCG-TT〉: Structure determination and molecular dynamics

Summary The circular DNA decamer 5-dpCGC-TT-GCG-TT-3 was studied in solution by means of NMR spectroscopy and molecular dynamics in H₂O. At a temperature of 269 K, a 50/50 mixture of two dumbbell structures (denoted L2L2 and L2L4) is present. The L2L2 form contains three Watson-Crick C-G base pairs and two two-residue loops in opposite parts of the molecule. On raising the temperature from 269 K to 314 K, the L2L4 conformer becomes increasingly dominant (95% at 314 K). This conformer has a partially disrupted G(anti)-C(syn) closing base pair in the 5-GTTC-3 loop with only one remaining (solvent-accessible) hydrogen bond between NH of the cytosine dC(1) and O6 of the guanine dG(8). The opposite 5-CTTG-3 loop remains stable. The two conformers occur in slow equilibrium (rate constant 2–20 s^–1). Structure determination of the L2L2 and L2L4 forms was performed with the aid of a full relaxation matrix approach (IRMA) in combination with restrained MD. Torsional information was obtained from coupling constants. Coupling constant analysis (³J_HH, ³J_HP, ³J_CP) gave detailed information about the local geometry around backbone torsion angles , , and , revealing a relatively high flexibility of the 5-GTTC-3 loop. The values of the coupling constants are virtually temperature-independent. Weakly constrained molecular dynamics in solvent was used to sample the conformational space of the dumbbell. The relaxation matrices from the MD simulation were averaged over r^–3 to predict dynamic NOE volumes. In order to account for the 1:1 conformational mixture of L2L2 and L2L4 present at 271 K, we also included S² factors and r^–6 averaging of the r^–3-averaged relaxation matrices. On matrix averaging, the agreement of NOE volumes with experiment improved significantly for protons located in the thermodynamically less stable 5-GTTC-3 loop. The difference in stability of the 5-CTTG-3 and 5-GTTC-3 loops is mainly caused by differences in the number of potential hydrogen bonds in the minor groove and differences in stacking overlap of the base pairs closing the minihairpin loops. The syn conformation for dC(1), favored at high temperature, is stabilized by solvation in the major groove. However, the conformational properties of the dC(1) base, as deduced from R-factor analysis and MD simulations, include a large flexibility about torsion angle .     

Defective remethylation of homocysteine is related to decreased synthesis of coenzymes B2 in thyroidectomized rats

Summary. We investigated the influence of hypothyroidism on homocysteine metabolism in rats, focusing on a hypothetical deficient synthesis of FAD by riboflavin kinases. Animals were allocated in control group (n=7), thyroidectomized rats (n=6), rats with diet deficient in vitamin B2, B9, B12, choline and methionine (n=7), thyroidectomized rats with deficient diet (n=9). Homocysteine was decreased in operated rats (2.6±1.01 vs. 4.05±1.0mol/L, P=0.02) and increased in deficient diet rats (29.56±4.52 vs. 4.05±1.0mol/L, P=0.001), when compared to control group. Erythrocyte-Glutathione-Reductase-Activation-Coefficient (index of FAD deficiency) was increased in thyroidectomized or deficient diet rats (P=0.004 for both). Methylenetetrahydrofolate-reductase and methionine-synthase activities were decreased in thyroidectomized rats but not in those subjected to deficient diet. Cystathionine--synthase was increased only in operated rats. Taken together, these results showed a defective re-methylation in surgical hypothyroidism, which was due in part to a defective synthesis of vitamin B2 coenzymes. This defective pathway was overcompensated by the increased Cystathionine--synthase activity.     

The taxonomic significance of the trunk limbs of the chydoridae (Cladocera)

Summary The differences in the structure of the trunk limbs allow to outline three sections of Chydoridae (see table I and fig. 1), coinciding with the sections distinguished according to the structure of the head pores.

---

Chydoridae (Cladocera)

Chydoridae (. ), , .

     

Darwin’s Methodological Evolution

A necessary condition for having a revolution named after you is that you are an innovator in your field. I argue that if Charles Darwin meets this condition, it is as a philosopher and methodologist. In 1991, I made the case for Darwins innovative use of thought experiment in the Origin. Here I place this innovative practice in the context of Darwins methodological commitments, trace its origins back into Darwins notebooks, and pursue Darwins suggestion that it owes its inspiration to Charles Lyell.     

Nuclear Overhauser effect investigation on GM1 ganglioside containingN-glycolyl-neuraminic acid (II3Neu5GcGgOse4Cer)

The conformational properties of the oligosaccharide chain of GM1 ganglioside containingN-glycolyl-neuraminic acid, -Gal-(1-3)--GalNAc-(1-4)-[-Neu5Gc-(2-3)]--Gal-(1-4)--Glc-(1-1)-Cer, were studied through NMR nuclear Overhauser effect investigations on the monomeric ganglioside in dimethylsulfoxide, and on mixed micelles of ganglioside and dodecylphosphocholine in water. Several interresidual contacts for the trisaccharide core--GalNAc-(1-4)-[-Neu5Gc-(2-3)]--Gal-were found to fix the relative orientitation of the three saccharides, while the glycosidic linkage of the terminal -Gal-was found to be quite mobile as the -Gal-(1-3)--GalNAc-disaccharide exists in different conformations. These results are similar to those found for two GM1 gangliosides containingN-acetyl-neuraminic acid and neuraminic acid [1].Abbreviations Ganglioside nomenclature is in accordance with Svennerholm [23] and the IUPAC-IUB Recommendations [24] GM3(Neu5Ac) II³Neu5AcLacCer, -Neu5Ac-(2-3)--Gal-(1-4)--Glc-(1-1)-Cer - GM3(Neu5Gc) II³Neu5GcLacCer, -Neu5Gc-(2-3)--Gal-(1-4)--Glc-(1-1)-Cer - GM1(Neu5Ac) II³Neu5AcGgOse₄Cer, -Gal-(1-3)--GalNAc-(1-4)-[-Neu5Ac-(2-3)]--Gal-(1-4)--Glc-(1-1)-Cer - GM1(Neu5Gc) II³Neu5GcGgOse₄Cer, -Gal-(1-3)--GalNAc-(1-4)-[-Neu5Gc-(2-3)]--Gal-(1-4)--Glc-(1-1)-Cer - GM1(Neu) II³NeuGgOse₄Cer, -Gal-(1-3)--GalNAc-(1-4)-[-Neu-(2-3)]--Glc-(1-1)-Cer - GD1a IV³Neu5AcII³Neu5AcGgOse₄Cer, -Neu5Ac-(2-3)--Gal-(1-3)--GalNAc-(1-4)-[-Neu5Ac-(2-3)]--Gal-(1-4)--Glc-(1-1)-Cer - GalNAc-GD1a IV⁴GalNAcIV³Neu5AcII³Neu5AcGgOse₄Cer, -GalNAc-(1-4)-[-Neu5Ac-(2-3)]--Gal-(1-3)--GalNAc-(1-4)-[-Neu5Ac-(2-3)]--Gal-(1-4)--Glc-(1-1)-Cer - Neu neuraminic acid - Neu5Ac N-acetyl-neuraminic acid - Neu5Gc N-glycolyl-neuraminic acid - Cer ceramide     

Retention of lead within the digestive vacuole inTetrahymena

Summary The ciliateTetrahymena pyriformis was exposed to lead acetate. Cell proliferation in the presence of 0.1% lead salt (with or without EDTA) equaled, after a variable lag period, that of the control cells. The lead (550 ppm) forms a fluffy precipitate with the organic growth medium; this was in part prevented by addition of EDTA. The cells primarily ingested the fluffy precipitate whereby they became exposed to large amounts of lead. Within the digestive vacuole, the fluffy precipitate became converted into refractile structures (3 m in diameter) which were egested and accumulated at the bottom of the culture flask. The lead content of these defecation balls was higher than that of the fluffy precipitate. In addition to the lead-containing vacuoles, the cells contained small, refractile granules. The apparent, high tolerance ofTetrahymena towards lead is believed to be due in part to the low ionic concentration of lead under the present conditions and in part to a detoxication mechanism consisting of retention of lead within the digestive vacuoles and perhaps of accumulation of lead within the small, refractile granules.     

Purification and partial characterization of an endo-(1→3)-β-D-glucanase fromEuphausia superba Dana (Antarctic Krill)

Summary We have found out that cell-free extracts from frozen krill decompose many oligo-and polysacharides, particularly with (13)--and (14)--linkages. Two individual proteins have very high activity with laminaran as the substrate. One of them has been isolated and purified 980-fold. Polyacrylamide-gel electrophoresis of purified preparation of krill (13)--glucanase [(13)--D-glucan glucanohydrolase, EC 3.2.1.6] demonstrated that it was slightly contaminated by one protein band inactive in laminaran hydrolysis. Studies on the hydrolysis of different substrates showed that the enzyme was able to break down only (13)--D-linkages by an endo-splitting mechanism. Glucono--lactone and heavy metal ions such as Hg²⁺ inhibited enzyme activity. The activity of the endo-(13)--glucanase of krill strictly depended on free thiol groups in a enzyme molecule. The Michaelis constant value for laminaran was 0.063 mg/ml. Optimal determined temperature was 65°C and optimal pH 5.0. Because of this enzyme's strong interaction with concavalin A-Sepharose it is suggested that it might be a glycoprotein.This work was supported by the Institute of Ecology of Polish Academy of Sciences as a part MR I/29 programme     

Is haemoglobin Gα Philadelphia linked to α-thalassaemia?

Summary The question, Is Hb G Philadelphia linked to -thalassaemia? was first posed because the abnormal haemoglobin is found in heterozygotes at a concentration greater than 25%, the proportion predicted from a 4 -chain gene model. Globin chain biosynthesis was studied in a West Indian family in which one parent had ⁺ thalassaemia and the other was heterozygous for the G Philadelphia chain gene. The former had a globin chain production ratio / well above 1, while the latter had a ratio significantly less than 1. One child of the marriage had inherited the ⁺ thallassaemia from one parent and the G Philadelphia chain gene from the other and showed the typical picture of /-thalassaemia (/ ratio slightly above normal). It is explained in the discussion that the evidence favours a close linkage of 2 -chain genes.     

Effects of exogenous linoleic acid on fatty acid composition,receptor-mediated cAMP formation,and transport functions in rat astrocytes in primary culture

We have examined the effects of culturing neonatal rat-brain astrocytes in medium containing delipidated serum, with or without added linoleic acid (LA, 18:26), on membrane fatty-acid composition and functions. After 18–21 days in culture, polyunsaturated fatty acids (PUFA) constituted24 mol% of the total fatty acids in the astrocytes grown in delipidated media (controls); these proportions were increased by 35–40% to33 mol% when the cells were supplemented with 35M LA. Notable differences in the PUFA profiles of the cells cultured with or without added LA included: (a) higher proportions of 6 PUFA in the LA-supplemented astrocytes (25%, relative to10% in controls) that were accompanied by an increase in the ratio of 6/3 PUFA (from <2 in controls to 5), and (b) higher proportions of 20:39 and 22:39 in the control astrocytes (>5%) relative to the LA-supplemented cells (1%). The major metabolites in the 6 PUFA-enriched cells were arachidonic (20:46), adrenic (22:46) and docosapentaenoic (22:56) acids (15, 5 & 3 mol%, respectively). Enrichment of the astrocytes in 6 PUFA did not alter basal levels of cAMP, nor did it affect the amounts of cAMP formed in response to forskolin, isoproterenol, adenosine or histamine. However, dopamine-dependent increases in cAMP formation in the presence of the phosphodiesterase inhibitor, Ro 20-1724, were reduced by 25% relative to those in controls. LA supplementation modified uptake of [³H]adenosine into the astrocytes; values for K_t for a high affinity transport were increased relative to controls, and maximum capacity of a lower affinity process was reduced. Uptake of [³H]glutamate was not altered in the 6 PUFA-enriched astrocytes. This study demonstrated that cultured astrocytes take up exogenous linoleic acid and incorporate its metabolites into, phospholipid, and that the resulting changes in membrans PUFA composition modify only specific cell functional properties.Abbreviations PUFA polyunsaturated fatty acid(s) - EFA essential fatty acid(s) - LA linoleic acid - AA arachidonic acid - DHA docosahexaenoic acid - BSA bovine serum albumin - DMEM Dulbecco's modified Eagle's medium - TBARS thiobarbituric-acid-reactive substances - NECA 5-N-ethylcarboxamidoadenosine Special issue dedicated to Dr. Leon S. Wolfe.     

Is There a Field-Theoretic Explanation For Precursor Biopolymers?

A Hu-Barkana-Gruzinov cold dark matter scalarfield may enter a weak isospin invariant derivative interactionthat causes the flow of right-handed electrons to align parallelto (). Hence, in the outer regions of galaxies where () islarge, as in galactic halos, the derivative interaction mayinduce a chirality-imbued quantum chemistry. Such a chirality-imbued chemistry would in turn be conducive to the formation ofabundant precursor biopolymers on interstellar dust grains,comets and meteors in galactic halo regions, with subsequentdelivery to planets in the inner galactic regions where and() are concomitantly near zero and left-right symmetricterrestrial quantum chemistry prevails.     

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.