α-Isopropylmalate synthase from Alcaligenes eutrophus H 16

The purified isopropylmalate synthase of Alcaligenes eutrophus H 16 reacted with the following -keto acids and acyl-coenzyme A derivatives (in the sequence of decreasing affinities): -ketoisovalerate, -keto-n-valerate, -ketobutyrate and pyruvate; acetyl-CoA, propionyl-CoA, butyryl-CoA. malonyl-CoA, valeryl-CoA, and crotonyl-CoA. -Ketoisocaproate, however, is a strong inhibitor of the enzyme. All reactions catalyzed by isopropylmalate synthase were inhibited to the same extent by the endproduct l-leucine. the substrate saturation curves of -ketoisovalerate or other -keto acids and of acetyl-coenzyme A or other acyl-CoA derivatives had intermediary plateau regions; the Hill coefficient alternated between n _H -values higher and lower than 1.0, indicating changes from positive to negative and from negative to positive cooperativity for the substrates. The products, isopropylmalate and free coenzyme A, showed competitive inhibition patterns against both substrates (-ketoisovalerate and acetyl-CoA). Free coenzyme A (1 M) inactivated the enzyme irreversibly. The 3-phosphate of coenzyme A and the free carboxyl group of -ketoisovalerate were involved in optimal binding of these substrates, but 3-dephospho-acetyl-coenzyme A and the methylester of -ketoisovalerate were also converted by this enzyme. A CH₃–CH₂-grouping of the -keto acids seemed to be necessary for binding this substrate.Abbreviations Used CoA Coenzyme A - Tris Tris(hydroxymethyl)aminomethane hydrochloride - DTNB 5,5-dithiobis-(2-nitrobenzoic acid) - IPM -Isopropylmalate - KIV -Ketoisovalerate Prepared from doctoral thesis of the University of Göttingen 1973     

Interaction between photosynthetic and respiratory electron-transfer chains in the membranes of Anabaena variabilis

The rate of CO₂- and p-benzoquione-dependent photosynthetic O₂ evolution by Anabaena variabilis cells remained unaltered and the rate of O₂ uptake observed after switching off the light (endogenous respiration) was enhanced by a factor of 6–8 when the O₂ concentration was increased from 200 to 400 M. Photosystem-I-linked O₂ uptake and respiration of the cells incubated with ascorbate and N,N,NN-tetramethyl-p-phenylenediamine was not appreciable influenced by the O₂ concentration. 2-Iodo-6-isopropyl-3-methyl-2,4,4-trinitrodiphenyl ether, blocking electron transfer at the plastoquinone level, suppressed O₂ evolution and had no influence on endogenous respiration. 2-n-Heptyl-4-hydroxyquinoline-N-oxide, an inhibitor of electron transfer between photosystems II and I, as well as the cytochrome-oxidase inhibitors N ₃ ^- , CN^- and NH₂OH, caused a 35–50% retardation of endogenous respiration and blocked photosynthetic O₂ evolution. The molar ratio of cytochromes b₆, f, c-553, aa₃ and photosystem-I reaction centers in the isolated membranes equalled approx. 2:1:2:0.7:2. It is inferred that endogenous respiration of A. variabilis cells is inhibited by the light-induced electron flow through both photosystems at the level of the plastoquinone-plastocyanin-oxidoreductase complex.Abbreviations DCMU 3-(3,4-dichlorophenyl)-1,1-dimethylurea - DNP-INT 2-iodo-6-isopropyl-3-methyl-2,4,4-trinitrodiphenyl ether - Hepes 4-(2-hydroxyethyl)-1-piperazine ethansulfonic acid - TMPD N,N,NN-tetramethyl-p-phenylenediamine     

sym 18. A novel gene conditioning altered strain specificity in Pisum sativum cv. ‘Sparkle’

An induced mutant of pea Pisum sativum cv. Sparkle forms few nodules with R. leguminosarum bv. viciea from temperate regions, exemplified by strain PRE, but nodulates normally with some rhizobia from Middle East soils, exemplified by strain TOM. The mutant gene is not an allele of sym2, found in the primitive cultivar Afghanistan. Mutant line E54 has a specificity similar to Afghanistan but forms more nodules with temperate strains, especially PF₂ which nodulates Afghanistan only poorly. The new phenotype is conditioned by gene sym18, which can act as recessive or semi-dominant depending on the rhizobial strain. Also sym18 is distinguished from sym 2 by its location on a different linkage group. Sym18 was mapped 9cM from k on linkage group II.     

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.     

Foam behavior of biological media

Summary The surface tension and foaminess of (a) unlimited, (b) substrate limited, and (c) oxygen transfer limited growth media of Hansenula polymorpha were measured using methanol, ethanol or glucose as a substrate.The time dependence of can be described by the Avrami-Überreiter relationship: log (2.3 log V)=n log t+log b, where V = (_O – _eq/(_t – _eq, and _O, _t and _eq are at t_M=0, t_M=t and t_M (equilibrium value).The constants n and b are functions of the fermentation time t_F as long as the growth is unlimited but they are constant in the state of limited growth. With glucose substrate, the foaminess can be presented as a definite function of the time, t_DG, which is necessary to attain _eq. With alcohol as a substrate no definite (t_DG) function was found.Symbols b constant in Eq. (1) - n constant in Eq. (1) - S substrate concentration - T temperature - t_M time h (measured from the beginning of the determination of the surface tension ) - t_F cultivation time h (measured from the time of inoculation) - t_DG time (min) necessary to attain the equilibrium surface tension ) - X dry biomass concentration (gl^–1) - V (_O – _eq)/(_t – _eq) - V_S equilibrium volume of the foam (cm³) - V_G volumetric gas flow rate during the estimation of (cm³ s^–1) - vvm volumetric gas flow rate with regard to the volume of the medium (min^–1) - w_SG superficial gas velocity (cm s^–1) - _m maximum specific growth rate (h^–1) - V_S/V_G foaminess (s) - surface tension, mMm^–1 (milli Newton m^–1) - _O at t_M=0 - _eq equilibrium surface tension ( at t_M) - _t at t_M=t - HP probes from Hansenula polymorpha cultivation - NLG non limited growth - OTLG oxygen transfer limited growth - SLG substrate limited growth     

Genetic analysis of resistance to whitebacked planthopper in twenty-one varieties of rice,Oryza sativa L.

Summary The inheritance of resistance to whitebacked planthopper Sogatella furcifera (Horvath) was studied in 21 rice varieties. Reactions of F₁; F₂ and F₃ progenies of the crosses of 21 resistant varieties with the susceptible variety TN 1 revealed that a single dominant gene governs resistance in Mushkan 41, Santhi, Siahnakidar 195, SM2-34, Tirisurkh 251, Zirijowaian 245, 18, 24A, 39, 76 S, 78, 180, 213 B, 267, 293, CI 6037-4, NP97, S39 JKW and Bansphul. In varieties 65 and 274 A, resistance is governed by one dominant and one recessive gene which segregate independently of each other. Tests for allelism with the Wbph 1 gene originally identified in N 22 revealed that the dominant gene present in all the test varieties is the same as Wbph 1. Further studies are required to determine the allelic relationships of the recessive gene found in varieties 65 and 274 A.     

Identification of functionally important cysteines in the alpha-subunit of transducin by chemical cross-linking techniques

Transducin (T), the G-protein in the visual system, is a heterotrimer arranged as two functional units, T and T. N, N-1, 2-phenylenedimaleimide (o-PDM) and N, N-1, 4-phenylenedimaleimide (p-PDM), two cysteine specific-homobifunctional agents, were used to covalently cross-link T and its units. A complete inhibition in T function was observed in the presence of these compounds. Incubation of T with o-PDM or p-PDM resulted in the formation of high-molecular-weight oligomers of 70-, 105-, 140-, and 200 kDa, as well as intramolecular cross-linked polypeptides that migrated as 35- and 37-kDa bands. Additionally, the treatment of T with both reagents produced a major species of 46-kDa. The combination of intact T and o-PDM- or p-PDM-treated T reconstituted T native activities. On the contrary, when o-PDM- or p-PDM-modified T was incubated with intact T, more than 90% inhibition on T function was observed. Hence, the cysteines modified and/or cross-linked on T represent functionally important residues of T.     

Heritable variation in the phaseolin protein of nondomesticated common bean,Phaseolus vulgaris L.

Summary Crude protein extracts from single seeds of nondomesticated Mexican bean accessions were analysed by SDS polyacrylamide gel electrophoresis for variability in phaseolin protein. Six new phaseolin types; M1, M2, M3, M4, M5, M6, which contained polypeptides within the same range of molecular weights (51,000 to 45,000 daltons) as occur in the S, T and C phaseolin types of cultivated beans were identified. No T and C types were found among the non-domesticated Mexican accessions, and the S type occurred in less than 7% of the seeds screened. Genetic analyses of F₂ progenies from crosses between Sanilac (S), and five of the M types showed that each M phaseolin phenotype was allelic to the S type and expressed codominantly.     

Synthesis of Nα,Nδ-dicarbobenzoxy-L-ornithyl-β-alanine benzyl ester,a derivative of salty peptide,in 1,1,1-trichloroethane with polyethylene glycol-modified papain

Summary N,N-Dicarbobenzoxy-L-ornithyl--alanine benzyl ester, a derivative of salty peptide, was synthesized from N,N-dicarbobenzoxy-L-ornithine ethyl ester and -alanine benzyl ester in 1,1,1-trichloroethane using papain modified with polyethylene glycol. The peptide bond formation proceeded in a transparent organic solvent at room temperature and the product was obtained as precipitates from the reaction system.     

Untersuchungen über die anisotrope 1:9-Dimethyl-Methylenblau- und N,N′-Diäthylpseudoisocyaninchloridfärbung der Glykokalyx

Zusammenfassung In den vorliegenden Untersuchungen wird die anisotrope 1:9-Dimethyl-Methylenblau- bzw. N,N-Diäthylpseudoisocyaninchloridfärbung an der Erythrocytenmenbran studiert und mit der topooptischen Toluidinblaufärbung verglichen.Die Abweichung zwischen anisotroper Toluidinblau- und 1:9-Dimethyl-Methylenblaufärbung sind (außer nach KMnO₄-Oxydation) nur quantitativer Natur. Demgegenüber sind die Unterschiede der N,N-Diäthylpseudoisocyaninchloridfärbung zur Toluidinblau- und zu den 1:9-Dimethyl-Methyllenblaufärbungen nach enzymatischen und chemischen Abbaureaktionen beträchtlich, denn nach den Vorbehandlungen ist die N,N-Diäthylpseudoisocyaninchloridfärbung praktisch ausgelöscht.Die Membrandoppelbrechung nach diesen Behandlungen ist durch eine anschließende Aldehyd-Bisulfitbildung oder KMnO₄-Oxydation mit 1:9-Dimethyl-Methylenblaufärbung vollkommen restaurierbar, die N,N-Diäthylpseudoisocyaninchloridfärbung ist es nur nach einer anschließenden KMnO₄-Oxydation.Nach Methylierung bzw. Acetylierung ist die Membrandoppelbrechung aufgehoben, jedoch nach KMnO₄-Oxydation mit beiden topo-optischen Färbungen wieder vorhanden. Nach der Digitonin-Behandlung haben wir eine Umorientierung der Glykokalyxkomponenten gesehen.Die Befunde weisen auf die Bedeutung der räumlichen Orientierung der Membranglykoproteine an Erythrocyten hin. Die durchgeführten histochemischen Vorbehandlungen demonstrieren die Rolle der Glykokalyx für die drei topo-optische Reaktionen.

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Investigation on the anisotropy of glycocalyx stained with 1.9-dimethyl methylene blue and N,N-diethylpseudoisocyanine chloride

Summary In the present study the anisotropic staining of the erythrocyte membrane with 1.9-dimethyl methylene blue and N,N-diethylpseudoisocyanine chloride was studied and simultaneously compared with the toluidine blue topo-optical staining. The difference between anisotropic toluidine blue and 1.9-dimethyl methylene blue staining, except after KMnO₄-oxidation, was only of quantitative nature. On the contrary, striking differences were observed between N,N-diethylpseudoisocyanine chloride staining, and toluidine blue or 1.9-dimethyl methylene blue staining. Enzymatic and chemical degradation resulted the disappearance of N,N-diethylpseudoisocyanine chloride staining.Following these treatment membrane birefringence could be restored by aldehyde bisulfate and/or KMnO₄-oxidation, while the N,N-diethylpseudoisocyanine chloride staining was restored only after KMnO₄-oxidation.After methylation or acetylation the membrane birefringence disappears, while after KMnO₄-oxidation both topo-optical reactions return. The digitonin reaction brought about a rearrangement of the glycocyalyx components. The results draw attention to the spatial orientation of the glycoprotein of the erythrocyte membrane. The role of glycocalyx in the three topo-optical reactions was thus clearly demonstrated.

     

Correlation between 15N NMR chemical shifts in proteins and secondary structure

Summary An empirical correlation between the peptide ¹⁵N chemical shift, ¹⁵N_i, and the backbone torsion angles _i, _i–1 is reported. By using two-dimensional shielding surfaces (_i1–1), it is possible in many cases to make reasonably accurate predictions of ¹⁵N chemical shifts for a given structure. On average, the rms error between experiment and prediction is about 3.5 ppm. Results for threonine, valine and isoleucine are worse (4.8 ppm), due presumably to ₁-distribution/-gauche effects. The rms errors for the other amino acids are 3 ppm, for a typical maximal chemical shift range of 15–20 ppm. Thus, there is a significant correlation between ¹⁵N chemical shift and secondary structure.     

Hydrogen isotope discrimination in higher plants: Correlations with photosynthetic pathway and environment

Summary The ratio of deuterium to hydrogen (expressed as D) in hydrogen released as water during the combustion of dried plant material was examined. The D value (metabolic hydrogen) determined on plant materials grown under controlled conditions is correlated with pathways of photosynthetic carbon metabolism. C₃ plants show mean D values of-132 for shoots and -117 for roots; C₄ plants show mean D values of -91 for shoots and-77 for roots and CAM plants a D value of-75 for roots and shoots. The difference between the D value of shoot material from C₃ and C₄ plants was confirmed in species growing under a range of glasshouse conditions. This difference in D value between C₃ and C₄ species does not appear to be due to differences in the D value (tissue water) in the plants as a result of physical fractionation of hydrogen isotopes during transpiration. In C₃ and C₄ plants the hydrogen isotope discrimination is in the same direction as the carbon isotope discrimination and factors contributing to the difference in D values are discussed. In CAM plants grown in the laboratory or collected from the field D values range from-75 to +50 and are correlated with ¹³C values. When deprived of water, the D value (metabolic hydrogen) in both soluble and insoluble material in leaves of Kalanchoe daigremontiana Hamet et Perr., becomes less negative. These changes may reflect the deuterium enrichment of tissue water during transpiration, or in field conditions, may reflect the different D value of available water in areas of increasing aridity. Whatever the origin of the variable D value in CAM plants, this parameter may be a useful index of the water relations of these plants under natural conditions.     

Lactate conversion to acetate,CO2 and H2 in cell suspensions of Desulfovibrio vulgaris (Marburg): indications for the involvement of an energy driven reaction

Cell suspensions of Desulfovibrio vulgaris were found to catalyze, in the absence of sulfate, the complete conversion of 1 lactate to 1 acetate, 1 CO₂, and 2 H₂ (G₀=-8.8 kJ/mol) and of 1 pyruvate to 1 acetate, 1 CO₂, and 1 H₂ (G₀=-52 kJ/mol). Protonophores, the proton translocating ATPase inhibitor N,N-dicyclohexylcarbodiimide, and arsenate specifically inhibited H₂ formation from lactate but not from pyruvate. The results suggest that lactate oxidation to pyruvate and H₂ (G ₀=+43.2 kJ/mol) is energy driven.     

Unambiguous through-bond sugar-to-base correlations for purines in 13C, 15N-labeled nucleic acids: The HsCsNb,HsCs(N)bCb,and HbNbCb experiments

Summary A set of three 3D (¹H, ¹³C, ¹⁵N) triple-resonance correlation experiments has been designed to provide H1-H8 intraresidue sugar-to-base correlations in purines in an unambiguous and efficient manner. Together, the H_sC_sN_b, H_sC_s(N)_bC_b, and H_bN_bC_b experiments correlate the H1 sugar proton to the H8 proton of the attached base by means of the {H1, C1, N9, C8, H8} heteronuclear scalar coupling network. The assignment strategy presented here allows for unambiguous H1-H8 intraresidue correlations, provided that no two purines have both the same H1 and C1 chemical shifts and the same C8 and N9 chemical shifts. These experiments have yielded H1-H8 intraresidue sugar-to-base correlations for all five guanosines in the [¹³C, ¹⁵N] isotopically labeled RNA duplex r(GGCGCUUGCGUC)₂.     

Spatial variability of soil total C and N and their stable isotopes in an upland Scottish grassland

As preparation for a below ground food web study, the spatial variability of three soil properties (total N, total C and pH) and two stable isotopes (¹³C and ¹⁵N of whole soil) were quantified using geostatistical approaches in upland pastures under contrasting management regimes (grazed, fertilised and ungrazed, unfertilised) in Scotland. This is the first such study of upland, north maritime grasslands. The resulting patterns of variability suggest that to obtain statistically independent samples in this system, a sampling distance of 13.5 m is required. Additionally, temporal change (a decline of 1) was observed in whole soil ¹⁵N for the grazed, fertilised plot. This may have been caused by new inputs of symbiotically-fixed atmospheric N₂.     

The energy transmission in ATP synthase: From the γ-c rotor to the α3β3 oligomer fixed by OSCP-b stator via the βDELSEED sequence

ATP synthase (F₀F₁) is driven by an electrochemical potential of H⁺ (H⁺). F₀F₁ is composed of an ion-conducting portion (F₀) and a catalytic portion (F₁). The subunit composition of F₁ is ₃₃. The active ₃₃ oligomer, characterized by X-ray crystallography, has been obtained only from thermnophilic F₁ (TF₁). We proposed in 1984 that ATP is released from the catalytic site (C site) by a conformational change induced by the DELSEED sequence via -F₀. In fact, cross-linking of DELSEED to stopped the ATP-driven rotation of in the center of ₃₃. The torque of the rotation is estimated to be 420 pN·å from the H⁺ and H⁺-current through F₀F₁. The angular velocity () of is the rate-limiting step, because H⁺ increased theV _max of H⁺ current through F₀, but not theK _m (ATP). The rotational unit of F₀ (=ab₂c₁₀) is /5, while that in ₃₃ is 2/3. This difference is overcome by an analog-digital conversion via elasticity around DELSEED with a threshold to release ATP. The distance at the C site is about 9.6 å (2,8-diN₃-ATP), and tight Mg-ATP binding in ₃₃ was shown by ESR. The rotational relaxation of TF₁ is too rapid (=100 nsec), but the rate of AT(D)P-induced conformational change of ₃₃ measured with a synchrotron is close to . The ATP bound between the P-loop and E188 is released by the shift of DELSEED from RGL. Considering the viscosity resistance and inertia of the free rotor (-c), there may be a stator containing OSCP (= of TF₁) and F₀-d to hold free rotation of ₃₃.     

Inhibition of ADP-ribosylation of histone H1 by analogs of diadenosine 5′, 5‴-p1,p4-tetraphosphate

The effects of analogs of diadenosine 5,5-p¹,p⁴-tetraphosphate (Ap4A) were examined on the ADP-ribosylation reaction of histone Hl catalysed by purified bovine thymus poly(ADP-ribose)transferase. Among the compounds tested, Ap4A and ApCH₂PPPA were shown to be the most efficient inhibitors of the enzyme. From kinetic studies of their action, it appears that Ap4A and ApCH₂pppA might be mixed type inhibitors.Abbreviations ADP-ribose adenosine diphosphate ribose - ADPRT poly-(ADP-ribose)transferase - Ap4A diadenosine 5,5-p₁,p₄-tertraphosphate - Ap4A diadenosine 5,5-p¹,p⁴(-1,N⁶-ethenyl-)tetra-phosphate - ApAA diadenosine 5,5-p¹,p⁴(-N⁶(-1,N⁶-)bisethenyl-)tetraphosphate - ApCH₂pppA diadenosine 5,5-p¹,p⁴(-p¹,p²-methylene-)tetraphosphate - AppCH₂ppA diadenosine 5,5-p¹,p⁴(-p²,p³methylene-)tetraphosphate - AppNHppA diadenosine 5,5-p¹,p⁴(-p²,p³-amino-)tetraphosphate - AppCHBrppA diadenosine 5,5-p¹,p⁴(-p²,p³-bromine methyno-)tetraphosphate - CpCH₂ppCH₂PC dicytidine 5,5-p¹,p⁴(-p¹,p²-p³,p⁴-bismethylene-)tetraphosphate - ApCH₂ppCH₂pA diadenosine 5,5-p¹,p⁴(-p¹,p²-p³,p⁴-bismethylene-)tetraphosphate.     

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     

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 generalized model of a resource-population system

Summary A system of nonlinear differential equations describing a resource-population system is analyzed in terms of the existence and characteristics of its equilibrium states.It is proved that, under the condition that k< (necessary condition for the population being able to grow under optimal conditions), it is a necessary and sufficient condition for the system to have a steady state that the resource input rate to the system be constant.When the resource input rate is a constant different from zero, the system has only one equilibrium point, at M ⁰=/⁰/k, A ⁰=–(/⁰/k)ln(1–k/), and this equilibrium point is always stable. In other words, the system population-resource will always reach the steady state, either monotonically (node) or by damped oscillations (focus), from any arbitrary initial condition in the positive quadrant.When the resource input rate is equal to zero, the system has an infinite number of equilibrium points at M ₀=0, A ₀=constant. All these equilibrium points are unstable in the sense that any slight increase in M will move the system away from the equilibrium states, except for the point M ₀=0, A ₀=0, which is the only stable equilibrium point, to which the system will tend. This stable equilibrium point corresponds to the condition of complete annihilation of both resource and population.Finally, it is proved that the system does not have limit cycles in the positive quadrant and is therefore incapable of self-oscillations.This work was partially supported by a Ford Foundation fellowship and various Cornell University fellowships.