Determination of bilayer thickness and lipid surface area in unilamellar dimyristoylphosphatidylcholine vesicles from small-angle neutron scattering curves: a comparison of evaluation methods

Small-angle neutron scattering (SANS) experiments were performed on unilamellar 1,2-dimyristoylphosphatidylcholine (DMPC) vesicles prepared in heavy water by extrusion through polycarbonate filters with 500 Å pores. The data obtained at 30±0.1 °C were evaluated using a five-strip function model of the bilayer coherent neutron scattering length density, three different approximate form factors describing scattering from vesicles, and different methods of evaluation of the experimental data. It is shown that the results obtained from the SANS data in the range of scattering vector values 0.0316 Å^–1<q<0.0775 Å^–1 are not sensitive to the vesicle form factor, nor to the evaluation method. Using the hollow sphere model of vesicles convoluted with the Gaussian distribution of their sizes, a constrained bilayer polar region thickness of 9 Å and a DMPC headgroup volume of 325.5 ų, it was possible to obtain from the experimental data the DMPC surface area as 58.9±0.8 Ų, the bilayer thickness as 44.5±0.3 Å and the number of water molecules as 6.8±0.2 per DMPC located in the bilayer polar region.     

Fractal dimension of humic acids

Small-angle neutron scattering experiments have been made on solutions of humic acid aggregates with an acidity corresponding to pH 5.0 and at 0.1 M ionic strength. We observe power-law decay of the intensity over one decade of the scattering vector, Q, indicating that the aggregates are fractal. We explain the normalized intensity in the entire Q-range by assuming that the humic acid particles can be described by building units of a radial size, 25 Å, aggregated into clusters with an average radius of 400–500 Å. For humic acids obtained from two different sources, we determine the fractal dimension, D = 2.3 ± 0.1. For small values of Q, the measured data of one of the samples extend into the Guinier range giving an average radius of gyration of 320 ± 20 Å. Correspondence to: R. Österberg     

Vibrational modes of hemoglobin in red blood cells.

Equine red blood cells were washed in saline heavy water (2H2O) to exchange the hydrogen atoms of the non-hemoglobin components with deuterons. This led to novel neutron scattering measurements of protein vibrations within a cellular system and permitted a comparison with inelastic neutron scattering measurements on purified horse hemoglobin, either dry or wetted with 2H2O. As a function of wavevector transfer Q and the frequency transfer v the neutron response typified by the dynamic structure factor S(Q, v) was found to be similar for extracted and cellular hemoglobin at low and high temperatures. At 77 K, in the cells, a peak in S(Q, v) due to the protein was found near 0.7 THz, approximately half the frequency of a strong peak in the aqueous medium. Measurements at higher temperatures (170 and 230 K) indicated similar small shifts downwards in the peak frequencies of both components. At 260 K the low frequency component became predominantly quasielastic, but a significant inelastic component could still be ascribed to the aqueous scattering. Near 295 K the frequency responses of both components were similar and centered near zero. When scattering due to water is taken into account it appears that the protein neutron response in, or out of, red blood cells is little affected by hydration in the low frequency regime where Van der Waals forces are thought to be effective.     

Large-scale oscillatory motions in myoglobin

Elastic and inelastic components of neutron scattering from lyophilized myoglobin were measured at wavevector transfers, Q of 1.0, 1.4, 1.85, and 3.0 Å^-1 and at temperatures of 77 and 298 K. The elastic scattering determines an overall effective mean square atomic displacement which was employed in a simple harmonic Langevin formalism to obtain effective force constants describing molecular deformations. These force constants and the inelastic data are compatible with alpha helices as a vibrating species at room temperature, and with amino acid residues as the vibrating entities at 77 K. The present measurements are consistent with recent molecular dynamics calculations.     

What can we learn about the lipid vesicle structure from the small-angle neutron scattering experiment?

Small-angle neutron scattering (SANS) on the unilamellar vesicle (ULV) populations (diameter 500 and 1,000 Å) in D₂O was used to characterize lipid vesicles from dimyristoylphosphatidylcholine (DMPC) at three phases: gel L_β′, ripple P_β′ and liquid L_α. Parameters of vesicle populations and internal structure of the DMPC bilayer were characterized on the basis of the separated form factor (SFF) model. Vesicle shape changes from nearly spherical in the L_α phase to elliptical in the P_β′ and L_β′ phases. This is true for vesicles prepared via extrusion through pores with the diameter 500 Å. Parameters of the internal bilayer structure (thickness of the membrane and the hydrophobic core, hydration and the surface area of the lipid molecule) were determined on the basis of the hydrophobic–hydrophilic (HH) approximation of neutron scattering length density across the bilayer ρ(x) and of the step function (SF) approximation of ρ(x). DMPC membrane thickness in the L_α phase (T=30°C) demonstrates a dependence on the membrane curvature for extruded vesicles. Prepared via extrusion through 500 Å diameter pores, vesicle population in the L_α phase has the following characteristics: average value of minor semi-axis 266±2 Å, ellipse eccentricity 1.11±0.02, polydispersity 26%, thickness of the membrane 48.9±0.2 Å and of the hydrophobic core 19.9±0.4 Å, surface area 60.7±0.5 Ų and number of water molecules 12.8±0.3 per DMPC molecule. Vesicles prepared via extrusion through pores with the diameter 1,000 Å have polydispersity of 48% and membrane thickness of 45.5±0.6 Å in the L_α phase. SF approximation was used to describe the DMPC membrane structure in L_β′ (T=10°C) and P_β′ (T=20°C) phases. Extruded DMPC vesicles in D₂O have membrane thickness of 49.6±0.5 Å in the L_β′ phase and 48.3±0.6 Å in the P_β′ phase. The dependence of the DMPC membrane thickness on temperature was restored from the SANS experiment.     

Characterization of a half-molecular fragment obtained by reduction of human α2-macroglobulin with dithiothreitol

A half-molecular fragment of ₂-macroglobulin has been prepared by reducing and alkylating the inter-subunit disulfide bonds in the tetrameric ₂-macroglobulin molecule with 1 mM dithiothreitol (40 min) and 3 mM iodoacetamide (40 min). Further purification was made by gel chromatography and the homogeneous population of halfmolecules has been characterized by the techniques of small-angle X-ray and neutron scattering. The radii of gyration found by the two methods are 57.0 and 58.0 Å, respectively. The match point, obtained by neutron scattering from solutions with different H₂O/D₂O rations, is at 43% D₂O; the data are consistent with a particle having a higher scattering density at large distances from the particle centre. From the X-ray and neutron intensities scattered at zero angle, the specific volume was determined to be 0.73 cm³/g at+5°C and the molecular weight to be 390,000; the latter value is associated with a relatively large error due to the uncertainty in the concentration determination. Shape analysis indicates that the best-fitting scattering-equivalent threeaxial bodies are oblate shaped, with two of their axial dimensions about three to four times larger than the third one. From the volume of the best-fitting scattering-equivalent three-axial bodies, 0.72×10⁶ ų, we obtain a water content equal to 0.38 g H₂O/g protein (dry weight).Abbreviations SANS small-angle neutron scattering - SAXS small-angle X-ray scattering - ₂ M ₂-macroglobulin - DTT dithiothreitol - Tris tris(hydroxymethyl)aminomethane     

Three-dimensional structure of the Hck SH2 domain in solution

The hematopoietic cellular kinase (Hck) is a member of the Srcfamily of non-receptor protein-tyrosine kinases that is expressedpredominantly in granulocytes, monocytes and macrophages. Recentobservations suggest that Hck may be activated in HIV-infected macrophagesand in chronic myelogenous leukemia cells that express Bcr-Abl. In order toincrease our understanding of the structural basis for regulation of Hckactivity under normal and pathological conditions, we have solved thesolution structure of the uncomplexed Hck SH2 domain using NMR spectroscopy.A novel procedure that uses intraresidueH^NH distances as references forconverting NOE intensities into distance restraints has been described. Atotal of 1757 significant experimental restraints were derived from NMRspectroscopic data including 238 medium-range and 487 long-range distancerestraints and 177 torsion angle restraints. These restraints were used in asimulated annealing procedure to generate 20 structures with the programDYANA. Superimposition of residues 5–104 upon the mean coordinate setyielded an average atomic rmsd values of 0.42 ± 0.08 Å for theN,C,C atoms and 0.81 ± 0.08 Å forall heavy atoms. Rmsd values for those residues in the regions of orderedsecondary structure were 0.27 ± 0.04 Å for theN,C,C atoms and 0.73 ± 0.06 Å forall heavy atoms.     

Change in substrate metabolism in isolated mouse hearts following ischemia-reperfusion

Several genetic and transgenic mouse models are currently being used for studying the regulation of myocardial contractility under normal conditions and in disease states. Little information has been provided, however, about myocardial energy metabolism in mouse hearts. We measured glycolysis, glucose oxidation and palmitate oxidation (using ³H-glucose, ¹⁴C-glucose and ³H-palmitate) in isolated working mouse hearts during normoxic conditions (control group) and following a 15 min global no-flow ischemic period (reperfusion group). Fifty min following reperfusion (10 min Langendorff perfusion + 40 min working heart perfusion) aortic flow, coronary flow, cardiac output, peak systolic pressure and heart rate were 44 ± 4, 88 ± 4, 57 ± 4, 94 ± 2 and 81 ± 4% of pre-ischemic values. Rates of glycolysis and glucose oxidation in the reperfusion group (13.6 ± 0.8 and 2.8 ± 0.2 mol/min/g dry wt) were not different from the control group (12.3 ± 0.6 and 2.5 ± 0.2 mol/min/g dry wt). Palmitate oxidation, however, was markedly elevated in the reperfusion group as compared to the control group (576 ± 37 vs. 357 ± 21 nmol/min/g dry wt, p < 0.05). This change in myocardial substrate utilization was accompanied by a marked fall in cardiac efficiency measured as cardiac output/oxidative ATP production (136 ± 10 vs. 54 ± 5 ml/mol ATP, p < 0.05, control and reperfusion group, respectively). We conclude that ischemia-reperfusion in isolated working mouse hearts is associated with a shift in myocardial substrate utilization in favour of fatty acids, in line with previous observations in rat.     

Lipid bilayer structure determined by the simultaneous analysis of neutron and X-ray scattering data

Quantitative structures were obtained for the fully hydrated fluid phases of dioleoylphosphatidylcholine (DOPC) and dipalmitoylphosphatidylcholine (DPPC) bilayers by simultaneously analyzing x-ray and neutron scattering data. The neutron data for DOPC included two solvent contrasts, 50% and 100% D₂O. For DPPC, additional contrast data were obtained with deuterated analogs DPPC_d62, DPPC_d13, and DPPC_d9. For the analysis, we developed a model that is based on volume probability distributions and their spatial conservation. The model's design was guided and tested by a DOPC molecular dynamics simulation. The model consistently captures the salient features found in both electron and neutron scattering density profiles. A key result of the analysis is the molecular surface area, A. For DPPC at 50°C A = 63.0 Å², whereas for DOPC at 30°C A = 67.4 Å², with estimated uncertainties of 1 Å². Although A for DPPC agrees with a recently reported value obtained solely from the analysis of x-ray scattering data, A for DOPC is almost 10% smaller. This improved method for determining lipid areas helps to reconcile long-standing differences in the values of lipid areas obtained from stand-alone x-ray and neutron scattering experiments and poses new challenges for molecular dynamics simulations.     

Stable sulfur isotopic biogeochemistry of the Hubbard Brook Experimental Forest, New Hampshire

In natural ecosystems, differences often exist in the relative abundanceof stable S isotopes (°³⁴S) that can provide clues as tothe source, nature, and cycling of S. Values of °³⁴S inprecipitation, throughfall, soils, soil solution, and stream waters weremeasured at the Hubbard Brook Experimental Forest (HBEF), New Hampshire.Values of °³⁴S in precipitation and throughfall weresimilar to each other but differed seasonally. Precipitation°³⁴S values were higher in the dormant season[°³⁴S = 5.9±0.6 (17)][Mean + SE(N)]than in the growing season [°³⁴S = 5.0±0.6(40)] but throughfall growing-season values were higher[°³⁴S = 5.6±0.6(68)] than for the dormantseason [°³⁴S = 4.9±0.7 (9)]. Different treespecies did not affect throughfall °³⁴S values. In soilsolution, °³⁴S values were higher in the growing season(°³⁴S = 8.9±2.8; 8.8±1.7;and 4.0±0.6 for Oa, Bh, and Bs horizons, respectively) thanin the dormant season (°³⁴S = 5.6±1.5;3.7±2.4; and 3.4±1.2 for Oa, Bh, and Bshorizons, respectively). These seasonal differences in°³⁴S were probably caused by biological isotopicfractionation. The °³⁴S values in streams were generally2 lower and more variable than those in precipitation andthroughfall, suggesting fractionation and/or different isotopic sources inthe soil.     

Environmentally induced formation of plasmatic filaments in the protonema ofCeratodon purpureus

Summary Incubation of spores ofCeratodon in 0.1% sucrose solution in darkness causes the formation of abundant filamentous bundles with an average width of 0.39±0.02 . The center-to-center distance of adjacent filaments is 216±1.4 Å. The individual filaments have an electron-dense tubular part with a diameter of 108±0.6 Å. Dictyosome-derived coated vesicles, which enlarge to ER-like coated tubuli, are always associated with the filaments. In younger cultures these electron-dense coated tubuli seem to spin filaments from their sides.     

New insights into the structure and hydration of a stratum corneum lipid model membrane by neutron diffraction

The structure and hydration of a stratum corneum (SC) lipid model membrane composed of N-(-hydroxyoctadecanoyl)-phytosphingosine (CER6)/cholesterol (Ch)/palmitic acid (PA)/cholesterol sulfate (ChS) were characterized by neutron diffraction. The neutron scattering length density across the SC lipid model membrane was calculated from measured diffraction peak intensities. The internal membrane structure and water distribution function across the bilayer were determined. The low hydration of the intermembrane space is a major feature of the SC lipid model membrane. The thickness of the water layer in the SC lipid model membrane is about 1 Å at full hydration. For the composition 55% CER6/25% Ch/15% PA/5% ChS, in a partly dehydrated state (60% humidity) and at 32°C, the lamellar repeat distance and the membrane thickness have the same value of 45.6 Å . The hydrophobic region of the membrane has a thickness of 31.2 Å . A decrease of the Ch content increases the membrane thickness. The water diffusion through the SC lipid model multilamellar membrane is a considerably slow process relative to that through phospholipid membranes. In excess water, the membrane hydration follows an exponential law with two characteristic times of 93 and 44 min. At 81°C and 97% humidity, the membrane separates into two phases with repeat distances of 45.8 and 40.5 Å . Possible conformations of CER6 molecules in the dry and hydrated multilayers are discussed.     

Contrast variation studies of clathrin coated vesicles by small-angle neutron scattering

Structural information on clathrin coated vesicles has been obtained by small angle neutron scattering using contrast variation. A characteristic peak in the neutron scattering profile, which is apparent in 75 % D₂O, as well as in H₂O, disappears when contrast matching the protein component of the coated vesicles in 42% D₂O. Neutron, as well as dynamic, light scattering give a coated vesicle size of about 900 Å in H₂O and D₂O, but for neutron scattering the diameter decreases when matching out the protein coat of the clathrin coated vesicles. From the match point for the clathrin coated vesicles it is demonstrated that the clathrin cages do contain internal membrane. The mass of 34 MD and composition of 75% protein and 25% lipid found from the analysis of the small-angle scattering data are both in good agreement with the values reported in the literature. Electron microscopy gives an average outer diameter of 880 Å for the coated vesicles and an average diameter of 460 Å for the vesicle itself. Offprint requests to: Correspondence to: R. Bauer     

1H and 15N NMR assignment and solution structure of the SH3 domain of spectrin: Comparison of unrefined and refined structure sets with the crystal structure

The assignment of the ¹H and ¹⁵Nnuclear magnetic resonance spectra of the Src-homology region 3 domain ofchicken brain -spectrin has been obtained. A set of solutionstructures has been determined from distance and dihedral angle restraints,which provide a reasonable representation of the protein structure insolution, as evaluated by a principal component analysis of the globalpairwise root-mean-square deviation (rmsd) in a large set of structuresconsisting of the refined and unrefined solution structures and the crystalstructure. The solution structure is well defined, with a lower degree ofconvergence between the structures in the loop regions than in the secondarystructure elements. The average pairwise rmsd between the 15 refinedsolution structures is 0.71 ± 0.13 Å for the backbone atoms and1.43 ± 0.14 Å for all heavy atoms. The solution structure isbasically the same as the crystal structure. The average rmsd between the 15refined solution structures and the crystal structure is 0.76 Å forthe backbone atoms and 1.45 ± 0.09 Å for all heavy atoms. Thereare, however, small differences probably caused by intermolecular contactsin the crystal structure.     

Plasma hormonal and electrolyte alterations in cycling buffaloes (Bubalus bubalis) during hot summer months

Plasma levels of progesterone, prolactin, luteinizing hormone, and electrolytes were monitored by radioimmunoassay in ten cycling buffaloes maintained at Punjab Agricultural University, Ludhiana during the hot summer months of June–July. The plasma progesterone concentration ranged from 0.28±0.04 to 3.09±0.03 ng/ml at various stages of the oestrous cycle. Prolactin values ranged from 319±23 to 371±25 ng/ml and LH levels from 0.95±0.05 to 1.35±0.08 ng/ml. Concentrations differed significantly (P0.05) at various stages of the cycle. Levels of electrolytes, viz. Ca^{+ +}, Na⁺ and K⁺, were well within the normal range. The high levels of prolactin, progesterone and LH during the hot summer were assessed in relation to poor reproductive efficiency in buffaloes.     

Shape of phosphofructokinase fromEscherichia coli in solution

Summary Small angle X-ray scattering measurements and electron microscopic studies were carried out onE. coli phosphofructokinase (E.C. 2.7.1.11; ATP: D-fructose-6-phosphate-1-phosphotransferase). The results suggest a tetrahedral arrangement of the protomers resulting in a radius of gyration of the enzyme of R=34.6 Å and a Stokes' radius of R₀=44.0 Å. The stereochemical arrangement of the four protomers, each of a molecular weight of 35,000, within theE. coli enzyme was further substantiated by a comparison of theoretical scattering functions with the experimental scattering measurements in dilute solutions of phosphofructokinase under physiological conditions. Moreover, from other hydrodynamic measurements,e.g., intrinsic viscosity and sedimentation coefficient, theMandelkern-Scheraga factor, , was calculated to be 2,095×10⁶, which is significantly lower than the ₀ for rigid spheres of 2,112×10⁶. This low -value might be due to a considerable porosity of the four protomers for mobile water molecules. The -value of 2,095×10⁶ is an indication of a porous sphere of almost uniform density at aDebye shielding ratio of 6.5, corresponding to a sphere radius of 22.0 Å for one protomer and an inverse hydrodynamic shielding length of 0.45 Å^–1.Fachrichtung Biochemie der Pflanzen undFachrichtung Feinstrukturforschung und Elektronenmikroskopie.     

Conformation of the high molecular weight form ofDunaliella salina phosphofructokinase in solution by means of small-angle X-ray diffraction and viscosity measurements

Summary The intrinsic viscosity of phosphofructokinase fromDunaliella salina in different states of aggregation was determined. The instrinsic viscosity [], of the biologically active tetramer, with a molecular weight of 320,000, was found to be 6.5 ml·g^–1 at 4°C. Moreover, for the inactive dimer, with a molecular weight of 160,000, a value of []=8.0 ml·g^–1 was determined. The high molecular weight aggregate of phosphofructokinase fromDunaliella salina, that shows little activity, has an intrinsic viscosity of 23.2 ml·g^–1, which is significantly higher than that found for the active tetramer and the inactive dimer.Small angle X-ray scattering experiments in solution of this high molecular from of phosphofructokinase fromDunaliella salina reveal a radius of gyration of the cross section ofR _c=49.0 Å at an ionic strength of 0.15 M and_pH 7.2. Furthermore, a comparison of the values obtained for the tetramer and the radius of gyration (R _g=52.9 Å) with those of typical spherical proteins (3–4 ml·g^–1) shows that the values of [] andR _g are significantly larger for the high molecular weight form of phosphofructokinase than for the spherical proteins. The high intrinsic viscosity of the polymeric form of phosphofructokinase suggests an end-to-end aggregation consisting of monomeric units with heights,h=80–90 Å, and a cylindrical diameter of approximately 140.0 Å, resulting in a long rod of a total length of 1,800 Å and a molecular weight of two million. On the basis of the experimentally observedR _c and [] values, using a prolate ellipsoid of revolution as a model, the hydrodynamic volume and the hydration, the axial ratio could be determined to be 12. The native tetrameric form contains 0.4 g H₂O/g protein, whereas the higher aggregate structure corresponds to a hydration of 0.60 g H₂O/g protein.     

The ultrastructure and flexibility of thylakoid membranes in leaves and isolated chloroplasts as revealed by small-angle neutron scattering

We studied the periodicity of the multilamellar membrane system of granal chloroplasts in different isolated plant thylakoid membranes, using different suspension media, as well as on different detached leaves and isolated protoplasts—using small-angle neutron scattering. Freshly isolated thylakoid membranes suspended in isotonic or hypertonic media, containing sorbitol supplemented with cations, displayed Bragg peaks typically between 0.019 and 0.023 Å^− 1, corresponding to spatially and statistically averaged repeat distance values of about 275–330 Å. Similar data obtained earlier led us in previous work to propose an origin from the periodicity of stroma thylakoid membranes. However, detached leaves, of eleven different species, infiltrated with or soaked in D₂O in dim laboratory light or transpired with D₂O prior to measurements, exhibited considerably smaller repeat distances, typically between 210 and 230 Å, ruling out a stromal membrane origin. Similar values were obtained on isolated tobacco and spinach protoplasts. When NaCl was used as osmoticum, the Bragg peaks of isolated thylakoid membranes almost coincided with those in the same batch of leaves and the repeat distances were very close to the electron microscopically determined values in the grana. Although neutron scattering and electron microscopy yield somewhat different values, which is not fully understood, we can conclude that small-angle neutron scattering is a suitable technique to study the periodic organization of granal thylakoid membranes in intact leaves under physiological conditions and with a time resolution of minutes or shorter. We also show here, for the first time on leaves, that the periodicity of thylakoid membranes in situ responds dynamically to moderately strong illumination. This article is part of a Special Issue entitled: Photosynthesis research for sustainability: Keys to produce clean energy.     

Molecular structure and intra- and intermolecular magnetic interactions in chloro-bridged copper(II) dimers

Magnetic interactions in binuclear copper(II) complexes, [Cu₂(apyhist)₂Cl₂](ClO₄)₂ (1) and [Cu₂(2-pyhist)₂Cl₂](ClO₄)₂ (2) with tridentate diimine ligands and chloro-bridged groups (where apyhist=(4-imidazolyl)ethylene-2-amino-1-ethylpyridine and 2-pyhist=(4-imidazolyl)ethylene-2-aminomethylpyridine) were studied with the aim of better elucidating magneto-structural correlations in such species, both in solution and in solid state. X-ray analyses revealed that chloro-bridged ligands keep the copper(II) ion coordinated to adjacent unit, at Cu-Cl distances of 2.271 and 2.737 Å, and a Cu-Cl-Cu angle of 87.46° in compound 1. Each Cu^II atom is also coordinated to three N atoms from the imine ligand, in a distorted tetragonal pyramidal environment. Magnetic measurements carried out in temperatures from 0.8 to 290 K and in magnetic field up to 170 kOe indicated that besides the intramolecular magnetic coupling between the copper centers [J/k=−(1.93±0.05) K] further interactions between adjacent dimers [J^′z/k=−(1.3±0.1) K] should be taken into account. Similar results were observed for compound 2, for which [J/k=−(4.27±0.05) K] and [J^′z/k=−(3.7±0.1) K]. In solution, the interconversion of the dimer 1 and the related monomer species [Cu(apyhist)(H₂O)₂] (ClO₄)₂ (3) monitored by EPR spectra, was verified to be very dependent on the solvent.     

Population growth of some genera of cladocerans (Cladocera) in relation to algal food (Chlorella vulgaris) levels

We studied the patterns of population growth of 7 cladoceran species (Alona rectangula, Ceriodaphnia dubia, Daphnia laevis, Diaphanosoma brachyurum, Moina macrocopa, Scapholeberis kingi and Simocephalus vetulus) using 6 algal densities, viz. 0.05×10⁶, 0.1×10⁶, 0.2×10⁶, 0.4×10⁶, 0.8×10⁶ and 1.6×10⁶ cells ml^–1, of Chlorella vulgaris for 18 – 30 days. In terms of carbon content these algal concentrations corresponded to 0.29, 0.58, 1.16, 2.33, 4.65 and 9.31 g ml^–1, respectively. Cladocerans in the tested range of algal levels responded similarly, in that increasing the food concentrations resulted in higher numerical abundance and population growth rates (r). The peak population densities were (mean±standard error) 71±5; 17.1±0.4, 3.6±0.3, 12.7±1.1, 18.2±2.7, 15.8±1.0 and 10.9±0.02 ind. ml^–1, respectively for A. rectangula, C. dubia, D. laevis, D. brachyurum, M. macrocopa, S. kingi and S. vetulus. In general, the lowest r values were obtained for D. laevis (0.01±0.001) at 0.05×10⁶ cells ml^–1 food level while the highest was 0.283±0.004 for A. rectangula at 1.6×10⁶ cells ml^–1 of Chlorella. When the data of peak population density for each cladoceran species were plotted against the body length, we found an inverse relation, broadly curvilinear in shape. From regression equations between the food level and rate of population increase, we calculated the theoretical food quantity (the threshold level) required to maintain a zero population growth (r = 0) for each cladoceran species, which varied from 0.107 to 0.289 g ml^–1 d^–1 depending on the body size. When we plotted the cladoceran body size against the corresponding threshold food levels, we obtained a normal distribution curve. From this it became evident that for up to 1300 m body size, the threshold food level increased with increasing body size; however, beyond this, the threshold level decreased supporting earlier observations on rotifers and large cladocerans.