Generation of density gradients. Approximations to equivolumetric gradients for zonal rotors

The use of a “density gradient generating function” allows the concentration profile of a density gradient to be written explicitly in terms of the required distribution of sedimentation coefficients in place of the previous implicit formulations. This function, which is easily implemented in a computer program, permits calculation of density gradients for a number of applications. This approach is applied to computation of a variety of equivolumetric gradients of sucrose for zonal rotors and yields a formula for the calibration of such gradients. An accurate approximation has been found which allows the generation of virtually all equivolumetric gradients of sucrose for a given rotor using a single program for the gradient generator employed; the adjustment for different particle densities and for different concentrations at the top of the gradient is made by varying only the initial and final concentrations of sucrose used.     

Components of the plasma membrane of growing axons. II. Diffusion of membrane protein complexes

Intramembrane particles (IMPs) of the plasmalemma of mature, synapsing neurons are evenly distributed along the axon shaft. In contrast, IMPs of growing olfactory axons form density gradients: IMP density decreases with increasing distance from the perikarya, with a slope that depends upon IMP size (Small, R., and K. H. Pfenninger, 1984, J. Cell Biol., 98: 1422-1433). These IMP density gradients resemble Gaussian tails, but they are much more accurately described by the equations formulated for diffusion in a system with a moving boundary (a Stefan Problem), using constants that are dependent upon IMP size. The resulting model predicts a shallow, nearly linear IMP density profile at early stages of growth. Later, this profile becomes gradually transformed into a steep nonlinear gradient as axon elongation proceeds. This prediction is borne out by the experimental evidence. The diffusion coefficients calculated from this model range from 0.5 to 1.8 X 10(-7) cm2/s for IMPs between 14.8 and 3.6 nm, respectively. These diffusion coefficients are linearly dependent upon the inverse IMP diameter in accordance with the Stokes-Einstein relationship. The measured viscosity is approximately 7 centipoise. Our findings indicate (a) that most IMPs in growing axons reach distal locations by lateral diffusion in the plasma membrane, (b) that IMPs-- or complexes of integral membrane proteins--can diffuse at considerably higher rates than previously reported for iso-concentration systems, and (c) that the laws of diffusion determined for macroscopic systems are applicable to the submicroscopic membrane system.     

Localization of the membrane-associated CTP:phosphocholine cytidylyltransferase in Chinese hamster ovary cells with an altered membrane composition

The subcellular localization of the membrane-associated CTP:phosphocholine cytidylyltransferase was determined in Chinese hamster ovary cells in which the phospholipid composition had been altered by growth in the presence of N-methylethanolamine or treatment with phospholipase C. Cell homogenates were fractionated on Percoll density gradients, and marker enzyme activities were used to determine the location of the cellular membrane fractions. The peak of cytidylyltransferase activity occurred in the gradient at a density intermediate to that of the peaks of endoplasmic reticulum and plasma membrane markers. The profile of cytidylyltransferase activity most closely resembled that of the Golgi membrane marker; however, upon sucrose gradient centrifugation, the profile of the Golgi apparatus was very different from that of cytidylyltransferase. Differential centrifugation suggested a nuclear membrane association of the enzyme. Cytidylyltransferase was associated with a membrane fraction that sedimented when subjected to very low speed centrifugation (65 x g, 5 min). From Percoll gradient fractions, nuclei were identified by microscopy, and they migrated with cytidylyltransferase activity. The data are consistent with a localization of cytidylyltransferase in the nuclear membrane.     

Density gradient proportionality constants,density distributions,and pressure effects for three salt solutions

Earlier determinations of density gradient proportionality constants β⁰, density distributions ρ(r), and the effect of pressure on density gradients in the analytical ultracentrifuge have been of limited precision and usefulness in the study of proteins and polypeptides. Reasons for these difficulties are that numerous intermediate relationships were required in the calculations, and the density ranges studied were generally above 1.2 g/ml. Relations are derived in the present paper to directly compute β⁰(ρ) values and β⁰′(ρ) values from the original data without any intermediate expansions or approximations. Data are presented for CsCl, CsBr, and Cs₂SO₄ and compared with literature values. Density distributions are computed for all three salts under a wide variety of experimental conditions of density, column length, and angular velocity. These values of ρ(r) and r_e are obtained by a numerical iterative technique. Values obtained by this new method are compared with values obtained using closed-form expressions. The effects of pressure on the composition density gradient for the three salts given above are calculated and found to be significant for Cs₂SO₄ solutions.     

Differential effects of EGF gradient profiles on MDA-MB-231 breast cancer cell chemotaxis

Chemotaxis, directed cell migration in a gradient of chemoattractant, is an important biological phenomenon that plays pivotal roles in cancer metastasis. Newly developed microfluidic chemotaxis chambers (MCC) were used to study chemotaxis of metastatic breast cancer cells, MDA-MB-231, in EGF gradients of well-defined profiles. Migration behaviors of MDA-MB-231 cells in uniform concentrations of EGF (0, 25, 50, and 100 ng/ml) and EGF (0-25, 0-50, and 0-100 ng/ml) with linear and nonlinear polynomial profiles were investigated. MDA-MB-231 cells exhibited increased speed and directionality upon stimulation with uniform concentrations of EGF. The cells were viable and motile for over 24 h, confirming the compatibility of MCC with cancer cells. Linear concentration gradients of different ranges were not effective in inducing chemotactic movement as compared to nonlinear gradients. MDA-MB-231 cells migrating in EGF gradient of 0-50 ng/ml nonlinear polynomial profile exhibited marked directional movement toward higher EGF concentration. This result suggests that MDA-MB-231 cancer cell chemotaxis depends on the shape of gradient profile as well as on the range of EGF concentrations.     

Tumor cell haptotaxis on covalently immobilized linear and exponential gradients of a cell adhesion peptide

The movement of cells up an adhesive substratum gradient has been proposed as a mechanism for directing cell migration during development and metastasis. Critical evaluation of this hypothesis (haptotaxis) benefits from the use of quantifiable, stable substratum gradients of biologically relevant adhesion molecules. We report covalent derivatization of polyacrylamide surfaces with quantifiable gradients of a nonapeptide containing the adhesive Arg-Gly-Asp sequence. Cell migration was studied by seeding derivatized surfaces evenly with B16F10 murine melanoma cells. Within 8 hr, cells on gradients redistributed markedly; higher cell densities were found at gel positions having higher immobilized peptide densities. In contrast, cells seeded on control gels with uniform concentrations of adhesive peptide did not redistribute. Redistribution occurred on gradients in both serum-free and serum-containing media. Experiments with uniform density peptide-derivatized gels demonstrated that redistribution on gradients was not due to preferential initial cell attachment or preferential growth on the higher density of immobilized peptide, but must have been due to cell translocation. Cells on exponential gradients of immobilized peptide migrated to a position on the gel surface corresponding to the highest immobilized peptide density, while cells on linear gradients of the same peptide migrated to a position of intermediate peptide density. These data suggest that the B16F10 cells respond to proportional changes in immobilized peptide density rather than to absolute changes, implying a sensing mechanism which utilizes adaptation. These results demonstrate that (1) a gradient of a small adhesive peptide is sufficient to generate redistribution of cell populations and (2) controlled quantifiable substratum gradients can be produced and used to probe the underlying cellular mechanisms of this behavior.     

Global fit and structure optimization of flexible and rigid macromolecules and nanoparticles from analytical ultracentrifugation and other dilute solution properties

The calculation of hydrodynamic and other solution properties from structural information (size and shape or flexibility) of macromolecules and nanoparticles is feasible thanks to existing theories and computational tools. Here we review our recent advances in the inverse problem of extracting structural information from those properties. The concepts of equivalent radii and ratios of radii are particularly useful in global-fitting structural analysis, when one has to treat simultaneously with various properties, eventually for a series of samples. Based on the equivalent radii or their ratios, we define target functions that measure the adequacy of a given structure to fit a set of experimental properties. Structural determination is carried out by minimization of those target functions. We review a variety of examples. Some of them refer to the simple, yet important models like ellipsoids, cylinders and wormlike chains, whose structure is determined by optimization of the model parameters. In other, more complex cases, properties are calculated with computational tools like programs in the HYDRO suite. We have devised other tools to make the structure optimization from the results of those calculations in a quite direct, simple and systematic manner.     

Production of Ficoll, Percoll, and albumin gradients by the freeze-thaw method.

Ficoll, sucrose, albumin, and Percoll, a modified colloidal silica centrifugation medium, all form density gradients upon freezing and thawing. The data suggest that any density gradient material will form gradients upon freezing and thawing, provided the material is stable to freezing.     

Within-community vegetation structure in the conifer woodlands of the Siskiyou Mountains,Oregon

The conifer woodlands found on serpentine-derived soils in southwest Oregon, USA, are characterized by a debse but discontinuous shrub stratum and a species-rich herbaceous stratum. Quantitative analysis of shrub and herb distributions within 10 sites showed that small-scale patterns within the conifer woodland sites are as important as landscape-scale patterns in community organization. Gradient analysis was used to describe the distribution of herbaceous species with respect to gradients of shrub influence (shading, decreased soil temperature, increased soil moisture, increased litter depth) within sites and topographic moisture among sites. Regression analysis of the resulting species distributions and calculations of alpha and beta diversity showed that (a) the shrub-influence microgradient significantly affected distributions for 15 out of 20 major herbaceous species, and the topographic-moisture gradient influenced 13 out of the 20 species, (b) species richness was higher under intermediate conditions along both gradients, and (c) beta diversity within communities was 2.5 to 3.8 times the beta diversity of the site-to-site topographic-moisture gradient.     

Insights into the association of FcgammaRII and TCR with detergent-resistant membrane domains: isolation of the domains in detergent-free density gradients facilitates membrane fragment reconstitution

Plasma membrane rafts are routinely isolated as detergent-resistant membranes (DRMs) floating in detergent-free density gradients. Here we show that both the presence and exclusion of TX-100 during the density gradient fractionation have profound effects on the location of FcgammaRII and TCR in DRM fractions. The presence of TX-100 during fractionation promoted solubilization of non-cross-linked FcgammaRII when the receptor was insufficiently dissolved upon cell lysis. In the detergent-supplemented gradients, TX-100 micelles floated, further enhancing dissociation of FcgammaRII and TCR from DRMs and promoting a shift of the receptors toward higher-density fractions. Hence, fractionation of cell lysates over the detergent-containing gradients enables isolation of DRMs devoid of weakly associated proteins, like nonactivated FcgammaRII and TCR. On the other hand, in a detergent-free gradient, non-cross-linked FcgammaRII, fully soluble in 0.2% TX-100, was recovered in DRM fractions. Moreover, employment of the TX-100-free gradient for refractionation of intermediate-density fractions, derived from detergent-supplemented gradients and containing FcgammaRII and TCR, resulted in flotation of the receptors to buoyant fractions. An analysis of the TX-100 concentration revealed that after fractionation of 0.2% TX-100 cell lysates in the absence of detergent, the level of TX-100 in DRM fractions was reduced to 0.01%, below the critical micelle concentration. Therefore, fractionation of detergent cell lysates over detergent-free gradients can mimic conditions for a membrane reconstitution, evoking association of a distinct subset of membrane proteins, including FcgammaRII and TCR, with DRMs.     

Neurite growth in 3D collagen gels with gradients of mechanical properties

We have designed and developed a microfluidic system to study the response of cells to controlled gradients of mechanical stiffness in 3D collagen gels. An 'H'-shaped, source-sink network was filled with a type I collagen solution, which self-assembled into a fibrillar gel. A 1D gradient of genipin--a natural crosslinker that also causes collagen to fluoresce upon crosslinking--was generated in the cross-channel through the 3D collagen gel to create a gradient of crosslinks and stiffness. The gradient of stiffness was observed via fluorescence. A separate, underlying channel in the microfluidic construct allowed the introduction of cells into the gradient. Neurites from chick dorsal root ganglia explants grew significantly longer down the gradient of stiffness than up the gradient and than in control gels not treated with genipin. No changes in cell adhesion, collagen fiber size, or density were observed following crosslinking with genipin, indicating that the primary effect of genipin was on the mechanical properties of the gel. These results demonstrate that (1) the microfluidic system can be used to study durotactic behavior of cells and (2) neurite growth can be directed and enhanced by a gradient of mechanical properties, with the goal of incorporating mechanical gradients into nerve and spinal cord regenerative therapies.     

Occurrence, isolation, and characterization of polyribosomes in yeast

This report details the procedural requirements for preparing cell-free extracts of yeast rich in polyribosomes. This enabled us to demonstrate the occurrence of polyribosomes in yeast, to show their role in protein synthesis, and to devise methods for their resolution and isolation. When certain precautions are met (the use of log phase cells, rapidly halting cell growth, gentle methods of disruption, sedimentation through exponential density gradients, etc.), individual polyribosome size classes ranging up to the heptosome can be fractionated and separated from their nearest neighbors. Larger size classes are resolved partially among themselves, free of smaller polyribosomes. This was confirmed by extensive electron micrographic studies of material from the various fractions obtained upon density gradient centrifugation of yeast extracts. Modifications of the gradients and procedure should allow fractionation and isolation of the larger polyribosomes, including those containing polycistronic messages. Yeast polyribosomes are disaggregated to single ribosomes by longer term grinding, cell disruption by the French pressure cell, the Hughes press, or by incubation with dilute RNAse. Yeast polyribosomes are active in the incorporation of amino acids into polypeptide; the single ribosomes exhibit only slight activity. The latter activity is probably due to the presence of a small fraction of monosomes still containing mRNA. Poly-U stimulates amino acid incorporation only in the single ribosomes.     

Fractionation of cell-wall preparations from grass leaves by centrifuging in non-aqueous density gradients.

1. Dried preparations of cell walls from perennial-ryegrass (Lolium perenne) and Italian-ryegrass (L. multiflorum) leaves were suspended in mixtures of carbon tetrachloride with light-petroleum (b.p. 45--50 degrees C) or alcohols and layered on density gradients formed from the same solvents. 2. On centrifugation, the cell walls become distributed throughout a suitably chosen gradient. Fractions corresponding to various regions of the gradient were separated, examined under the microscope and analysed. 3. Cell-wall preparations made from leaf material ground in liquid N2, or in a triple roll mill, showed considerable heterogeneity in particle size, and their behaviour in the density gradient was variable, although there was a general indication that walls derived from vascular bundles were less dense than those from sclerenchyma. 4 Treatment in a vibratory ball mill decreased the size of the particles and produced a more uniform material, but made it impossible to distinguish the origins of the particles. This material behaved more reproducibly in the density gradient. 5. Some fractionations were also made by successive centrifugation in media of increasing relative density. 6. Analyses of the fractions obtained by each method indicated that the less dense had a greater proportion of xylose in the polysaccharide components, and higher contents of acetyl groups and lignin, confirming the close relationship between these components in plant cell walls. 7. The results show that there are differences in polysaccharide composition between the cell-wall types in the grass leaf, the vascular tissue being richer in hemicellulose relative to cellulose than the sclerenchyma.     

beta-Glucosidase Activity in Corn Roots: Problems in Subcellular Fractionation

Preliminary results from differential centrifugation experiments, washing treatments, and enrichment in linear sucrose gradients at a density of 1.09 grams per cubic centimeter all indicated that β-glucosidase activity in corn root homogenates was associated with a membrane such as tonoplast. A subsequent sucrose density gradient centrifugation time course showed that the β-glucosidase was actually a soluble enzyme which moved into the gradients. The problem of soluble enzymes contaminating light density membranes in sucrose gradients and the question of centrifugation time necessary for membrane vesicles to reach isopycnic conditions are addressed.     

Interaction in vitro of nonepithelial intermediate filament proteins with total cellular lipids, individual phospholipids, and a phospholipid mixture

The interaction of nonepithelial intermediate filament (IF) proteins with vesicles produced from total Ehrlich ascites tumor cell lipids results in the formation of complexes which in sucrose density gradient centrifugation attain positions distinctly different from those of the original reactants. In KBr density gradient equilibrium centrifugation, the IF protein-lipid adducts accumulate as thin proteolipid films on top of the KBr gradients, whereas in the absence of lipids the proteins remain distributed within the density gradients. Similar results were obtained with vesicles derived from individual phospholipids and a mixture thereof. The affinity of IF proteins for negatively charged phospholipids is greater than that for vesicles derived from uncharged phospholipids. Limited digestion of IF proteins with various proteinases demonstrated that for optimal association of the reactants IF proteins must carry an intact N terminus and that the isolated N-terminal polypeptide itself shows strong reactivity with lipid vesicles. Arginine-phosphate interactions between the N terminus and phospholipids seem to be partly responsible for this association. However, as shown by hydrophobic interaction chromatography on phenyl- and octyl-Sepharose 4B, IF proteins and their proteolytic derivatives also appear to have high affinities for aromatic and aliphatic substructures of biologically important molecules. The results are discussed in terms of a possible functional role of IF protein-lipid interactions in the association of nonepithelial intermediate filaments with intracellular membrane systems.     

Boundary centrifugation in isovolumetric and isokinetic cesium sulfate density gradients: application to cartilage proteoglycans and other macromolecules

A boundary sedimentation methodology is described that avoids plateau dilution and simplifies the calculation of centrifugal parameters. The technique is designed for the preparative ultracentrifuge and uses a newly developed sectorial cell. It is based on previous developments of the transport method and depends on isokinetic or isovolumetric Cs2SO4 density and viscosity gradients. These gradients are prepared with a single-chamber mixing device, and the only two parameters required for their calculations are presented in a tabulated form for general use with most available rotors and cell sizes. Conditions are specified (1) to assure that the density and shape of the sedimenting molecules remain invariant through the selected electrolytic gradient, (2) to monitor the gradient profiles, and (3) to verify attainment of isokinetic or isovolumetric sedimentations. A set of equations is presented to calculate the average and transport sedimentation coefficients and the differential sedimentation coefficient distribution for both the isokinetic and isovolumetric centrifugal regimes. The method was applied to slowly diffusing polydisperse proteoglycan monomers, to a paucidisperse DNA from bacteriophage PM2, and to a diffusible monodisperse system (purified bovine serum albumin). In all cases, the expected results were obtained.     

A physical explanation for multiple-cell classes after centrifugation in colloidal silica gradients.

When cells of Dictyostelium discoideum were centrifuged to density equilibrium in linear gradients of colloidal silica (Ludox), approximately 40 discrete bands appeared. This suggested that there could be at least 40 different cell types. A similar result was found for formalinized red blood cells and plastic bends. Isolated bands of cells rebanded faithfully in new gradients and band spacing depended upon gradient steepness. However, the cell bands resulted from microscopic modifications in the linear gradients of Ludox caused by centrifugation. When the gradients were analyzed in the analytical ultracentrifuge, absorbance scans revealed that cell bands coincided with “bands” of Ludox, which formed even without cells. Evidence ruling out other possible causes for cell bands is presented. Additionally, procedures which avoid this condition are described.     

Precision of sensing cell length via concentration gradients

Unicellular organisms are typically found to have a characteristic cell size. To achieve a homeostatic distribution of cell sizes over many generations requires that cell length is actively sensed and regulated. However, the mechanisms by which cell size is controlled remain poorly understood. Recent experiments in fission yeast have shown that cell length is controlled in part by polar gradients of the protein Pom1 together with localized measurement of concentration at midcell. Dilution as the cell grows leads to a reduction in the midcell protein concentration, which lifts a block on mitosis. Here we analyze the precision of this mechanism for length sensing in the presence of inevitable intrinsic noise in the processes leading to formation and measurement of this gradient. We find that the use of concentration gradients allows for more robust length sensing than a comparable spatially uniform system, and allows for reliable length determination even if the average protein concentration throughout the cell remains constant as the cell grows. Optimal values for the gradient decay length and receptor dissociation constant emerge from maximizing sensitivity while minimizing the impact of density fluctuations.     

Elevational gradients in bird diversity in the Eastern Himalaya: an evaluation of distribution patterns and their underlying mechanisms

Background

Understanding diversity patterns and the mechanisms underlying those patterns along elevational gradients is critically important for conservation efforts in montane ecosystems, especially those that are biodiversity hotspots. Despite recent advances, consensus on the underlying causes, or even the relative influence of a suite of factors on elevational diversity patterns has remained elusive.

Methods and Principal Findings

We examined patterns of species richness, density and range size distribution of birds, and the suite of biotic and abiotic factors (primary productivity, habitat variables, climatic factors and geometric constraints) that governs diversity along a 4500-m elevational gradient in the Eastern Himalayan region, a biodiversity hotspot within the world''s tallest mountains. We used point count methods for sampling birds and quadrats for estimating vegetation at 22 sites along the elevational gradient. We found that species richness increased to approximately 2000 m, then declined. We found no evidence that geometric constraints influenced this pattern, whereas actual evapotranspiration (a surrogate for primary productivity) and various habitat variables (plant species richness, shrub density and basal area of trees) accounted for most of the variation in bird species richness. We also observed that ranges of most bird species were narrow along the elevation gradient. We find little evidence to support Rapoport''s rule for the birds of Sikkim region of the Himalaya.

Conclusions and Significance

This study in the Eastern Himalaya indicates that species richness of birds is highest at intermediate elevations along one of the most extensive elevational gradients ever examined. Additionally, primary productivity and factors associated with habitat accounted for most of the variation in avian species richness. The diversity peak at intermediate elevations and the narrow elevational ranges of most species suggest important conservation implications: not only should mid-elevation areas be conserved, but the entire gradient requires equal conservation attention.     

Isolation and physicochemical characterization of mitochondrial DNA from cultured cells ofPetunia hybrida

Summary Mitochondrial DNA ofPetunia hybrida was purified from cell suspension cultures. Up to 50% of the DNA could be isolated as supercoiled DNA molecules by CsCl-ethidium bromide density gradient centrifugation. The DNA purified from DNase-treated mitochondria bands at a single buoyant density of 1.760 gcm^–3 in neutral density gradients and runs on agarose gels as a single band with an apparent molecular weight exceeding 30 megadaltons (Md). Summing of the restriction endonuclease fragment lengths indicates a mitochondrial genome size of at least 190 Md. Electron microscopic analysis reveals the presence of a heterogeneous population of circular DNA molecules, up to 60 Md in size. Small circular DNA molecules, ranging in size from 2–30 Md are present, but unlike in cultured cells of other plant species they do not form discrete size classes and furthermore, they constitute less than 5% of the total DNA content of the mitochondria. The restriction endonuclease patterns of mitochondrial DNA do not qualitatively alter upon prolonged culture periods (up to at least two years).