Hydrodynamic characterization of the size and shape of atropinesterase from Pseudomonas putida

Atropinesterase from Pseudomonas putida has been investigated by means of different ultracentrifugation methods under native and denaturing conditions. The following quantities were determined: sedimentation coefficient, translational diffusion and friction coefficient, partial specific volume and molecular weight. From these data the size, shape and hydration of the enzyme molecule in solution were estimated. The results suggest that atropinesterase is a globular protein which consists of a single polypeptide chain with a molecular weight of about 30,000. In solution under non-denaturing conditions, it occurs mainly as a dimer which hydrodynamically behaves as a rigid impenetrable particle. Calculations based on the spheroid model indicate that this particle resembles a hydrated sphere with a diameter of 6.1 +/- 0.2 nm and a hydration of 0.4 +/- 0.1 g of H2O/g of protein rather than a significantly less hydrated ellipsoid of revolution. Under denaturing conditions dissociation into monomers takes place. The effects of sodium dodecyl sulphate (SDS) on size and shape suggest that dimerization results from side-by-side association of two elongated monomers rather than from end-to-end association. Approximately 57 molecules of SDS are bound per dimer before dissociation occurs concomitant with the additional binding of about 19 molecules of detergent.     

Comparison of surface potentials due to several singularity representations of the human heart

In electrocardiography the electrical potentials due to the heart actions can be analyzed by assuming the human body to be a conductor of homogeneous medium and the heart to be a combination of singularities within it. For a spherical conductor the “interior sphere theorem” of G. Ludford, J. Martinek, and G. Yeh (Proc. Cambridge Phil. Soc.,51, 389–93, 1955) renders potential expressions due to any singularity. For a conductor of prolate spheroidal shape the potential expressions due to a source-sink pair and a general dipole have been given by J. R. Wait (Jour. App. Physics,24, 496–97, 1953) and the authors (paper at the Conference on the Electrophysiology of the Heart, Feb. 16–17, 1956, in New York, to appear in theAnn. N. Y. Acad. Sciences) respectively. (A theorem which applies to any singularity inside a prolate or oblate spheroid will be published by the authors soon). This paper presents numerical and graphical results of potentials on the surfaces of a prolate spheroid and a sphere due to source-sink pairs and dipoles of several locations and directions and compares the various representations. A discussion on the judicious choice of heart models concludes the paper. This investigation was supported by The National Heart Institute under a research grant H-2263.     

Mechanical behavior of closed lamellar membranes as a possible common mechanism for the establishment of developmental shapes.

The mechanical behavior of a closed membrane composed of two layers in contact is described as it is obtained by finding the minimum of the membrane bending energy at constant membrane area, constant difference between the areas of the two layers, and constant enclosed volume. It is shown that the membrane bending energy is a discontinuous function of the volume (v) and difference between the layer areas (delta a) defined relative to the volume and area difference of a sphere with the same membrane area, respectively. However, for different classes of shapes it is possible to obtain regions in the v/delta a diagram within which the shapes change continuously with v and delta a. These regions are shown for the egg, dumbbell and cup shape classes, respectively. The results of the shape analysis are used in the discussion of cell polarity, cytokinesis and gastrulation. Cell polarity is related to the decrease in symmetry during the transition from the radially symmetrical spherical shape to the asymmetrical shapes of the egg class. It is proposed that symmetrical cytokinesis occurs within the dumbbell class and that asymmetrical cytokinesis occurs within the egg class. Gastrulation is described as shape transformations within the class of cup shapes.     

Human air space shapes, sizes, areas, and volumes.

The geometry of an enlarged reconstructed human acinus (i.e., a terminal bronchiole and distal airways and air spaces) was studied. Alveoli were categorized in six shapes: three-fourths of a spheroid, a slightly truncated cone, one-fourth of a spheroid, a cylindroid with a hemispherical bottom, a shallow cylindroid with a flat bottom, and a truncated deep ellipsoid. Sacs were usually either hemispheroids or shallow truncated cones. Ducts of eight generations were spheroid and gradually decreased in diameter (D) and length (L) as the generation number (z) increased. Considering the terminal bronchiole as the 15th generation and using Weibel's data for the first 10 generations, the dimensions, in mm, for z of 1-10 and 10-26 were reasonably described by D-z = 12e-(0.27-0.005z)z and L-z = 25e-0.187z. The predicted volume of the acinus at three-fourths total lung volume was 182.8 mm3, a volume equivalent to that of a sphere 7.04 mm in diameter. The reconstruction demonstrated a great increase in respiratory bronchiolar and ductal cross-sectional area and alveolar surface area, considerably more rapid than predicted by Weibel's model A.     

On the Correlation of the Volume of a Prolate-Spheroidal Cell, Tetrahymena as Determined by Electronic Particle Counters and by Morphometry

ABSTRACT. The cell volume provided by electronic particle counters may be incorrect. As a particle, or cell, passes the counting device, its volume is calculated as a sphere. The electronically derived, mean cell volume (electronic MCV) of a population of Tetrahymena (prolate spheroid) is smaller than the volume (morphometric MCV) calculated from measured cell length and width. This discrepancy was studied using a Coulter Multisizer particle counter and cell morphometry. The electronic MCV averaged 0.70 of the morphometric MCV (1.00) but changed from 0.72 (fast growth) to 0.63 and 0.76 (slow or no growth) for cells having a mean length/width of 2.05, 2.33, and 1.61, respectively. The measured diameter of latex particles (used for calibration) was identical to that stated, but the diameter of the electronic MCV was larger than the width of the cells which related to wehther the length/width of the cells was above, or below, 2.00. Hence, electron particle counters register primarily the width of a prolate-spheroidal cell, oriented with its long axis in the direction of flow, and uses this value as diameter for the calculated sphere, whereas for more spherical cells, tumbling without any orientation, a mean of the axes is used. Factors for correction of the electronic MCV of Tetrahymena are provided.     

Structure of bacteriophage T7. Small-angle X-ray and neutron scattering study.

Small-angle x-ray and neutron scattering techniques were applied to bacteriophage T7 solutions at different scattering densities. Scattering curves determined under a variety of experimental conditions were used to derive a set of parameters characterizing the shape, size, and weight of the whole phage particle and of its DNA and protein components. The T7 head has an icosahedral shape with an edge of 37.7 +/- 0.5 nm, a volume of (12.0 +/- 1.0) x 10(4) nm3, and a small tail amounting to 6--7% of the head volume. The intraphage DNA region is most probably a hollow sphere. The best fit to the data was obtained with a model in which the hollow sphere filled with a protein core with a diameter of 24 nm. The average degree of swelling (i.e., the ratio of the hydrated to the dry volume) of the particle is 2.3; the degree of swelling of the DNA component is higher, 3.2, and that of the protein part is lower, 1.2.     

Electrical Sizing of Particles in Suspensions: III. Rigid Spheroids and Red Blood Cells

The processes involved during the passage of a suspended particle through a small cylindrical orifice across which exists an electric field are investigated experimentally for an approximate prolate spheroid in the form of two tangent, rigid spheres (ragweed pollen particles) and for fresh, human red blood cells. Oscillograms of current pulses produced by both types of particles are presented and discussed in terms of particle shape and orientation and the effects of the hydrodynamic field. It is concluded that all the particles enter the orifice with their major axes aligned parallel to the orifice axis (electric field), but that during their passage some are rotated by the hydrodynamic field. Cells with their equatorial plane perpendicular to a radius of the orifice change their orientation with respect to the electric field as they are rotated, the others do not; only in the former case is there any deformation. It is shown that the bimodal or skewed size distributions can be explained on this basis, and that size (shape factor × volume) is actually a normally distributed variable (P > 95%). The average size of samples from 10 healthy adults was found to be 102.7 μ³ with a coefficient of variation of 1.8%. For a volume of 87 μ³, this corresponds to a shape factor of 1.18, an axial ratio (assuming a perfect oblate spheroid) of 0.26, and an equivalent major axis of 8.6 μ. The effect of high electric fields on red cell size distributions is mentioned.     

Effect of Particle Shape on Dry Particle Inhalation: Study of Flowability, Aerosolization, and Deposition Properties

The shape effects of dry particles on flowability, aerosolization, and deposition properties in inhalation drug delivery are studied. The properties are compared with similar size range particles of different shapes such as sphere, needle, cube, plate, and pollen. Flowability of the particles is characterized by Carr’s compressibility index and angle of slide (θ) method. The aerosolization and deposition properties of the particles are studied in vitro using an eight-stage Anderson cascade impactor with a Rotahaler®. Pollen-shaped particles are found to exhibit better flowability, higher emitted dose, and higher fine particle fraction than particles of other shapes in similar size range. They showed minimum θ of 35° and maximum emitted dose of 87% and fine particle fraction of 16%. The use of pollen-shaped particles can be a potential improvement in dry particle inhalation.     

Relationships among pressure, tension, and shape of the diaphragm

The shape of the diaphragm dome was calculated from transdiaphragmatic pressure and tension in the diaphragm. It was assumed that the muscle acts as a free membrane, attached at its edges to the inside of a vertical rib cage circular in cross section, that the attachments are inferior to the point at which the dome makes contract with the rib cage, and that the abdomen is filled with fluid with a hydrostatic gradient in pressure. The shape is different from a section of a sphere, with a radius of curvature substantially greater at the apex of the dome than at the sides. Observed shapes of human hemidiaphragm domes at functional residual capacity are not spherical but closely match the calculated shapes. Best-fitting shapes correspond to transdiaphragmatic pressures of about 3 cmH2O transdiaphragmatic pressure, suggesting that such a pressure and corresponding tension are present in the human diaphragm when it is at rest in an erect subject. In this model; as lung volume increases and the diaphragm shortens, its shape changes in such a way that the ratio between transdiaphragmatic pressure and tension in the diaphragm remains nearly constant, rather than increasing with volume. Such a model can explain the observation that the length-tension relationship of the muscle is much more important than curvature in determining the effectiveness of the diaphragm as a pressure generator.     

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics.     

Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain

Passive filling is a major determinant for the pump performance of the left ventricle and is determined by the filling pressure and the ventricular compliance. In the quantification of the passive mechanical behaviour of the left ventricle and its compliance, focus has been mainly on fiber orientation and constitutive parameters. Although it has been shown that the left-ventricular shape plays an important role in cardiac (patho-)physiology, the dependency on left-ventricular shape has never been studied in detail. Therefore, we have quantified the influence of left-ventricular shape on the overall compliance and the intramyocardial distribution of passive fiber stress and strain during the passive filling period. Hereto, fiber stress and strain were calculated in a finite element analysis of passive inflation of left ventricles with different shapes, ranging from an elongated ellipsoid to a sphere, but keeping the initial cavity volume constant. For each shape, the wall volume was varied to obtain ventricles with different wall thickness. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry along the muscle fiber directions. A realistic transmural distribution in fiber orientation was assumed. We found that compliance was not altered substantially, but the transmural distribution of both passive fiber stress and strain was highly dependent on regional wall curvature and thickness. A low curvature wall was characterized by a maximum in the transmural fiber stress and strain in the mid-wall region, while a steep subendocardial transmural gradient was present in a high curvature wall. The transmural fiber stress and strain gradients in a low and high curvature wall were, respectively, flattened and steepened by an increase in wall thickness.     

Heat transfer from spheres and other animal forms.

A general predictive relation for the convection heat transfer from animal forms is developed. This relation is based on the convection equation for a sphere, and employs a simple, unique characteristic dimension to represent the animal which is the cube root of the animal volume. The accuracy of this relation is established through comparison with available convection results from animal shapes ranging in size and shape from spiders to cows. This relation allows an extrapolation to animal shapes for which data are not available. Results are also presented for the enhancement of convection heat transfer due to natural turbulence. A procedure is outlined for estimating the convecture heat loss from an animal in the natural outdoor environment.     

Physical characteristics of human transferrin from small angle neutron scattering.

The technique of small angle neutron scattering has been used to determine the molecular shape, the volume, and the molecular weight of pooled human transferrin in an aqueous solution isotonic with blood. Analysis of the measurements assuming a spheroidal molecular shape indicates that an oblate spheroid with semi-axes of length 46.6 +/- 1.4, 46.6 +/- 1.4 and 15.8 +/- 3.8 A, and a molecular volume of (144 +/- 45) X 10(3) A3 is the best simple approximation to the shape of the transferrin molecule. The radius of gyration, Rg, determined from a Guinier plot is 30.25 +/- 0.49 A, in agreement with Rg calculated for the oblate spheroidal shape. The molecular weight is determined to be (75 +/- 5) X 10(3). The shape-independent molecular volume is found to be (98 +/- 10) X 10(3) A3. The difference in the two volumes suggests that transferrin is not a uniform spheroid but may have a more complex shape.     

Introducing the shape of globe as a predisposing factor for glaucoma

Glaucoma is a common blinding disease worldwide with a number of risk factors such as intraocular pressure, myopia, gender, race and hyperopia. Here we introduce eyeball's shape as a predisposing factor for glaucoma. If the eyeball is a sphere, the stress distribution is homogenous. We assume the eyeball as a non sphere. Then, the distribution of stress will not be homogenous. Different individuals have different eyeball's shapes and different patterns of stress distribution in their eyes. So based on the eyeball's shape deviation from a sphere they will have different risks for glaucoma. The eyeball is routinely considered as a sphere, but some evidences show that the globe is not a sphere. Two empirical observations are consistent with the hypothesis. The first is that ethnicity and sex are established risk factors for glaucoma. On the other hand there are several morphological differences in the body structure among individuals. According to these anatomical differences, eye's shape is different among different races and between two sexes. Secondly, there are some conditions such as myopia and hyperopia in them the shape of the globe has been changed. These conditions are risk factors for glaucoma too. Glaucoma screening program for early detection of high risk individuals is very important. Current diagnostic procedures of glaucoma do not take the shape of eyeball into account. We suggest using eyeball's shape for early glaucoma detection. There are three other factors in addition to eyeball's shape, including thickness of the globe's wall, intraocular pressure, and inner radius that should be measured together for each individual and stress load should be calculated in different points of the globe. Then eyes with more stress load in site of injury are more prone for glaucoma. More accurate measurements of the factors which are contributing in stress value for each case, lead us toward better glaucoma screening.     

Surface Plasmon Coupling Effect of Gold Nanoparticles with Different Shape and Size on Conventional Surface Plasmon Resonance Signal

The labeling strategy with gold nanoparticles for the conventional surface plasmon resonance (SPR) signal enhancement has been frequently used for the sensitive determination of small molecules binding to its interaction partners. However, the influence of gold nanoparticles with different size and shape on SPR signal is not known. In this paper, three kinds of gold nanoparticles, namely nanorods, nanospheres, and nanooctahedrons with different size, were prepared and used to investigate their effects on the conventional SPR signal at a fixed excitation wavelength 670 nm. It was found that the SPR signal (i.e., resonant angle shift) was varied with the shapes and sizes of gold nanoparticles in suspension at a fixed concentration due to their different plasmon absorbance bands. For gold nanorods with different longitudinal absorbance bands, three conventional SPR signal regions could be clearly observed when the gold nanorod suspensions were separately introduced onto the SPR sensor chip surface. One region was the longitudinal absorbance bands coinciding with or close to the SPR excitation wavelength that suppressed the SPR angle shift. The second region was the longitudinal absorbance bands at 624 to 639 and 728 to 763 nm that produced a moderate increase on the SPR resonant angle shift. The third region was found for the longitudinal absorbance bands from 700 to 726 nm that resulted in a remarkable increase in the SPR angle shift responses. This phenomenon can be explained on the basis of calculation of the correlation of SPR angle shift response with the gold nanorod longitudinal absorbance bands. For nanospheres and nanooctahedrons, the SPR angle shift responses were found to be particle shape and size dependent in a simple way with a sustaining increase when the sizes of the nanoparticles were increased. Consequently, a guideline for choosing gold nanoparticles as tags is suggested for the SPR determination of small molecules with binding to the immobilized interaction partners.     

The impact of diet,habitat use,and behaviour on head shape evolution in homalopsid snakes

An organism's morphology is driven by selection on function while being constrained by phylogenetic and developmental factors as well as functional trade‐offs. If selection on function is strong and solutions limited, then convergence is expected. In this paper we quantify head shape in a group of ecologically diverse snakes (homalopsid snakes) differing in habitat use and diet using three‐dimensional geometric morphometric approaches. Using data on head shape we explore whether snakes eating different prey show different morphologies. Moreover, we test whether head shape is constrained by other factors such as habitat use, burrow use, or activity pattern. Our results demonstrate similar head shapes in species consuming similar prey. Snakes that capture elusive prey under water differ from those that capture and swallow prey like frogs or crustaceans. Moreover, habitat use, the use of burrows, and activity pattern also significantly impact head shape in this group of snakes. However, this signal appears to be partly confounded by the diet signal. For axes discriminating specifically between habitat use groups or animals that use burrows vs. those that do not shapes were in accordance with our predictions. Our results suggests an adaptive signal in the evolution of head shape in homalopsid snakes with diet, habitat use and the use of burrows all influencing the evolution of head shape in the group.     

Allometric scaling and morphological variation in sinking rate of phytoplankton

Since the first decades of the last century, several hypotheses have been proposed on the role of phytoplankton morphology in maintaining a favorable position in the water column. Here, by an extensive review of literature on sinking rate and cell volume, we firstly attempted to explore the dependency of sinking rate on morphological traits using the allometric scaling approach. We found that sinking rate tends to increase with increasing cell volume showing the allometric scaling exponent of 0.43, which is significantly different than the Stokes’ law exponent of 0.66. The violation of the 2/3 power rule clearly indicates that cell shape changes as size increases. Both size and shape affect how phytoplankton sinking drives nutrient acquisition and losses to sinking. Interestingly, from an evolutionary perspective, simple and complex cylindrical shapes can get much larger than spherical and spheroidal shapes and sink at similar rates, but simple and complex cylindrical shapes cannot get small enough to sink slower than small spherical and spheroidal shapes. Cell shape complexity is a morphological attribute resulting from the combination of two or more simple geometric shapes. While the effect of size on sinking rate is well documented, this study deepens the knowledge on how cell shape or geometry affect sinking rates that still needs further consideration.     

Model Studies of the Magnetocardiogram

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid.