A simple tool for calculating egg shape,volume and surface area from digital images

The geometrical properties of eggs – such as volume and surface area – have uses ranging from ecological, physiological and morphological studies in birds, to predictions of chick condition in the poultry industry. Although measurements of an egg's length and breadth can be used to approximate its geometry, the coefficients used in these models are specific to the original test population, and intraspecific variation in egg shape means these methods cannot be used reliably beyond that population. Here I present a novel mathematical formula to describe the curvature of a bird's egg that can be used to calculate the shape, volume and surface area of an egg precisely from digital images. Using data from several species I demonstrate that the model has a greater level of accuracy than length‐ and breadth‐based methods, and release the user‐friendly tool for others to use for measuring eggs from digital images.     

Quantitation of 'junctional feet' content in two types of muscle fiber from hind limb muscles of the rat

1. Transverse tubules in fibers from rat soleus and extensor digitorum longus (EDL) muscles of the rat were infiltrated with silver dichromate (black reaction of Golgi). This provides a faithful, high-contrast outline of the tubules, which allows distinction between segments involved in junction formation with the sarcoplasmic reticulum and segments that are free. 2. Electron micrographs of semithin transverse sections were used to quantitate T tubule parameters and to measure cross-sectional area and perimeter of individual fibers. Thin sections and data from the literature were used to obtain the contribution of caveolae to external surface area and the frequency of junctional feet along the junctional T tubule membrane. 3. From the above data we calculate the ratio of number of feet to total external surface area for a given fiber segment. The ratio is compared with data in the literature on the total amount of 'charge movement' (in nC/uF of total external surface area). 4. The average feet/surface area ratio is twice as large in EDL than in soleus fibers, while the charge movement is up to five-fold larger. Probably some of the total charge movement is not directly associated with events related to the turning on of the SR permeability to calcium.     

A marker-based measurement procedure for unconstrained wrist and elbow motions.

A protocol is proposed to obtain the joint angles of wrist and elbow from tracked triads of surface markers on each limb segment. Cuffs placed on the limb support the rigidity of the triads. Additional markers are used to mark the approximate positions of joints. Corrections of surface marker data for skin motion are derived from a priori knowledge about plausible joint motions. In addition, ill-conditioned states are trapped when the elbow is nearly fully extended. The protocol is applied to sample motions which demonstrate the use and the effect of the corrections. The results show that the model assumptions are reasonable and that accurate joint rotations can be obtained. The correction steps prove to be an essential part of upper-extremity movement analysis.     

Regeneration of the segment boundary in Oncopeltus

The segment boundary of Oncopeltus is a compartment border. It is also an element in the pattern of the abdomen, being marked by a groove in the surface of the cuticle and an abrupt change in the pigmentation of the cells. If the segment boundary is either burnt or extirpated, the surviving cells of the two neighbouring segments migrate into the wounded area and form a new segment boundary where they confront each other. Grafting experiments with genetically marked cells demonstrate that a boundary is regenerated wherever cells from remote locations in the anteroposterior axis of any segment are apposed; thus anterior and posterior cells from the same segment form an ectopic boundary when brought together, while cells from equivalent positions in two segments heal together without forming a boundary. We consider the segment boundary to be an element in a pattern which reiterates down the longitudinal axis of the body—whenever cells from different positions in this pattern are brought together intercalation occurs. The intercalation can either be within a segment (no boundary forms) or between segments (a boundary forms). The route of intercalation appears to be the shortest available, so that when the apposed cells are more than half a segment length apart a new boundary forms.     

New mathematical definition and calculation of axial rotation of anatomical joints

In the field of joint kinematics, clinical terms such as internal-external, or medical-lateral, rotations are commonly used to express the rotation of a body segment about its own long axis. However, these terms are not defined in a strict mathematical sense. In this paper, a new mathematical definition of axial rotation is proposed and methods to calculate it from the measured Euler angles are given. The definition and methods to calculate it from the measured Euler angles are given. The definition is based on the integration of the component of the angular velocity vector projected onto the long axis of the body segment. First, the absolute axial rotation of a body segment with respect to the stationary coordinate system is defined. This definition is then generalized to give the relative axial rotation of one body segment with respect to the other body segment where the two segments are moving in the three-dimensional space. The well-known Codman's paradox is cited as an example to make clear the difference between the definition so far proposed by other researchers and the new one.     

Elevated galactosyltransferase activity on t-bearing sperm segregates with T/t-complex distorter loci-2

Sperm bearing complete t-haplotypes are preferentially transmitted during fertilization from heterozygous +/t males, often in excess of 95% relative to their (+)-bearing meiotic partner. Sperm from t-bearing males have an approximate two- to fourfold increase in beta 1,4-galactosyltransferase (GalTase) activity, a cell surface protein that mediates sperm binding to the egg zona pellucida. The elevated GalTase activity strictly correlates with the preferential transmission of t-sperm from +/t males, since eight other enzymes show normal levels of activity on t-sperm. Furthermore, sperm bearing proximal partial t-haplotypes, which are no longer favoured during fertilization, have normal levels of GalTase activity. Nevertheless, it has been unclear whether the elevated sperm GalTase activity on t-sperm is due to specific loci in the distal segment of the T/t-complex, or rather, is an indirect consequence of the abnormal sperm function characteristic of +/t and tx/ty males. In this study, it is shown that the elevated sperm GalTase activity is due specifically to factors that reside within the distal segment of the T/t complex, which also contains Tcd-2, the strongest of the distorter loci. Since the structural locus for GalTase is located on mouse chromosome 4, these results also show that T/t-complex alleles on chromosome 17 are regulatory in nature and affect the expression of sperm surface components critical for normal fertilization. Models are presented to explain how elevated GalTase activity could contribute to sperm transmission distortion.     

Analysis of membrane binding equilibria of peripheral proteins: Allowance for excluded area of bound protein

When peripheral proteins bind to phospholipid membranes lacking discrete binding sites, steric repulsion between bound protein molecules may result in a reduction of the surface area available to additional bound protein by an amount significantly greater than the actual area occupied by bound protein. An approximate treatment of this effect demonstrates that neglect of area exclusion by bound protein may lead to significant errors in the evaluation of equilibrium association constants and the fractional coverage of membrane surface area.     

On the evaluation of data from flow-dialysis experiments

Flow dialysis can be used to measure (i) ligand binding to macromolecules and (ii) the size of transmembrane ion gradients. Generally an approximate method is used to calculate the binding or gradient parameters from the raw data. Here we present a simple but exact method and evaluate the errors that may arise when the approximate method is used to calculate the magnitude of ion gradients. In addition, equations are presented that allow for a correction for sampling from or additions to the upper compartment of a flow-dialysis vessel during the measurements. Setty and Hendler [(1982) J. Biochem. Biophys. Methods 7, 35-46] have reported artifacts in the measurement of ion-gradients caused by the addition of electron donors to the upper compartment of a flow-dialysis cell. Here we extend their observations and suggest additional methods to prevent such artifacts.     

A precise and non-destructive method to calculate the surface area in living scleractinian corals using X-ray computed tomography and 3D modeling

The surface area of corals represents a major reference parameter for the standardization of flux rates, for coral growth investigations, and for investigations of coral metabolism. The methods currently used to determine the surface area of corals are rather approximate approaches lacking accuracy, or are invasive and often destructive methods that are inapplicable for experiments involving living corals. This study introduces a novel precise and non-destructive technique to quantify surface area in living coral colonies by applying computed tomography (CT) and subsequent 3D reconstruction. Living coral colonies of different taxa were scanned by conventional medical CT either in air or in sea water. Resulting data volumes were processed by 3D modeling software providing realistic 3D coral skeleton surface reconstructions, thus enabling surface area measurements. Comparisons of CT datasets obtained from calibration bodies and coral colonies proved the accuracy of the surface area determination. Surface area quantifications derived from two different surface rendering techniques applied for scanning living coral colonies showed congruent results (mean deviation ranging from 1.32 to 2.03%). The validity of surface area measurement was verified by repeated measurements of the same coral colonies by three test persons. No significant differences between all test persons in all coral genera and in both surface rendering techniques were found (independent sample t-test: all n.s.). Data analysis of a single coral colony required approximately 15 to 30 min for a trained user using the isosurface technique regardless of the complexity and growth form of the latter, rendering the method presented in this study as a time-saving and accurate method to quantify surface areas in both living coral colonies and bare coral skeletons. Communicated by Biology Editor Dr Michael Lesser     

The effects of wall thickness, axial strain and end proximity on the pressure-area relation of collapsible tubes

Segments of silicone rubber tube were suspended between rigid pipes and subjected to slowly varying transmural pressure covering a range from slight distension to collapse with osculation. The local inside cross-sectional area at a chosen axial site was simultaneously measured via catheter by an electrical impedance method. Pressure-area relations were recorded thus at various axial sites, under varying conditions of axial tube wall tension, in tubes of two different wall thickness (0.3 and 0.4 of mean radius). Unsupported tube segment length was also varied by means of an insert device. The relations were used to calculate the variation of wave velocity with area according to Young's equation. First opposite wall contact during collapse was shown to occur at a smaller fraction of undistended circular cross-sectional area than in the thin-walled tubes investigated previously by others.     

Regional interdependence in calf lungs

We measured K, an index of interdependence in sublobar segments of both intact and excised calf lungs. In excised and intact lungs, segment volume was held constant while the lung was inflated. K in excised lungs was of small magnitude but was greater in caudal than in cranial and middle lobes. When isolated segments in a variety of regions and with a variety of shapes were studied, K was positively correlated with the interface area between the segment and the remainder of the lung, was negatively correlated with the pleural surface area of the segment, but was not correlated with segment volume. In a given region of lung, however, small segments had a greater interdependence than large segments. In intact lungs of anesthetized calves, K was an order of magnitude greater than in excised lungs, confirming that the chest wall is the major determinant of interdependence. There were no lobar differences in K in intact lungs.     

Interaction of the M4 segment with other transmembrane segments is required for surface expression of mammalian α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors

Ionotropic glutamate receptors (GluRs) are ligand-gated ion channels with a modular structure. The ion channel itself shares structural similarity, albeit an inverted membrane topology, with P-loop channels. Like P-loop channels, prokaryotic GluR subunits (e.g. GluR0) have two transmembrane segments. In contrast, eukaryotic GluRs have an additional transmembrane segment (M4), located C-terminal to the ion channel core. However, the structural/functional significance of this additional transmembrane segment is poorly defined. Although topologically similar to GluR0, mammalian AMPA receptor (GluA1) subunits lacking the M4 segment do not display surface expression. This lack of expression is not due to the M4 segment serving as an anchor to the ligand-binding domain because insertion of an artificial polyleucine transmembrane segment does not rescue surface expression. Specific interactions between M4 and the ligand-binding domain are also unlikely because insertion of polyglycines into the linker connecting them has no deleterious effects on function or surface expression. However, tryptophan and cysteine scanning mutagenesis of the M4 segment, as well as recovery of function in the polyleucine background, defined a unique face of the M4 helix that is required for GluR surface expression. In the AMPA receptor structure, this face forms intersubunit contacts with the transmembrane helices of the ion channel core (M1 and M3) from another subunit within the homotetramer. Thus, our experiments show that a highly specific interaction of the M4 segment with an adjacent subunit is required for surface expression of AMPA receptors. This interaction may represent a mechanism for regulating AMPA receptor biogenesis.     

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.     

ST segment depression: the possible role of global repolarization dynamics

Background  

At least some clinical data suggests that, regardless of which major coronary artery is narrowed, the early ST segment body surface pattern is characterized by a minimum near precordial lead V5 and a broad area of left precordial negative potentials. Some clinical data also suggests that late ST segment potentials can localize an ischemic heart region.     

A method to estimate in vivo dynamic articular surface interaction

This paper describes a method to calculate and visualize the proximity of subchondral bone surfaces during dynamic movement. This method combines high-speed biplane radiographic image data and three-dimensional (3D) bone surface information derived from computed tomography to determine subchondral bone motion during dynamic activities. Knowledge of in vivo subchondral bone motion may be useful in the study of osteoarthritis, in biomechanical modeling, and in identifying normal and pathological joint mechanics. This method can be used to identify the regions of close contact during dynamic motion, to calculate the surface area of subchondral bone within close contact, and to determine the changing position of the close contact area during dynamic activities. None of this informations can be obtained using other currently available 3D motion analysis techniques. Example applications showing dynamic in vivo tibio-femoral bone surface motion during canine gait and human one-legged hopping are presented.