(n.) A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.
Example Sentences:
(1) After covalent inactivation of a variable proportion of the receptors with I-PTA-PON3, the occupancy-response relationship for platelet aggregation resulted in a similar hyperbola indicating an excess of low-affinity receptors coupled to aggregation (spare receptors).
(2) When phenylalanine was present, a pronounced deviation from the Michaelis-Menten hyperbola occurred.
(3) Flow-insensitive ranges of tcpO2-vs-flow hyperbolas were reduced by both leg lowering and moving the electrode towards proximal measuring sites.
(4) This logistic relationship is more general than the rectangular hyperbola or linear methods, provides excellent goodness of fit, and can be used as a "global" method for the entire calibration curve, rather than as a "local" method for small segments of the curve.
(5) Hill's rectangular hyperbola fitted the force-velocity data if the load during shortening was less than 70% of Fo.
(6) One parameter of the hyperbola is equivalent to the asymptotic response rate and the other parameter is equivalent to the rate of reinforcement that maintains a one-half asymptotic response rate.
(7) Analysis of these inhibition curves as double hyperbolae revealed two binding sites in the presence of DTT and only one low affinity site in the absence of DTT.
(8) The maximum velocity of shortening (Vm), determined by extrapolation from a hyperbola that is fitted to force-velocity data at finite loads, is substantially lower than V0.
(9) In contrast to hog kidney D-amino acid oxidase, the v vs s plots of D-amino acid oxidase in homogenized rat kidney did not have the form of a rectangular hyperbola, and showed an apparent negative cooperativity.
(10) The ligand self-association alone can cause deviation of the profile of the binding curve (r vs Lft plot) from a hyperbola, resulting in a nonlinear Scatchard plot.
(11) Binding was found to be saturable at higher membrane concentrations when using a fixed amount of ligand and showed a hyperbola analogous to enzyme-substrate binding.
(12) Then, we compared G to the conventional slope of the CO2-ventilation response line (S) and that of the metabolic hyperbola (SL).
(13) The difference in estimates of V0 and Vm is a function of: (i) the degree of heterogeneity of the muscle with respect to Vmax(i) and the curvature of the force-velocity relationship of the individual fibres, and (ii) the force range used to establish the hyperbola from which Vm is derived.
(14) The relationship between the slope of the plot and the substrate concentration shows characteristic features depending on the inhibition type: for partial competitive inhibition, the straight line converging on the abscissa at--Ks, the dissociation constant of the enzyme-substrate complex; for non-competitive inhibition, a constant slope independent of the substrate concentration; for uncompetitive inhibition, a hyperbola decreasing with the increase in the substrate concentration; for mixed-type inhibition, a hyperbola increasing with the increase in the substrate concentration.
(15) The data were in reasonable agreement with the theoretical hyperbola.
(16) It was established that there was a relationship between the half-life and the initial titre of antibody of each specificity which could be described by a rectangular hyperbola.
(17) A robust modified hyperbola was found to be superior for determining molecular weights and base-pair numbers for a set of known standards when compared with the conventional log transformation and a similar hyperbolic model.
(18) At low concentrations (42-1260 microM), the relationship between linoleic acid concentration and its absorption rate fitted best to a rectangular hyperbola.
(19) Likewise, the relationship could be described by a hyperbola with a linear relationship between intrapulmonary pressure and the inverse of breath duration.
(20) On the other hand, when mannosylphosphoryldolichol synthase activity was measured in the presence of amphomycin and as a function of dolichylmonophosphate (Dol-P) concentrations, the shape of the substrate velocity curve changed from a rectangular hyperbola to a sigmoid.
Hyperboloid
Definition:
(n.) A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
(a.) Having some property that belongs to an hyperboloid or hyperbola.
Example Sentences:
(1) When the myoepithelial cells contract they force the axial protrusion forward and transform the papilla into a hyperboloidal configuration.
(2) The cup-shaped adhesive papillae of Distaplia occidentalis evert at the onset of metamorphosis and each transforms into a hyperboloidal configuration.
(3) It has been shown previously that the hyperboloid can be considered as a scaffold describing the parallel beta-barrel structure.
(4) The sinuses are subsequently arranged into 4 classes, according to their similarity to solids of revolution such as: semi-ellipsoid (class a: 15% of specimens); paraboloid (class b: 30%); hyperboloid (class c: 47%) and cone (class d: 8%).
(5) We calculate values of SLk for the helical wrapping of a constant length of DNA on protein surfaces having the shapes of cylinders and of ellipsoids and hyperboloids of revolution.
(6) This could be demonstrated by a simple structural principle of the myocardium namely the myocardium fibres and connective tissue strands are arranged in the form of intermeshed hyperboloids.
(7) Eight-stranded beta-sheets in nine protein structures containing "TIM (triose phosphate isomerase) barrels" are shown to be fitted satisfactorily by hyperboloids, the generating lines of which pass through the beta-strands.
(8) In addition, we show how the hyperboloid model and the ensuing formalism can serve to derive useful geometric and graphic tools for computer-aided protein design de novo.
(9) ER binding capacity tended to be correlated with age: this correlation could be described with a hyperboloid regression curve (r = -0.5931; 0.06 > p > 0.05).
(10) The beta barrel fits a simple hyperboloid model as other T.I.M.
(11) Basic design features of the beta-sheet portion in parallel alpha beta barrels in known protein structures are analysed in the context of a model of a regular hyperboloid.
(12) Simple parameterizations of the hyperboloid model are then used to determine the constraints that govern key parameters, such as the number of strands in the barrel, and to rationalize the remarkable conservation of strand number, observed to be eight, in nearly all the known examples of parallel beta-barrels.
(13) It has been shown that the shape of the beta-sheet portion of the barrel can be approximated by a hyperboloid.
(14) If the equatorial radius of the protein is fixed, change in shape from a cylinder to a hyperboloid increases SLk, while the corresponding change to an ellipsoid reduces SLk.