Steep curves

There are instances where the observable kinetics of elimination clearly are not due to first-order exit from a single compartment. For example, a steep curve relating drug concentration and time may indicate a two-compart-ment system in which the drug exits in two phases, one fast... 

Fig. 11.5 Rate constants in HOH and DOD as a function of pL (two bottom bell shaped curves) for an enzyme catalyzed reaction with three protomeric forms and an isotope effect of 2. L is the H+ or D+ concentration as appropriate. The steep curve shows the erroneously calculated isotope effect from the rate constants at pH = pD. The correct flat line is calculated taking the IE s at corresponding pL (pD = pH + 0.5) (Schowen, R. L. J. Label Compd Radiopharm. 50, 1052 (2007), with permission Wiley Interscience)...

The EU TGD (EC 2003) recognized that the NOAEL is not very accurate with respect to the degree to which it corresponds with the (unknown) true NAEL. In the case of a steep curve the derived NOAEL can be considered as more reliable (the greater the slope, the greater the reduction in response to reduced doses) in the case of a shallow curve, the uncertainty in the derived NOAEL may be higher and this has to be taken into account in the assessment. If a LOAEL has to be used in the assessment, then this value can only be considered reliable in the case of a very steep curve. According to KEMI (2003), extrapolation factors of between 3-5 are used for LOAEL-to-NOAEL extrapolation without any scientific basis in risk assessment reports of existing substances within the European Union. 

The more steeply rising curve is the longitudinal or compression mode. The less steep curve at — 0 is the torsional mode. The quadratic curves at 9 = 36 are beam bending modes. The dashed curve is the dispersion obtained after taking into account the coupling to water. 

With the fatty acids on distilled water the very steep curve I continues almost down to zero pressure. On dilute acid solutions, however, this steep curve only occurs above about 17 dynes per cm., and below this pressure there is a second, nearly straight portion of the curve (see curve III), cutting the abscissa at about 25 sq. A. Both the upper and lower parts of these curves are very little changed when the number of carbon atoms in the acid is altered from 14 to 22 carbon atoms the steep curve always tends to an area within 1 sq. A. of 20 5 the lower part on acid solutions tends to 25 sq. A. for the medium-chain aoids, about 16 carbons, and to very slightly smaller areas for longer chain acids (24 for the 22... 

The model curves calculated for different TLM models (inner sphere complex, one proton released) are compared in Fig. 5.131. To avoid overcrowding, two groups of nearly identical curves were plotted as one curve each. The difference between the most and the least steep curve does not exceed typical scatter of experimental data points in adsorption measurements. 

The influence of temperature and temperature variations depends on the solubility of the solids. Fig. 5.72 shows four different temperature-solubility curves. Whereas the solubility of sodium chloride changes little with temperature, this is not true for potassium chloride (or potash) and potassium nitrate, for example. Especially the latter features a very steep curve. Some salts, such as sodium sulfate, exhibit various temperature dependent solubility ranges. 

Known substances with very steep curves are phosgene, hydrocyanic acid, nitrogen dioxide, and hydrogen sulfide. Relevant effects can be seen where the NOAEL for these substances is only slightly exceeded, while in other cases lethality is observed only where the NOAEL is exceeded tenfold. 

When all the dew points measured in this way are coimected, a steep curve to the right is the result, the so-called boiling pressure curve or vapor pressure curve (Fig. 11.7). It gives the values of pressure and temperature at which gas and... 

Figure 6.17. Warhaftig diagram The upper portion represents the probability of a particular ion at a specified energy. The lower portion represents the rate constant of a unimolecular fragmentation of the ABCD+ radical cation as a function of internal energy the steep curve is for a direct cleavage reaction, and the shallow curve is for a rearrangement reaction. (Redrawn from F. W. McLafferty and F. TureCek, Interpretation of Mass Spectra, 4th ed.)...

The linear part in which the film is used. The steepness of the curve is the gradation (hard films with strong contrast have steep curves). The slope is related to the grain size. 

Electrochemically reversible reactions produce steep curves whereas for irreversible reactions the slope may be much shallower, and it may be necessary to go to high potentials to reach the limiting current. 

Figure 21.16 Curve A shows a partial agonist curve with a reported potency just below 1 pM at around 30% effect. Curve B represents a bell-shaped curve. Curve C is a steep curve with a slope factor far above 1.

Steep curve behavior can also be seen for covalently binding compounds or very potent inhibitors with the value below the target protein concentration of the assay. For enzymes, this is known as zone behavior [28,29]. By applying the mass action law, inhibition becomes a linear function of the enzyme concentration if the Kd value of the inhibitor is far below the enzyme concentration. The steepness of the concentration response curve also increases with the amount of enzyme added. 

Most of the curves showed steep curve behavior with a top effect up to 120% that indicates complete inhibition of cAMP production and might be caused by cell toxicity. Other compounds had bell-shaped curves. 

The concentration profiles are as shown in Fig. 3.6.1-1. The diffusion resistance causes a concentration profile in the pellet because reactants cannot diffuse in from the bulk at a sufficient rate. A small diffusion resistance (say, large De gives a rather flat profile, whereas a steep curve is obtained for a large diffusion resistance. As the rate of reaction at any point in the slab equals kpsCs( ), this profile causes an average rate which is lower than that obtained at the surface concentration C. The ratio of available area between a porous and an impervious catalyst is so large that this penalty is minimal when compared to the gain in productivity associated with the porosity. 

Fig. 14.139. Demagnetization curve (B-H vs. H) ranges for SmCos magnets from three major manufacturers, Brand A, B and C (Strnat, 1976b). The unlabeled group of steep curves represents the corresponding B vs. H curves.

The answer s3 IIFI b (6)J. The slope of the LD50 curve shows the range between no effect and maximal effect (I-D,qq) and is thus a measure of the probability of surviving a lethal dose (l.e., a lethal dose is likely to kill most of a population exposed). For example, a compound with a steep curve would make an effective rodenticide because the lethal dose range is narrow and survivors are unlikely. 

Figure 5.106 shows the strong influence of static strain in the investigated interval from 44 to 76% on weathering time for a carbon-black filled, effectively stabilized SBR hose material, exemplified by the steep curve of crack depth between T1 and T2 and also calls attention to the positive effect of a good antiozonant [698]. 

The chloride content profile of different mixes of 28-day cured concretes subjected to 60-day exposure to NaCl solution is presented in Figure 11.9. The figure shows the measured chloride concentration at different depths, and the chloride concentration inside of the concrete is measured by the percentage of the concrete s weight. In the chloride content profile, the rate of chloride diffusion can be determined from the steepness of the curve. A less steep curve indicates that the concentration of chloride inside of the concrete equals the concentration on the concrete s surface. On the other hand, the steep curve indicates the slow chloride ion diffusion inside of the concrete due to very slow chloride penetration from the concrete s surface. 

Fig. 30. Conformity of viscosity curves around the gel point with the percolation modd. Steep curves are for rigid network gels and the less si curve is for flexible network. All systems ate aromatic polyamide networks formed in a oim-step polycond ation procedure...

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