Hill slope

Hence, a plot of log (pAR /(I -pAR)) against log [A] should give a straight line with a slope of one. Such a graph is described as a Hill plot, again after A. V. Hill, who was the first to employ it, and it is often used whenpAR is measured directly with a radiolabeled ligand (see Chapter 5). In practice, the slope of the line is not always unity, or even constant, as will be discussed. It is referred to as the Hill coefficient (%) the term Hill slope is also used. 

With this setup, the IR field affects the nuclear dynamics in the lower electronic state (injects energy) in the time interval from f0 to T, i.e., prior to excitation to the upper electronic state. In the limit where this time interval is small, the IR field simply boosts the momentum of the wave packet. This implies that the UV delta pulse instead of creating a Franck-Condon wave packet at rest on a down-hill slope on V2 creates a Franck-Condon wave packet with a positive (mean) velocity. 

In the absence of activators AMP aminohydrolase from brain (149), erythrocytes (143, 150), muscle (145), and liver (128) gave sigmoid curves for velocity vs. AMP concentration which were hyperbolic after the addition of monovalent cations, adenine nucleotides, or a combination of monovalent cations and adenine nucleotides. For the rabbit muscle enzyme (145), addition of K+, ADP, or ATP produced normal hyperbolic saturation curves for AMP as represented by a change in the Hill slope nH from 2.2 to 1.1 Fmax remained the same. The soluble erythrocyte enzyme and the calf brain enzyme required the presence of both monovalent cations and ATP before saturation curves became hyperbolic. In contrast, the bound human erythrocyte membrane enzyme did not exhibit sigmoid saturation curves and K+ activation was not affected by ATP (142). 

Carboxylic acids have been reported either to have no effect (129, ISO), to activate (135), or to inhibit (7SS) AMP aminohydrolase. While the activation of the rabbit muscle enzyme was not thoroughly examined (135), the reported inhibition of this enzyme by citrate, succinate, and maleate was most effective in the absence of activators or in the presence of ADP (133). Enzymic activity in intact myofibrils was activated by ATP, ADP, and ITP in succinate buffer but not in citrate buffer (154)-With the rat enzyme citrate, succinate, cacodylate, acetate, and lactate increased both the apparent Km and Hill slope for AMP Pmai decreased only slightly (147). 

In Equation 4.4, ymm is the minimum y value of the curve, ymax is the maximum y value of the curve, cone, is the test concentration, and n is the Hill slope of the curve. We found that the Kv. 3 current was sensitive to inhibition by the Stichodactyla helianthus peptide, ShK, as well as ShK-Dap22, charybdotoxin (all pre-dissolved in water, with 0.1% BSA present during the experiment), and 4-aminopyridine (4-AP), which was dissolved directly in D-PBS (Figure 4.6A). 

Concentration-response curve fitting of activity value y to obtain IC50 (or EC50) ymx and are fitted maximum and minimum values of data if data do not define maximum or minimum asymptote, ymx can be fixed to 100% and yrain to 0% respectively n is hill-slope coefficient and c is inhibitor (or activator) concentration... 

The potency of compounds derived from concentration response assays is expressed most commonly as IC50 or EC50 defined as the compound concentration that produces half maximum response. A common model is the four-parameter Hill-slope equation (Table 14.1). A three-parameter model can be used if a maximum or minimum asymptote is not available because compound potency falls outside the concentration range. One recommendation is to fit the logarithm (loglO) of IC50 or EC50 instead of the untransformed concentration because the concentration response errors are normally... 

From this equation, we can construct an example that is extremely useful in visually examining receptor data, indeed any data fitting the simple mass action model of Eq. (19.1). This means that a toxicant under study is competing with the radioligand for one, and only one, population of sites. By definition, the Hill slope (often called nH) must equal 1. It turns out that by memorizing the numbers 9 and 91, one can do a very useful preliminary analysis of data fit to such a mass-action model. The reason for this is as follows ... 

For this particular choice of canopy density, Lc = 5 m the magnitude of the perturbations induced by the hill are of order the hill slope, H/L. In a canopy with hc = 20 m this corresponds to a Leaf Area Index (LAI) of 4. If LAI = 2 but the other parameters remain unchanged, the magnitude of the perturbation terms all double because the ratio of the momentum absorption distance Lc to the hill lengthscale L plays an important dynamic role in determining the velocity perturbations that drive the scalar fluctuations in the canopy. 

Notice that runoff can add to or subtract from infiltration depending upon the topography. Runoff moves toward low-lying areas or wetlands (+R) and away from hill slopes (-R), for exam-... 

The extent of surface weathering of crystalline rocks or of sedimentary rocks such as shales or carbonates, and thus rock permeability (and yield to wells), decreases rapidly with depth. Also, rock weathering is deeper under valley bottoms than on ridges or hill slopes. This reflects the fact that the weathering, which is facilitated by joints, fractures, and faults, tends to create valley bottoms in the first place. Valley bottoms continue to concentrate runoff (R is then a positive term in the infiltration equation) and so remain the locus of deeper development of secondary rock porosity and permeability and thus of enhanced groundwater storing and transmitting capacity. 

Soil structure, geologic strata, and topography influence the location and movement of variable source areas of surface runoff in a watershed. Eragipans or other layers, such as clay pans of distinct permeability changes, can determine when and where perched water tables occur. Shale or sandstone strata also influence soil moisture content and location of saturated zones. For example, water will perch on less permeable layers in the subsurface profile and become evident as surface flow or springs at specific locations in a watershed. Converging topography in vertical or horizontal planes, slope breaks, and hill slope depressions or spurs, also influence... 

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