Hill constant

Outside this region, the experimental curve deviates from the straight line. The value of h obtained from the slope of equation 10.6 in the region of 50% saturation is known as the Hill constant. It is a measure of cooperativity. The higher h is, the higher the cooperativity. At the upper limit, h is equal to the number of binding sites. If h = 1, there is no cooperativity if h > 1, there is positive cooperativity if h < 1, there is negative cooperativity. 

Figure 10.8 Variation of the Hill constant with L for a tetrameric protein. [From M. M. Rubin and J.-P. Changeux, J. Molec. Biol. 21, 265 (1966).]...

The bell-shaped curve is of particular interest in the analysis of how structural changes in a protein affect L. The Hill constants of a wide series of modified and mutant hemoglobins fit such a curve (Figure 10.9).19... 

Figure 10.9 Variation of the Hill constant with L for the binding of oxygen to various mutant hemoglobins. [From I M. Baldwin, Progr. Biophys. Molec. Biol. 29, 3 (1975).]...

The choice of model often depends on the experiments involved. Workers in the area of, say, the effects of structural changes on the oxygen affinity and Hill constant for hemoglobin prefer the MWC model because it is essentially a structural theory. It provides a simple framework for the prediction and interpretation of experiments. Application of the theory to the Hill constant and other equilibrium measurements gives very acceptable results. Kineticists prefer the KNF model, since the kinetic measurements are more sensitive to the presence of intermediates. There are more variables in the KNF theory and there is more flexibility in fitting data. 

Heme—chemical models 307 Hemoglobin 289, 304-307 allosteric interactions 289-292, 302 Henderson-Hasselbalch equation 170 Heterotropic 290 Hexokinase 23, 51, 364 Hill constant 299, 300-302, 304 Hill equation 297 - 300 Hinge motions 48 HIV protease 486 Holoe nzyme 458 Homology 8, 9 Homology modeling 537 Homotropic 290 Hpr (histidine-containing... 

Source Effector/substrate So.s/Aq.s/Io.s (mM) Hill constant n Activation-fold Reference... 

Can the uniform steady state of (10.201) undergo a Turing instability If so, discuss the effect of increasing the Hill constant h. 

The Hill constant is an index of the affinity of the enzyme for the substrate, but it is not the enzyme-substrate dissociation constant. It has units of (concentration)", which makes comparison between reactions with different n values difficult. 

Figure 8.4. (a) Simulation of the effects of varying the HUl exponent (n) on the shape of the initial velocity versus substrate concentration curve for a coopantive enzyme. (b) Simulation of the effects of varying the Hill constant (it ) on the shape of the initial velocity versus substrate concentration curve for a coopraative enzyme. 

An advantage of the CT model, however, is the fact that it is possible to estimate the magnitude of the enzyme-substrate dissociation constant of the enzyme. This is not possible with the Hill equation. As described before, the Hill constant is a complex term that is related but is not equivalent to, the enzyme-substrate dissociation constant. By using the CT model, it is also possible to obtain estimates of the allosteric constant, L. This may prove useful in the study of allosteric modulators of enzyme activity. 

In the dark, ATP hydrolysis by soluble CF is reversibly inhibited by BzADP. It decreases increases the Hill constant from 1 in the... 

Full-Form Shaping. The third appHcation of ECM, hill-form shaping, uti1i2es a constant gap across the entire workpiece, and a constant feed rate in order to produce the type of shape used for the production of compressor and turbine blades. In this procedure, current densities as high as 100 A/cm ate used, and the current density remains high across the entire face of the workpiece. 

FIG. 14-5 Nnmher of overall gas-phase mass-transfer units in a packed absorption tower for constant mGf /LM solution of Eq. (14-23). (From Sherwood and Pigford, Absorption and Extraction, McGraw-Hill, New York, 1952. )... 

Estimation of fct for Reversible Reactions When the reaction is of the form A B, where B is a nonvolatile product and the equilibrium constant is defined by Cg = K Ca, the expressions for computing /cl become extremely complex. A good discussion of this situation is given in Mass Tran.sfer by Sherwood, Pigford, and Wilke (McGraw-Hill, New York, 1975, p. 317). Three limiting cases are hsted below ... 

For catalyst particles, Satterfield (Heterogeneous Cataly.si.s in Frae-tiee, McGraw-Hill, 1980) recommends the use of a value of tp = 4 when no other information is available, and this can be used for many adsorbents. In general, however, it is more rehable to treat the tortuosity as an empirical constant that is determined experimentally for any particular adsorbent. 

FIGURE A15.6 Hill plot of Hb showing its nonlinear nature and the fact that its asymptotes can be extrapolated to yield the dissociation constants, Ki and Kq, for the first and fourth oxygens. 

For maximum vehicle acceleration, the driver depresses the accelerator pedal to the floorboard and the engine operates with a tvide-open throttle. The power required curve traces the power needed by the car as a function of vehicle velocity when it is operated at constant speed in still air on a level road. At any given speed, the difference between these curves, Pa-Pr in Equation 1, is available for accelerating and hill climbing. 

Figure 3-50. Typical centrifugal pump characteristic curve vrith auxiliary specific speed curve. Double-suction, single-stage, 6-in. pump, operating at 1760 rpm constant speed. (By permission, Karassik, I. and Carter, B., Centrifugal Pumps, McGraw-Hill Book Co., inc., 1360, p. 197.)...

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