Hill model

Myosin as an ATPase Activation of Myosin ATPase by Actin Lymn and Taylor Model 1971 Eisenberg and Hill Model 1985... 

A model analogous to the Hill model (for enzymatic reactions), which describes a more accurate dependence of the observed rate constants on surfactant concentration, was developed by Piszkiewicz. This model is applicable especially at low surfactant concentration and the data may be treated without reference to CMC. According to this model, a substrate (S) and n number of detergent molecules (D), aggregate to form critical micelle (D S), which may react to yield the product... 

Potency comprises both achon and inhibition of achon and is predicted by the Hill model though a 50% level is chosen, it is an arbitrary percentage and other values such as 60 or 40% action can also be calculated and used. Potency is not a relevant factor xmless it is so low that the dose requirement is very high (to a level where nonlinear binding with albumin can be observed, resulting in nonlinear kinetics) or where the serious side effects are dose-dependent and make an effechve dose unacceptably toxic. The potency, EC50, is expressed in a mechanishc equilibrium model where the achon is direct ... 

In graded response one can resort to using surrogates, and the classic Hill model (or sigmoid model as described in Equation 18.16 above) is used to correlate observed effect (E(t)) with the concentration modified by an exponent that is called Hill coefficient in classic sigmoidal model, the Hill coefficient h) would be equal to 1 ... 

C(t) modeled according to two-compartment model with zero-order and first-order absorption Pharmacokinetic/pharmacodynamic relationship modeled using Hill model with first-order absorption. Modeled parameters matched experimental parameters when bicompartmental model with zero-order input was used. Linear PKs, anticlockwise hysteresis loop established for all doses studied. Apomorphine and growth hormone concentration predicted with good accuracy... 

Raupach et al 1992 [528] showed that in this region two other mechanisms become important in determining Ac x, c). The first is the changes induced by the hill in the eddy flux field Af(x, z) and hence in its divergence. The second is the change to the flux of c from the surface that occurs because the surface shear stress Ar(x, z) varies as the hill is traversed. The mechanism for this in the rough hill model of [528] is the... 

A more searching analysis of the Poole-Frenkel mechanism performed for polysiloxane on the basis of the Hill model ( ) showed that charge carrier emission should proceed from the isolated Coulomb centre and should take place in the hemisphere related to that centre. The depth of the centres, determined form the activation dependence of the temperature, was =... 

The Frenkel-Halsey-Hill model has also been extended to adsorption on small spherical particles, an important consideration in nucleation of condensation by foreign nuclei (75). 

FIGURE 48.3 The Hill model of muscle separates the artive properties of muscle into a contractile element, in series with a purely elastic element. The properties of the passive muscle are represented by the parallel elastic element. 

The influence of experimental conditions on Hill parameter estimation is described by Glende and Reich (1972). According to Reich et al. (1972), a nonlinear regression with a minimum of 15 measuring points should be used for an unbiased determination of parameters. Also, the Hill model has been extended by Adair (1925) to allow for the existence of stable, partly liganded intermediates. 

A novel kinetic model for micellar catalysis has been developed based on the assumption that the Stem layer is always saturated with respect to counterions. This means that the ground state for ions is the ion bound to the micellar surface and not the free-ion in the bulk phase. An analogy between micellar reactions and reactions catalysed by regulatory enzymes has led to the application of the Hill model to the dependence rate constants of micellar catalysed reactions upon the detergent concentration. The decrease in rate at high concentrations of detergent is interpreted in terms of substrate inhibition. ... 

If a P molecule binds to exactly n ligand molecules at a time, then the Hill model is useful ... 

Figure 28.8 Cooperativity described by the Hill model, (a) When the fraction v of sites filled is plotted versus ligand concentration. v. the steepness of the curve increases with n, the Hill coefficient, (b) The Hill plot linearizes the data. The slope gives the Hill coefficient i and the intercept gives the binding constant K.

Figure 28.9 For the maturation of frog eggs, the production of phosphorylated mitogen-activated protein kinase (MAPK-P) is governed by small changes in the concentration of the MOS protein. This relationship can be described by the Hill model. Source JE Ferrel and EM Machleder, Science 280, 895-898 (1998). 

If an enzyme requires n identical substrate molecules to bind at the same time before it can catalyze a reaction, and if each molecule binds with affinity K, the Hill model can be used to predict the rate v of product formation ... 

Figure 8.8. Analysis of the initial velocity versus substrate concentration data for a cooperative enz3me using (a) the Hill model and (b) the MWC model.

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