Hill equation application

The Hill equation is used to estimate Km for allosteric enzymes. Equations based on classic Michaelis-Menten kinetics are not applicable. 

The Hill equation has only limited applicability as a model to predict the expression of agonism, because the parameters from this empirical equation depend on both drug-specific and system-related properties, complicating the extrapolation and prediction from in vitro to in vivo systems. With a fully mechanistic model, Zuideveld was better able to predict the in vivo affinity and efficacy of 5-HTia receptor agonists from in vitro receptor binding assay. 

Piskiewicz [119] has developed a kinetic model of micellar catalysis, based on the Hill equation of enzyme kinetics, which assumes a cooperative interaction between reactants and surfactant to form reactive substrate-micelle complexes. This model is probably not applicable to systems in which the surfactant is in large excess over substrate, as in most micellar mediated reactions, but it gives a very reasonable explanation of the rate effects of very dilute surfactants. 

Fig. 29.1.3. Whole cell current responses of a neurone isolated from the CNS of Heliothis virescens after application of different neonicotinoids. The dose-response curve was fitted by the Hill equation. All currents were first normalized to mean amplitudes elicited b)/10 pM ACh before and after each test concentration was applied and then normalized to the relative amplitude elicited...

Should one use the Hill plot in practice to examine the initial velocity behavior of enzymes Because infinite cooperativity is assumed to be the basis of the Hill treatment, only rapidly equilibrating systems are suitable for the Hill analysis. However, enzyme systems displaying steady-state kinetic behavior will not satisfy this requirement for this reason, one must avoid the use of kinetic data in any application of the Hill equation to steady-state enzyme systems. 

Fuchs C, Bhattacharyya D and Fakirov S (2006) Microfibril reinforced polymer-polymer composites Application of Tsai-Hill equation to PP/PET composites. Compos Sci Technol 66 3161-3171. Fakirov S, Bhattacharyya D and Shields R J (2008) Nanofibril reinforced composites from polymer blends, Coll Surf A Physicochem Eng Aspects 313 2-8. 

Figure 13 (A) Nicotinic ACh receptor in NEB cells of neonatal hamster lung. ACh-iaduced inward current under normoxia and hypoxia conditions (p02 = 20 mmHg. Holding potential was —60 mV). (B) Application of nicotine evoked an inward current (a). Holding potential was —60 mV Effects of holding potential on inward currents evoked by 50 pM nicotine. Each plotted point is the mean peak inward current amphtude taken from between five and eight cells at each holding potential, (c) Nicotine evoked a membrane potential depolarization, (d) The peak currents evoked at each concentration are expressed relative to the peak current evoked by 50 mM nicotine and plotted against the log [nicotine] mean response taken from five to eight cells. The experimental data were fitted by the Hill equation with a Hill coefficient of 0.9 and EC50 = 4 pM.

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

D. A. Long. Raman Spectroscopy. McGraw-Hill, New York, 1977. A standard reference work on Raman spectroscopy with much theoretical detail on the underlying physics. Most of the needed equations for any application of Raman spectroscopy can be found in this book. 

Hill-Langmuir equation and the application of the law of mass action to the kinetics of drug-receptor interaction ... 

References Ablowitz, M. J., and A. S. Fokas, Complex Variables Introduction and Applications, Cambridge University Press, New York (2003) Asmar, N., and G. C. Jones, Applied Complex Analysis with Partial Differential Equations, Prentice-Hall, Upper Saddle River, N.J. (2002) Brown, J. W., and R. V Churchill, ComplexVariables and Applications, 7th ed., McGraw-Hill, New York (2003) Kaplan, W., Advanced Calculus, 5th ed., Addison-Wesley, Redwood City, Calif. (2003) Kwok, Y. K., Applied Complex Variables for Scientists and Engineers, Cambridge University Press, New York (2002) McGehee, O. C., An Introduction to Complex Analysis, Wiley, New York (2000) Priestley, H. A., Introduction to Complex Analysis, Oxford University Press, New York (2003). 

References Brown, J. W., and R. V. Churchill, Fourier Series and Boundary Value Problems, 6th ed., McGraw-Hill, New York (2000) Churchill, R. V, Operational Mathematics, 3d ed., McGraw-Hill, New York (1972) Davies, B., Integral Transforms and Their Applications, 3d ed., Springer (2002) Duffy, D. G., Transform Methods for Solving Partial Differential Equations, Chapman Hall/CRC, New York (2004) Varma, A., and M. Morbidelli, Mathematical Methods in Chemical Engineering, Oxford, New York (1997). 

Sim] Simmons, G.E, Differential Equations with Applications and Historical Notes, McGraw Hill, New York, 1972. 

A. Kolmogoroff, op. cit. in LI A. Friedman, Stochastic Differential Equations and Applications I (Academic Press, New York 1975) ch. I. See, however, the footnote on p. 296 of A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York 1965). 

P. D. Ritger and N. J. Rose, Differential Equations with Applications, McGraw-Hill, NY, pp. 285-288 (1968). 

Thomas K. Sherwood and C. E. Reed, Applied Mathematics in Chemical Engineering, McGraw-Hill, New York, 1939 William R. Marshall and Robert L. Pigford, The Application of Differential Equations to Chemical Engineering Problems, University of Delaware, Newark, 1947 A. B. Newman, Temperature Distribution in Internally Heated Cylinders, Trans. AlChE 24,44-53 (1930) T. B. Drew, Mathematical Attacks on Forced Convection Problems A Review, Trans. AlChE 26,26-79 (1931) Arvind Varma, Some Historical Notes on the Use of Mathematics in Chemical Engineering, pp. 353-387 in W. F. Furter, ed., A Century of Chemical Engineering [17]. 

The application of the 3-9 surface potential in physical adsorption was lucidly discussed by Brunauer (3) and later used by Hill (15) in Model 1 adsorption about the same time that the BET theory was reworked by the author and Pack (7,9) on the basis of Equation 6a as the adsorption potential function. 

Although we shall not be concerned experimentally with measuring heats of adsorption, it is appropriate to comment that Mi for the physical adsorption of a gas is always negative, since the process of adsorption results in a decrease in entropy. The isosteric heat of adsorption (the heat of adsorption at constant coverage 6) can be obtained by application of the Clausius-Clapeyron equation if isotherms are determined at several different temperatures the thermodynamics of adsorption have been fully discussed by Hill. ... 

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