Hill’s equation

To account for different strengths in tension and compression, Hoffman added linear terms to Hill s equation (the basis for the Tsai-Hill criterion) [2-23] ... 

For the quantitative description of the cooperative process in the macromolecule-low molecular weight ligand systems, Hill s equation is used. It expresses the dependence of the degree of macromolecule saturation with the ligand (Y) on the equilibrium concentration of the ligand in solution [67] ... 

The degree of saturation of carboxylic CP with protein (Y) is determined by the ratio of the amount of protein bonded under these conditions (at a predetermined concentration in solution) to the maximum amount Y = m/M. In this case, Hill s equation becomes... 

The theory of linked functions establishes the general thermodynamic meaning of the cooperative behavior of the system. On the basis of Hill s equation,... 

The rate-enhancing effect of cationic detergents was analyzed by using Hill s equation. The observed exponent (n = 3 — 4) suggests that polymer-bound detergents facilitate the subsequent binding acceleratively hence the sigmoidshaped dissociation behavior of hydroxamic acid. 

Irradiation of externally added NDI rods 31 at 635 nm was detected as an increase in intervesicular pH in response to a reduction of internal quinone (Figure 11.17). The change in HPTS emission, which reflects internal proton consumption, is analyzed with Hill s equation (n = 3.9 1.2), which indicates that the active helix photosystem 28 is quadruple (four rods form the helix) with an effective concentration of 1.3 (iM. However, the shortened length of the rigid-rod p-barrel scaffold to the NDI dimer 30 is inactive (Figure 11.17) [43]. 

This expression is known as Hill s equation and undergoes linear transformation to yield... 

THE FUNCTIONS OF MATHEMATICAL PHYSICS, Harry Hochstadt. Comprehensive treatment of orthogonal polynomials, hypergeometric functions. Hill s equation, much more. Bibliography. Index. S22pp. 55 x 854. 65214-9 Pa. 8.95... 

According to the recommendations, in quantitative measurements of biological activity drug action is expressed in terms of the effect, E, produced when an agonist, A, is applied at a concentration [A]. The relationship between E and [A] can often be described empirically by Hill s equation, which has the form ... 

Unfortunately, Hill s equation (Equation 6.1) is only a convenient mathematical idealization, which can be realized for ligand binding to the pure isolated receptor in vitro. In an intact biological object a ligand interacts with several or even many different macromolecules,and the final biological effect may dramatically differ from the simple relationship presented in Figure 6.1. 

Assuming that the strength of the relaxation is known (by means of a Cole-Cole plot or other procedure), the preceding four equations allow us to estimate the parameters appearing in Hill s equation. Notice that cOp does not correspond to the maximum frequency, that is, the frequency at the top of the peak (except in the case where m = I - n), although it is of the same order of magnitude as that frequency. 

T,RD = V /( u vX then a perturbation analysis of Hill s equation (11.11) shows that the uniform steady state of (11.1) with a temporally varying diffusion coeflBcient of the inhibitor is stable for sufficiently small oscillations, e < c 1 [436]. In other words, small oscillations in the diffusion coefficient have a stabilizing effect they delay the onset of the Turing instabihty. 

Magnus, W, Winkler, S. Hill s Equation. Dover, New York (1979)... 

If the peak cunent in the CV of complex C is used in the Hill s equation for the deteimination of the oxigenadon ratio, the result (Kq2 - 7900 M 0 compares well with that obained for the oxygoiation ratio of dielate B at the electrode surface. 

Some of the applicable muscle models include the Maxwell, Voigt, Hill and Carlson models (Figure 1). In particular, the Carlson (1957) equation is used in much of this work to describe the stress-velocity relationship of cardiac muscle over the entire cardiac cycle. Min et al. (1978) found very little difference in analyzing ventricular dynamics when he alternately used Carlson s equation only during isotonic contraction and Hill s equation during isovolumic contraction. 

The relationship between the hemoglobin saturation SOj (denoting either SAOj or SVOj) and the blood oxygen tension is given by Hill s equation (West et al, 1966) ... 

Fio. 15. Linear plot of Hill s equation. Half-maximal velocity corresponds to... 

Addition of formaldehyde to solutions of human hemoglobin also increases its oxygen affinity, but decreases heme-heme interaction (Guthe, 1954). At pH 7, the oxygen affinity increases more than 10-fold, but the value of n in Hill s equation, Eq. (7), decreases from 2.9 to 1.5 or less. 

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