Hill equation description

The Hill equation should be used only when a reasonable estimation of is possible and when data are gathered over the whole effect range. If data are available only from the lower part of the curve, the linear equation might just as well be used. The difference between the Hill equation and the linear or log-linear equation is that only the Hill equation gives a mechanistic-physiologic understanding of the effect. The other equations are merely descriptive. 

A Buckingham potential replaces the twelfth power term with an exponential, which is a better theoretical description of the repulsion expected between electron clouds. In both MM2 and MM3, an exponential-6 equation is used. This is a modified Hill equation, which is a particular formulation that contains only two adjustable parameters for the interaction between any two atoms. Equation [9] is for MM3. For MM2 the exponential part was slightly harder, with 12.50 instead of 12.00 in the exponent. 

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] ... 

Addition of substrate, which here is synonymous to the allosteric effector, shifts the equilibrium from the low affinity T-form to the substantially more catalytically active R-form. Since one substrate molecule activates four catalytically active sites, the steep rise in enzyme activity after only a slight increase in substrate concentration is not unexpected. In this model it is important that the RT conformation is not permitted. All subunits must be in the same conformational state at one time to conserve the symmetry of the protomers. The equation given by Hill in 1913, derived from the sigmoidal absorption of oxygen by hemoglobin, is also suitable for a quantitative description of allosteric enzymes with sigmoidal behavior ... 

The description of anisotropic creep via an equivalent stress according to Hill was tested for compression creep of WHIPOX . It allows a fast numerical estimation of the CMCs deformation behavior. The Hill model consists of few parameters which can easily be determined with a couple of measurements. One further advantage is the built-in implementation in commercial finite element software, e.g. ANSYS. However, the reliability of the results is limited. For WHIPOX , the most important limitations are the assumed isochoric behavior of the material, tension and compression symmetry as well as the fact that only one stress exponent and creep equation can be specified. 

---