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[7] [8] Because the slope of a Hill plot is equal to the Hill coefficient for the biochemical interaction, the slope is denoted by . A slope greater than one thus indicates positively cooperative binding between the receptor and the ligand, while a slope less than one indicates negatively cooperative binding.
The first description of cooperative binding to a multi-site protein was developed by A.V. Hill. [4] Drawing on observations of oxygen binding to hemoglobin and the idea that cooperativity arose from the aggregation of hemoglobin molecules, each one binding one oxygen molecule, Hill suggested a phenomenological equation that has since been named after him:
The lower the EC 50, the less the concentration of a drug is required to produce 50% of maximum effect and the higher the potency. The EC 10 and EC 90 concentrations to induce 10% and 90% maximal responses are defined similarly. There is a wide range of EC 50 values of drugs; they are typically
The length of the initial rate period depends on the assay conditions and can range from milliseconds to hours. However, equipment for rapidly mixing liquids allows fast kinetic measurements at initial rates of less than one second. [7] These very rapid assays are essential for measuring pre-steady-state kinetics, which are discussed below.
Hofmeyr and Cornish-Bowden first published the reversible form of the Hill equation. [1] The equation has since been discussed elsewhere [ 3 ] [ 4 ] and the model has also been used in a number of kinetic models such as a model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic β-cells [ 5 ] or a model of a glucose-xylose co ...
The quadratic Hill yield criterion for thin rolled plates (plane stress conditions) can be expressed as + (+) (+) + = where the principal stresses , are assumed to be aligned with the axes of anisotropy with in the rolling direction and perpendicular to the rolling direction, =, is the R-value in the rolling direction, and is the R-value perpendicular to the rolling direction.
Dose response curves are typically fitted to the Hill equation. The first point along the graph where a response above zero (or above the control response) is reached is usually referred to as a threshold dose. For most beneficial or recreational drugs, the desired effects are found at doses slightly greater than the threshold dose.
where is the Hill coefficient which quantifies the steepness of the sigmoidal stimulus-response curve and it is therefore a sensitivity parameter. It is often used to assess the cooperativity of a system. A Hill coefficient greater than one is indicative of positive cooperativity and thus, the system exhibits ultrasensitivity. [34]