Лиганд пен макромолекуланың байланысын сипаттаушы Хилл теңдеуі

Diagram showing the proportion of a receptor bound to a ligand
the Hill equation as an equation used in biochemical characterization

In biochemistry and pharmacology, the Hill equation refers to two closely related equations that reflect the binding of ligands to macromolecules, as a function of the ligand concentration. A ligand is "a substance that forms a complex with a biomolecule to serve a biological purpose" (ligand definition), and a macromolecule is a very large molecule, such as a protein, with a complex structure of components (macromolecule definition). Protein ligand binding typically changes the structure of the target protein, thereby changing its function in a cell. The distinction between the two Hill equations is whether they measure occupancy or response. The Hill equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand. This equation is formally equivalent to the Langmuir isotherm. Conversely, the Hill equation proper reflects the cellular or tissue response to the ligand: the physiological output of the system, such as muscle contraction. The Hill equation was originally formulated by Archibald Hill in 1910 to describe the sigmoidal O2 binding curve of haemoglobin. The binding of a ligand to a macromolecule is often enhanced if there are already other ligands present on the same macromolecule (this is known as cooperative binding). The Hill equation is useful for determining the degree of cooperativity of the ligand(s) binding to the enzyme or receptor. The Hill coefficient provides a way to quantify the degree of interaction between ligand binding sites. The Hill equation (for response) is important in the construction of dose response curves.

The Hill equation is commonly expressed in the following ways.

The Gaddum equation is a further generalisation of the Hill equation, incorporating the presence of a reversible competitive antagonist. Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose response relationship.

The Hill equation is used extensively in pharmacology to quantify the functional parameters of a drug and are also used in other areas of biochemistry. The Hill equation can be used to describe dose response relationships, for example ion channel open probability (P open) vs. ligand concentration.

Because of its assumption that ligand molecules bind to a receptor simultaneously, the Hill equation has been criticized as a physically unrealistic model. except when the binding of the first and subsequent ligands results in extreme positive cooperativity. There is a link between Hill Coefficient and Response coefficient, as follows. Altszyler et al. (2017) have shown that these ultrasensitivity measures can be linked.