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The Hill equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand. [1] [2] [nb 1] This equation is formally equivalent to the Langmuir isotherm. [3] Conversely, the Hill equation proper reflects the cellular or tissue response to the ligand: the physiological output of the system, such as muscle ...
The inflection point at which the increase in response with increasing ligand concentration begins to slow is the EC 50, which can be mathematically determined by derivation of the best-fit line. While relying on a graph for estimation is more convenient, this typical method yields less accurate and precise results. [6]
A ligand binding assay (LBA) is an assay, or an analytic procedure, which relies on the binding of ligand molecules to receptors, antibodies or other macromolecules. [1] A detection method is used to determine the presence and amount of the ligand-receptor complexes formed, and this is usually determined electrochemically or through a fluorescence detection method. [2]
The Hill equation can be used to describe dose–response relationships, for example ion channel-open-probability vs. ligand concentration. [9] Dose is usually in milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures. Other dose units include moles ...
Protein methods are the techniques used to study proteins.There are experimental methods for studying proteins (e.g., for detecting proteins, for isolating and purifying proteins, and for characterizing the structure and function of proteins, [1] often requiring that the protein first be purified).
Upon binding of an analyte to the ligand, the real-time kinetic rates (k on, k off) can be measured as changes in fluorescence intensity and the K d can be derived. This method can be used to investigate protein-protein interactions, as well as to investigate modulators of protein-protein interactions by assessing ternary complex formation.
One manifestation of this is enzymes or receptors that have multiple binding sites where the affinity of the binding sites for a ligand is apparently increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to a binding site. For example, when an oxygen atom binds to one of hemoglobin's four 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: