Terms and procedures used in the analysis of drug action: the quantification of ligand-receptor interactions

Term Suggested Usage Notes
“Concentration” of receptors [R] for notional concentration of ligand-free receptors; [R]T or [R]tot for total receptors.
Number of receptors, N The total number of receptors, expressed in terms of unit area of membrane, or per cell, or per unit mass of protein. Proportional to the quantity Bmax (the maximal specific binding of a ligand, often expressed in units of mol ligand/mg protein, or ligands bound/cell) measured in radioligand binding studies, in the absence of complications. The relationship between Bmax and N is influenced by the number of ligand binding sites possessed by each receptor. For ligand-gated ion channels, this is generally greater than one.
Also referred to as receptor density.
Proportion of receptors in specified states pR for proportion (fraction) of receptors or binding sites free of ligand. pLR for the proportion of receptors or binding sites occupied by the ligand L. If a distinction is made between inactive and active states of the receptor, then pLR refers to the inactive state. pLR* for the proportion of receptors in which L occupies its binding site(s) and which are in an active state. pLR′ for the proportion of receptors in which L occupies its binding site(s) and which are in a distinct (R′) state that differs from both the inactive and the fully active states. This may exhibit some classical signaling activity or it may differ from R or R* in another property such as activation of different effectors, rates of internalization, or cellular trafficking (Berg et al, 1998; Kenakin and Onaran, 2002).
Rate constants for the binding of a ligand k+1 for the association (forward) rate constant, and k–1 for the dissociation (backward) rate constant, in the reaction Embedded Image Units to be specified (M–1 s–1 or M–1 min–1 for k+1, s–1 or min–1 for k–1 in the scheme illustrated). Lowercase symbols to be used to denote rate constants (cf., uppercase for equilibrium constants). Where there are several ligands, alphabetical subscripts can be added: e.g., k+1A, k–1B. For more complicated schemes involving several reactions, subscripts 2, 3, etc., can be used: e.g.,Embedded Image
Here, L represents a ligand and R the unoccupied binding site.
Equilibrium dissociation constant for ligand-receptor interactions, K In the simple scheme below, K is numerically equal to the ratio of dissociation to association rate constants (k–1/k+1), and has the dimension M (mol/l). K can be used in combination with subscripts for clarity. Lowercase letter subscripts are used to designate the type of experimental approach used to determine the constant (e.g., Kd, Ki, Kb–see below) and uppercase letter subscripts designate the compound to which the constant refers (e.g., KA, KB, or KdA, KdB, for compounds A and B, respectively).
Embedded Image The choice of lowercase subscript that is used in combination with K is based on the following conventions:
(i) Kd refers to the equilibrium dissociation constant of a ligand determined directly in a binding assay using a labeled form of the ligand.
(ii) Ki refers to the equilibrium dissociation constant of a ligand determined in inhibition studies. The Ki for a given ligand is typically (but not necessarily) determined in a competitive radioligand binding study by measuring the inhibition of the binding of a reference radioligand by the competing ligand of interest under equilibrium conditions.
(iii) Kb refers to the equilibrium dissociation constant of a ligand (traditionally, a competitive antagonist) determined by means of a functional assay.
When a subscript indicates the type of method used, Kd, Ki and Kb should be used in preference to KD, KI, and KB, respectively.a. Uppercase subscripts (either alphabetical, e.g., KL, numerical, e.g., K2 or a combination of the two, e.g., K2L) are recommended only to identify the particular ligands and equilibria under consideration, especially when dealing with more complicated schemes involving several steps such as binding followed by isomerization. Two alternative examples of such a scheme are shown below:
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Note: The reciprocal of the equilibrium dissociation constant (the equilibrium association constant or affinity constant, in units of M–1) can also be used, although this is not preferred.
pK The negative logarithm to base 10 of the equilibrium dissociation constant, K in molar concentration units. The term can be used in combination with subscripts as described above for equilibrium dissociation constants (pKd, pKi, pKb, etc.). There are two major benefits to using the pK measures of pharmacological potency rather than the equilibrium constant (K) itself. Since pharmacological potency often ranges over many orders of magnitude (K values from 10—10 M to > 10—3 M), it is easier to present and discuss these differences in a pK form (i.e., values generally range from about 10 to 3). More importantly from a statistical point of view, concentration parameters are generally distributed in a log normal manner (Christopoulos, 1998) so standard deviations are symmetrical for pK values but not for K values.
Hill-Langmuir equation Embedded Image in which pLR is the fraction (proportion) of binding sites occupied by a ligand L at equilibrium. It is assumed that the interaction between L and the sites obeys the law of mass action and can be described by the simple scheme Embedded Image in which K is the equilibrium dissociation constant. Described as the Langmuir absorption isotherm in physical chemistry. More complicated expressions may hold, especially if L is an agonist (see Section IV. A.).
  • a The original usage of KB by Gaddum represented the binding constant of ligand B to distinguish it from that of ligand A. More recent usage of KB or pKB usually refers to values derived from pharmacological blocking experiments. Thus, to maintain consistency with the use of lower case subscripts for inhibition and direct binding experiments (i.e., Ki and Kd) we recommend using Kb or pKb for estimates of the dissociation constant that are derived from pharmacological blocking experiments (e.g., Schild plots.)