Agonists, inverse agonists, and antagonists all bind in a competitive fashion to primary binding sites in receptive complexes and thereby affect the function of receptors. The function of and binding to receptors and enzymes may further be modulated by allosteric compounds [1
]. Such modulators, conventionally termed "effectors" in enzymology, bind to sites sterically separate from the primary binding site. Thus, the effect of binding a modulator molecule resembles non-competitive kinetics.
Regulatory modulation of receptor and enzyme function may be divided into heterotropic and homotropic allosteric behavior as originally defined by Monod and co-workers [7
]. Heterotropic allostery
is seen when an effect of a bound agonist or an enzymatic conversion of substrate to product is altered by the binding of a different modulator molecule, eventually a product molecule, to a site different from the primary binding site on the receptive unit or the enzyme complex. Homotropic allostery
, on the other hand, is seen when the agonist or the substrate itself binds to a modulator site and thereby affects the function of receptors or enzymes. This latter type of allosteric behavior is characterized as co-operative, and as such the term "co-operative" is used here in its strict sense only related to auto-modulation [5
]. Dose-response relations with bell-shapes and terraces have been observed in single ligand applications both for enzymes [9
], channel-, pump-, and co-transporters [11
], carriers [15
], tyrosine kinase receptors [16
], and G protein-coupled receptors, GPCRs, for neurotransmitters, hormones, and chemokines [18
Some recent examples of treatment by model of bell-shaped dose-responses have been carried out for receptive units in general [26
], for monomeric enzymes [27
], for growth hormone receptors [28
], and for aggregation in antigen-antibody interactions [29
With the realization of widespread dimer and multimer formation in functional units, including GPCRs [30
], and the recognition of additional allosteric sites in these receptive unit [3
] as well as for ABC transporters [33
] and many others, it seems that there is still a need for mechanistic models where primary ligands (agonists) can operate as auto-modulators of function and simulate dose-response relations that display self-modulation in the form of either terraced curves or bell-shaped relations. One such model is the homotropic two-state model, HOTSM, presented here.
The HOTSM, which is a cubic ternary-complex reaction scheme, should be distinguished from two other recently developed cubic ternary-complex models. Thus, Hall has advanced a cubic ternary-complex reaction scheme with a receptor, an agonist, and a heterotropic modulator molecule in the form of an allosteric two-state model, ATSM [34
]. This model is well-suited for analyzing dose-response data when the concentration of either the agonist or the modulator are varied separately. Another cubic ternary-complex reaction scheme developed for signal transduction in G protein coupled receptors, the so-called cubic ternary-complex model, CTCM, has been thoroughly analyzed by Weiss et al [35
]. For the CTCM it is exclusively the activated and G protein-coupled receptor conformations that participate in the measured response.
Both agonism and agonist modulation appear simultaneously as the agonist concentration is varied in the HOTSM. Indeed, the HOTSM may describe self-modulatory phenomena of bell-shape, reverse bell-shape, terraces and reverse terraces found in dose-response relations. The HOTSM appears as an appropriate reaction scheme in the analysis of dose-response relations for functional dimers as well as for other multimeric systems with a single type of ligand present. A historical development leading to the HOTSM is placed in Appendix
Concepts and developed terms
Concentration-dependent auto-antagonism and time-dependent desensitization
When a self-inhibitory dose-response relation is considered from an aspect of its dependence on the CONCENTRATION of a primary agonist or substrate, we may refer to such type of self-inhibitory phenomena as auto-antagonism
or negative co-operativity
. Alternatively, when the TIME-dependent aspect of self-inhibitory reaction kinetics is at center stage, we speak about desensitization
. Auto-antagonism due to increasing ligand concentration is by definition the same as negative co-operativity, since the term "co-operative", here, is solely used for homotropic allostery [5
]. Meanwhile, "negative co-operativity" is related to shallow hyperbolic dose-response curves and usually does not cover bell-shaped dose-responses of auto-antagonism.