Cooperativity

Cooperativity is a phenomenon displayed by systems involving identical or near-identical elements, which act dependently of each other, relative to a hypothetical standard non-interacting system in which the individual elements are acting independently. One manifestation of this is enzymes or receptors that have multiple binding sites where the affinity of one binding site for a ligand is apparently increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to another binding site. For example, when dioxygen binds to one of hemoglobin's four binding sites, the affinity to oxygen of the three remaining available binding sites increases; i.e. oxygen is more likely to bind to a hemoglobin bound to one oxygen than to an unbound hemoglobin.^[1]

Cooperative binding

When a substrate binds to one enzymatic subunit, the rest of the subunits are stimulated and become active. Ligands can either have positive cooperativity, negative cooperativity, or non-cooperativity.^[1]

Subunit cooperativity

Cooperativity is not only a phenomenon of ligand binding, but also applies anytime energetic interactions make it easier or more difficult for something to happen involving multiple units as opposed to with single units. (That is, easier or more difficult compared with what is expected when only accounting for the addition of multiple units). For example, unwinding of DNA involves cooperativity: Portions of DNA must unwind in order for DNA to carry out replication, transcription and recombination.^[1]

Hill equation

A simple and widely used model for molecular interactions is the Hill equation, which provides a way to quantify cooperative binding by describing the fraction of saturated ligand binding sites as a function of the ligand concentration.^[1]

Hill coefficient

The Hill coefficient is a measure of ultrasensitivity (i.e. how steep is the response curve).^[1]

Response coefficient

Global sensitivity measures such as the Hill coefficient do not characterise the local behaviours of the s-shaped curves. Instead, these features are well captured by the response coefficient measure defined as:^[1]

Link between Hill coefficient and response coefficient

Altszyler et al. (2017) have shown that these ultrasensitivity measures can be linked by the following equation:^[1]

Ultrasensitivity in function composition

Consider two coupled ultrasensitive modules, disregarding effects of sequestration of molecular components between layers. In this case, the expression for the system's dose-response curve, F, results from the mathematical composition of the functions, fi, which describe the input/output relationship of isolated modules i=1,2:^[1]

Supramultiplicativity

Several authors have reported the existence of supramultiplicative behavior in signaling cascades (i.e. the ultrasensitivity of the combination of layers is higher than the product of individual ultrasensitivities), but in many cases the ultimate origin of supramultiplicativity remained elusive. Altszyler et al. (2017) framework naturally suggested a general scenario where supramultiplicative behavior could take place.^[1]