I.5: Homotropic Allosterism

Here, we use the random-ordered binding model to describe how common forms of atypical (non-hyperbolic) allosteric behavior may arise. We focus here on homotropic allosterism, where multiple molecules of a singly chemical species can bind the enzyme.

We know that the scheme above, showing a two-site random-ordered model, is described by the following velocity equation:

Different combinations of the parameters α and β can produce hyperbolic or allosteric behavior. For instance, if we set K_D1 = K_D2 = 5 μM with α = 1 (no cooperativity in binding) and β = 1 (ES and SES have identical activity), the overall velocity equation corresponds to a hyperbola with an apparent K_M of 5 μM.

K_D1 = K_D2 = 5 μM, α = 1, β = 1
Total velocity is shown in red, with contributions from ES in green and SES in blue. In the absence of binding cooperativity and substrate activation, with equal K_Ds for both binding sites, the velocity curve appears hyperbolic.

Sigmoidal kinetics can be caused by positive binding cooperativity (α < 1) or by substrate activation (β > 1).

K_D1 = K_D2 = 5 μM, α = 0.1, β = 1
Sigmoidal kinetics can result from positive binding cooperativity.

K_D1 = K_D2 = 5 μM, α = 1, β = 5
Sigmoidal kinetics can also result from substrate activation, even without binding cooperativity.

Biphasic kinetics can result from negative binding cooperativity (α > 1):

K_D1 = K_D2 = 5 μM, α = 10, β = 1

Substrate inhibition occurs when SES is less active than ES (β < 1):

K_D1 = K_D2 = 5 μM, α = 1, β = 0.1

Next: Inhibition and Activation