A versatile equation to describe reversible enzyme inhibition and activation kinetics: Modeling β-galactosidase and butyrylcholinesterase

Current treatments for Alzheimer's disease involve inhibiting cholinesterases. Conversely, cholinesterase stimulation may be deleterious. Homocysteine is a known risk factor for Alzheimer's and vascular diseases and its active metabolite, homocysteine thiolactone, stimulates butyrylcholinesterase. Considering the opposing effects on butyrylcholinesterase of homocysteine thiolactone and cholinesterase inhibitors, understanding how these molecules alter this enzyme may provide new insights in the management of dementia. Butyrylcholinesterase does not strictly adhere to Michaelis–Menten parameters since, at higher substrate concentrations, enzyme activation occurs. The substrate activation equation for butyrylcholinesterase does not describe the effects of inhibitors or non-substrate activators. To address this, global data fitting was used to generate a flexible equation based on Michaelis–Menten principles. This methodology was first tested to model complexities encountered in inhibition by imidazole of β-galactosidase, an enzyme that obeys Michaelis–Menten kinetics. The resulting equation was sufficiently flexible to permit expansion for modeling activation or inhibition of butyrylcholinesterase, while accounting for substrate activation of this enzyme. This versatile equation suggests that both the inhibitor and non-substrate activator examined here have little effect on the substrate-activated form of butyrylcholinesterase. Given that butyrylcholinesterase inhibition can antagonize stimulation of this enzyme by homocysteine thiolactone, cholinesterase inhibition may have a role in treating Alzheimer and vascular diseases related to hyperhomocysteinemia.