enzymatic rate law for reversible unireactant enzyme with a single hyperbolic modulator enzymatic rate law for irreversible unireactant enzyme with a single hyperbolic modulator Enzymatic rate law where the modifier can act as an activator or inhibitor, depending upon the values of the kinetic constants. The modifier can bind irreversibly to all forms of the enzyme and all enzyme-substrate complexes are reactive. 'a' represents the ratio of dissociation constant of the elementary step Enzyme-Substrate complex + Modifier = Enzyme-Substrate-Modifier complex) over that of Enzyme + Modifier = Enzyme-Modifier complex. 'b' represents ratio of the rate constant of elementary step Enzyme-Substrate-Modifier complex -> Enzyme-Modifier complex + Product over that of Enzyme-Substrate complex -> Enzyme + Product. <n0:math xmlns:n0="http://www.w3.org/1998/Math/MathML"> <n2:semantics xmlns:n2="http://biomodels.net/SBO/" definitionURL="http://biomodels.net/SBO/#SBO:0000062"> <n2:lambda> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000515"> substrate </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000518"> Modifier </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000027"> Km </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000324"> V </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000282"> Kd </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000381"> a </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000381"> b </n2:ci> </n2:bvar> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:ci> V </n2:ci> <n2:ci> substrate </n2:ci> <n2:apply> <n2:plus /> <n2:cn> 1 </n2:cn> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:ci> b </n2:ci> <n2:ci> Modifier </n2:ci> </n2:apply> <n2:apply> <n2:times /> <n2:ci> a </n2:ci> <n2:ci> Kd </n2:ci> </n2:apply> </n2:apply> </n2:apply> </n2:apply> <n2:apply> <n2:plus /> <n2:apply> <n2:times /> <n2:ci> Km </n2:ci> <n2:apply> <n2:plus /> <n2:cn> 1 </n2:cn> <n2:apply> <n2:divide /> <n2:ci> Modifier </n2:ci> <n2:ci> Kd </n2:ci> </n2:apply> </n2:apply> </n2:apply> <n2:apply> <n2:times /> <n2:ci> substrate </n2:ci> <n2:apply> <n2:plus /> <n2:cn> 1 </n2:cn> <n2:apply> <n2:divide /> <n2:ci> Modifier </n2:ci> <n2:apply> <n2:times /> <n2:ci> a </n2:ci> <n2:ci> Kd </n2:ci> </n2:apply> </n2:apply> </n2:apply> </n2:apply> </n2:apply> </n2:apply> </n2:lambda> </n2:semantics> </n0:math>