enzymatic rate law for reversible essential activation enzymatic rate law for reversible mixed activation Enzymatic rate law where the activator enhances the rate of reaction through specific and catalytic effects, which increase the apparent limiting rate and decrease apparent Michaelis constant. The activator can bind reversibly both the free enzyme and enzyme-substrate complex, while the substrate can bind only to enzyme-activator complex. Catalytic activity is seen only when enzyme, substrate and activator are complexed. <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:0000512"> product </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000524"> Activator </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000322"> Kms </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000323"> Kmp </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000324"> Vf </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000325"> Vr </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000363"> Kas </n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000363"> Kac </n2:ci> </n2:bvar> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:apply> <n2:minus /> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:ci> Vf </n2:ci> <n2:ci> substrate </n2:ci> </n2:apply> <n2:ci> Kms </n2:ci> </n2:apply> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:ci> Vr </n2:ci> <n2:ci> product </n2:ci> </n2:apply> <n2:ci> Kmp </n2:ci> </n2:apply> </n2:apply> <n2:ci> Activator </n2:ci> </n2:apply> <n2:apply> <n2:plus /> <n2:ci> Kas </n2:ci> <n2:ci> Activator </n2:ci> <n2:apply> <n2:times /> <n2:apply> <n2:plus /> <n2:apply> <n2:divide /> <n2:ci> substrate </n2:ci> <n2:ci> Kms </n2:ci> </n2:apply> <n2:apply> <n2:divide /> <n2:ci> product </n2:ci> <n2:ci> Kmp </n2:ci> </n2:apply> </n2:apply> <n2:apply> <n2:plus /> <n2:ci> Kac </n2:ci> <n2:ci> Activator </n2:ci> </n2:apply> </n2:apply> </n2:apply> </n2:apply> </n2:lambda> </n2:semantics> </n0:math>