modulated reversible Hill-type rate law modulated reversible Hill-type rate law with two modifiers <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:0000518">ModifierA</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000518">ModifierB</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000281">Keq</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:0000424">Shalve</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000423">Phalve</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000190">h</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000287">MAhalf</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000381">alphaA</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000287">MBhalf</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000381">alphaB</n2:ci> </n2:bvar> <n2:bvar> <n2:ci definitionURL="http://biomodels.net/SBO/#SBO:0000381">alphaAB</n2:ci> </n2:bvar> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:apply> <n2:divide /> <n2:apply> <n2:times /> <n2:ci>Vf</n2:ci> <n2:ci>substrate</n2:ci> </n2:apply> <n2:ci>Ks</n2:ci> </n2:apply> <n2:apply> <n2:minus /> <n2:cn>1</n2:cn> <n2:apply> <n2:divide /> <n2:ci>product</n2:ci> <n2:apply> <n2:times /> <n2:ci>substrate</n2:ci> <n2:ci>Keq</n2:ci> </n2:apply> </n2:apply> </n2:apply> <n2:apply> <n2:power /> <n2:apply> <n2:plus /> <n2:apply> <n2:divide /> <n2:ci>substrate</n2:ci> <n2:ci>Ks</n2:ci> </n2:apply> <n2:apply> <n2:divide /> <n2:ci>product</n2:ci> <n2:ci>Kp</n2:ci> </n2:apply> </n2:apply> <n2:apply> <n2:minus /> <n2:ci>h</n2:ci> <n2:cn>1</n2:cn> </n2:apply> </n2:apply> </n2:apply> <n2:apply> <n2:plus /> <n2:apply> <n2:divide /> <n2:apply> <n2:plus /> <n2:cn>1</n2:cn> <n2:apply> <n2:power /> <n2:apply> <n2:divide /> <n2:ci>ModifierA</n2:ci> <n2:ci>MAhalf</n2:ci> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> <n2:apply> <n2:power /> <n2:apply> <n2:divide /> <n2:ci>ModifierB</n2:ci> <n2:ci>MBhalf</n2:ci> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> </n2:apply> <n2:apply> <n2:plus /> <n2:cn>1</n2:cn> <n2:apply> <n2:times /> <n2:ci>alphaA</n2:ci> <n2:apply> <n2:power /> <n2:apply> <n2:divide /> <n2:ci>ModifierA</n2:ci> <n2:ci>MAhalf</n2:ci> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> </n2:apply> <n2:apply> <n2:times /> <n2:ci>alphaB</n2:ci> <n2:apply> <n2:power /> <n2:apply> <n2:divide /> <n2:ci>ModifierB</n2:ci> <n2:ci>MBhalf</n2:ci> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> </n2:apply> <n2:apply> <n2:times /> <n2:ci>alphaA</n2:ci> <n2:ci>alphaB</n2:ci> <n2:ci>alphaAB</n2:ci> <n2:apply> <n2:power /> <n2:apply> <n2:divide /> <n2:ci>ModifierA</n2:ci> <n2:ci>MAhalf</n2:ci> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> <n2:apply> <n2:power /> <n2:apply> <n2:divide /> <n2:ci>ModifierB</n2:ci> <n2:ci>MBhalf</n2:ci> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> </n2:apply> </n2:apply> </n2:apply> <n2:apply> <n2:power /> <n2:apply> <n2:plus /> <n2:apply> <n2:divide /> <n2:ci>substrate</n2:ci> <n2:ci>Ks</n2:ci> </n2:apply> <n2:apply> <n2:divide /> <n2:ci>product</n2:ci> <n2:ci>Kp</n2:ci> </n2:apply> </n2:apply> <n2:ci>h</n2:ci> </n2:apply> </n2:apply> </n2:apply> </n2:lambda> </n2:semantics> </n0:math> The modifiers can be either activators or inhibitors depending on the values of and alpha (activators for values larger than 1, inhibitors for values smaller than 1; no effect if exactly 1). The assumption is that the binding of one modifier affects the binding of the second. Modifiers are assumed to bind at different sites. The synergetic effects of the two modifiers depend on the parameter alpha (if unity then they are independent; if zero they compete for the same binding site). and reflect the effect of the presence of substrate and product on the binding of modifier A or modifier B. alphaA and alphaB factors account for the effect of substrate and product binding on the binding of modifier A and modifier B respectively. alphaAB accounts for the interaction of the modifiers on each others binding. (if < 1 Ma is inhibitor, if > 1 activator) alpha_2 : factor accounting for the effect of S and P on the binding of Mb (if < 1 Mb is inhibitor, if > 1 activator) alpha_3 : factor accounting for interaction of Ma to Mb binding to the enzyme (and v. v.).