Kinetics of Catalysis Catalyst speeds up a reaction by increasing Arrhenius factor A , or more commonly lowering activation energy Eaby providing a new activated complex of lower potential energy. Both forward and reverse reactions sped up by catalyst. Catalyst has noeffect on thermodynamics. Inhibitor slowsa reaction, often by increasing Ea. Useful to prevent undesirable reactions.
Enzyme Catalysis Kinetics of enzyme catalysis consistent with following mechanism: E +S k–1k1ESES k2→E +PE = free enzyme, S = substrate, ES = enzyme-substrate complex, P = product of reaction. Determine rate of formation of P by steady- state approximation: d[ES]dt=0 =k1[E][S] – k–1[ES] – k2[ES]Solve equation in terms of total enzyme concentration [E]0= [E] + [ES]. Replace [E] in above eqn by [E]0– [ES]. d[ES]dt=0 =k1[E]0[S] – k1[ES][S] – k–1[ES] – k2[ES]
Enzyme Catalysis Solve for [ES]: d[ES]dt=0 =k1[E]0[S] – k1[ES][S] – k–1[ES] – k2[ES][ES] =k1[E]0[S]k1[S]+k–1+k2()Define Km=k–1+k2k1Then [ES]=[E]0[S][S] +KmRate of formation of product is d[P]dt=k2[ES] =k2[E]0[S][S] + KmMichaelis-Menton equation
Enzyme Catalysis Rate linear at low [S] but levels off at high concentration. When [S] small, rate increases with increasing substrate conc.