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TStheoryenzymes - d[ES ╪ = k for[E[S(Appearance of T.S dt...

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Transition State Theory -enzymatic reactions are catalyzed by stabilizing the transition state. [ES] G E + P E + S G Rxn proceeds G is G of catalysis (activation energy) Find G in terms of thermodynamic parameters… G = -RTlnK eq G = -RTlnK eq = -RTln([ES] /[E][S]) (Equilibrium between E + S ES ) - G /RT = ln([ES] /[E][S]) (Divide by –RT) e - G /RT = [ES] /[E][S] (Take anti-log) [E][S] e - G /RT = [ES] (Isolate [ES] ) Now find [ES] in terms of kinetic parameters... -d[ES] = (constants)[ES] (Disappearance of T.S.) dt constants = k B T/h where k B = 1.38 x 10 -23 J/K Boltzman constant where T = temperature in K where h = 6.62 x 10 -34 Jsec Planck’s constant
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Unformatted text preview: d[ES] ╪ = k for [E][S] (Appearance of T.S.) dt Now set appearance of [ES] ╪ equal to the disappearance of [ES] ╪ … (Steady-state assumption) d[ES] ╪ =-d[ES] ╪ ; k for [E][S] = k B T/h[E][S] e-∆ G ╪ /RT (Cancel [E][S] terms) dt dt k for = k B T/h e-∆ G ╪ /RT (Kinetic k for related to thermodynamic ∆ G ╪ ) So, from the equation derived if ∆ G ╪ is large, then the k for will be low and the overall rate is slow. And if the ∆ G ╪ is small, then the k for will be high and the overall rate is fast. There is an inverse relationship between ∆ G ╪ and k for due to the e-∆ G ╪ term....
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