Chap 12. Enzyme-Substrate Complementary and the Use of Binding Energy in Catalysis Catalysis in model systems is still many orders of magnitude short of that found in enzymes Enzymes have evolved to use the binding energy between enzymes and substrates to provide the additional catalysis The binding energy can be used to lower chemical activation energies The use of binding energy lowers the activation energy of kcat/KM and the activation energy of kcat

A. Utilization of Enzyme-Substrate Binding Energy in Catalysis 1. Binding Energy Lowers the Activation Energy of kcat/KM E + S ES products KM kcat ΔGS ΔG‡ E + S ES‡ kcat/KM ΔGT‡ ΔGT‡ = ΔG‡ + ΔGS ΔGT‡ is activation energy proportional to kcat/KM (positive) ΔG‡ due to bond breaking/making (positive) ΔGS is binding energy of the substrate (negative)

2. Interconversion of Binding and Chemical Activation Energies Complementary structure: the maximum binding energy Complementary to the structure of the TS state  lowering the activation E of kcat Complementary to the structure of the unaltered substrate  increasing the activation E of kcat

[S] > KM ( = kcat[E]0) Stabilizing both ES and TS: no catalytic advantage Stabilizing ES only: increasing the activation E of kcat and decreasing the reaction rate Stabilizing TS only: lowering the activation E of kcat and increasing the reaction rate

[S] < KM (v = kcat/KM[E]0[S]) Stabilizing both ES and TS: lowering the activation E and increasing the reaction rate Stabilizing ES only: no catalytic advantage Stabilizing TS only: lowering the activation E of kcat

B. Experimental Evidence for the Utilization of Binding Energy in Catalysis and Enzyme-TS Complementarity for chymotrypsin and elastase, larger leaving groups increase kcat/KM (effect is almost all kcat) for pepsin larger side chain groups or additional amino acids raises kcat, while KM stays at ~0.1mM

C. Evolution of the Maximum Rate: Strong Binding of the Transition State add Weak Binding of the Substrate Better binding of TS than the substrates: maximizing kcat/KM The maximum reaction rate for a particular concentration depending on the individual kcat and KM KM < [S] KM > [S] weak binding

High KM Gives a Lower Activation Energy KM < [S] - low KM leads to a thermodynamic “pit” KM > [S] - high KM leads to “a step up the thermodynamic ladder” If KM >> [S], [E]0 = [E] constant kcat/KM and [S] KM = [S], half unbound of the enzyme = 50% of the maximum KM = 5[S], 5/6 unbound of the enzyme = 83% of the maximum

Control Enzymes are Exceptions to the Principle of High KM’s Control enzymes: evolved for the purpose of regulation The fist enzyme on metabolic pathway: A low KM may be advantage Hxokinase: the first enzyme in glycolysis KM = 0.1 mM, [glucose] = 5 mM

The KM/[S] Values of Most Enzymes in Glycolysis are in the range of 1 to 10 and 10 to 100 The glycolytic enzymes The majority of the enzymes are in the 1< KM/[S] < 10 range Regulatory enzymes would likely be here (e.g., hexokinase)

The Perfectly Evolved Enzyme for Maximum Rate have Maximum kcat/KM and High KM kcat/KM = 108 to 109 s-1 M-1 KM > [S] Ex. carbonic anhydrase and trisephosphate isomerase:

D. Molecular Mechanisms for the Utilization of Binding Energy Strain: substrates distorted to make the transition state contact better with the enzyme Induced fit: the enzyme distorted after binding occur Nonproductive binding: not a mechanism for increasing KM, but has a qualitatively similar effect on enzyme catalytic rate

Induced Fit Requires the Energy to Distort Enzyme K << 1 (kcat/KM)obs = K(kcat/KM) K’ >> 1 (kcat)obs = kcat (KM)obs = KM/K KM kcat Eact EactS S K K’ K’M Ein EinS S If all enzymes are in the active conformation, kcat is unchanged and KM is higher Thus, slows down catalysis (kcat/KM) Importance of induced fit: providing the means of access of substrates when the TS needs to be completely surrounded by groups on the enzyme

Strain, Induced Fit, and Nonproductive Binding do not Alter the Specificity Altering kcat and KM in a mutually compensating manner without changing kcat/KM