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 productsKM kcat

ΔGSΔG‡

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)

SM

cat GGh

kTRT

K

kRT ‡lnln

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 kcatand increasing the reaction rate

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 depe

nding 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 thethermodynamic ladder”

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

M

cat

K

kSEv ]][[If KM >> [S], [E]0 = [E]

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 majority of the enzymes are in the 1< KM/[S] < 10 range

Regulatory enzymes would likely be here(e.g., hexokinase)

The glycolytic enzymes

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 Energy1. Strain:

substrates distorted to make the transition state contact betterwith the enzyme

2. Induced fit: the enzyme distorted after binding occur

3. 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

Eact EactS

Ein EinS

KM

S

K’M

S

K’K

kcat K << 1(kcat/KM)obs = K(kcat/KM)K’ >> 1(kcat)obs = kcat(KM)obs = KM/K

• If all enzymes are in the active conformation,kcat is unchanged and KM is higherThus, 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