6.2 How Enzymes Work · Biochemistry 2027

Enzymes affect rate, not the equilibrium position

Equilibrium is the state where forward and reverse rates are equal, with K = [P]eq/[S]eq for a 1:1 reaction
Equilibrium is set by standard chemical potentials and temperature, and adding an enzyme does not change the free energies of reactants and products
An enzyme accelerates both directions, so it cannot change the equilibrium constant at the same conditions
The statement that an enzyme promotes only the forward reaction is wrong about equilibrium
Cells are open systems with continuous product removal and substrate supply, so metabolic flux depends strongly on enzyme amount and activity
ΔG = ΔG°′ + RT ln Q′ and at equilibrium ΔG°′ = -RT ln K′eq, for example K′eq = 4.0 gives ΔG°′ about -3.43 kJ/mol at 298 K

ΔG is the difference between product and reactant states, the thermodynamic tendency to proceed
ΔG-double-dagger is the barrier that must be crossed from the starting state to the transition state
A negative ΔG with a large ΔG-double-dagger can still give a very slow reaction
For an idealised single transition state, forward ΔG-double-dagger minus reverse ΔG-double-dagger equals the reaction ΔG
Example: reactants 0, products -10 and uncatalysed transition state +60 kJ/mol give 60 and 70, lowered by 30 to 30 and 40, while the difference stays -10
k is about (kB T/h) exp(-ΔG-double-dagger/RT), and at 298 K a ΔΔG-double-dagger of 17.1 kJ/mol gives roughly 1.0e3-fold if pre-exponential factors match
The Arrhenius Ea and the transition-state ΔG-double-dagger are related but not the same physical quantity

The active site promotes substrate approach, fixes orientation and preferentially stabilises transition-state charge and geometry
Transient covalent intermediates mean no single principle such as weakening one bond explains all catalysis
A transition state is a short-lived high-energy arrangement on the reaction coordinate, not a separable substance
Multi-step reactions have a transition state and intermediate per step, and the tallest peak alone does not fix the overall rate
Specificity is selective binding and product distribution, to be read as a large rate difference rather than absolute non-reaction
Induced fit and conformational selection are not exclusive, and real enzymes can show both

Hydrogen bonds, ionic interactions, van der Waals forces and the hydrophobic effect all contribute
Favourability must include the cost of stripping interactions the substrate and enzyme had with water
More contacts do not automatically mean faster catalysis
Over-stabilising the ground-state ES complex can raise the barrier to the transition state
Efficient catalysis stabilises the transition state preferentially and still releases product
A transition-state analogue mimics the structure and charge of the transition state, and tight binding makes it a competitive inhibitor

Binding free energy includes new interactions, changes in the interactions each partner had with water, and loss of flexibility
The claim that one new hydrogen bond stabilises by its full energy ignores water replacement and orientation costs
Binding energy is used three ways: selecting and orienting the correct substrate, stabilising the transition state, and positioning catalytic residues
Every case must also count the entropy cost and product release
At 298 K a 1,000-fold acceleration corresponds to ΔΔG-double-dagger = RT ln1000 of about 17.1 kJ/mol if pre-exponential factors match
Acceleration should not be explained by mechanically summing the energies of a few hydrogen bonds

General acid catalysis donates a proton and general base catalysis accepts one to modulate reactivity
The histidine imidazole can act as acid or base depending on microenvironment, as can Asp and Glu carboxyls and the Lys amino group
Covalent catalysis forms a transient bond between enzyme and substrate, with Ser, Cys and Lys as nucleophiles
Metal ions act as Lewis acids, stabilise charge, orient substrate and water, and form coordination bonds, as Zn2+ does in carbonic anhydrase
Proximity and orientation bring reacting atoms together and increase productive collisions
The oxyanion hole and the Asp102-His57-Ser195 triad of serine proteases show several principles combined
A pH-activity curve alone cannot identify the responsible residue; mutants, structures and isotope effects are needed

References

**표 6.2-1**Simulated calculation: catalysis does not shift equilibrium
Condition	k forward (s-1)	k reverse (s-1)	k forward/k reverse	Equilibrium P fraction
No catalyst	0.020	0.005	4.0	0.800
Simple model with catalyst	2.00	0.500	4.0	0.800

**표 6.2-2**Contributions of binding energy and their limits
Contribution	Effect	Limit to check
Substrate selection	Distinguishes shape, charge and stereochemistry	Strong ground-state binding is not catalysis
Reactant orientation	Increases productive collisions	Entropy cost of alignment and fixation
Transition-state stabilisation	Contributes to lowering ΔG-double-dagger	Consider the energy budget of the whole path
Product release	Allows the cycle to continue	Too-tight product binding slows turnover