BIOCHEM2027 Specialised Subject · 4.4
2027 · High School Specialised Subject · Biochemistry

6.2 How Enzymes Work

How enzymes work: catalysis and transition states

Enzymes and equilibrium, rate against activation free energy, catalytic power and specificity, use of binding energy, and acid-base, covalent, metal and proximity catalysis.

6 SECTIONS20 FIGURESEnglish edition
01

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
표 6.2-1Simulated calculation: catalysis does not shift equilibrium
Figure 6.2-21Uncatalysed and catalysed paths compared with identical free energies for the starting and product states
Figure 6.2-22Model calculation for a reversible first-order reaction with forward and reverse rate constants of 0.020 and 0.005 per second
02

Rate and equilibrium are different quantitative concepts

  • 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
Figure 6.2-23Diagram separating the free-energy difference ΔG from the barrier height ΔG-double-dagger; the values are illustrative
Figure 6.2-24Forward and reverse barriers compared in two panels; not one continuous reaction coordinate from a single measurement
Figure 6.2-25Theoretical ratio of rate constants at 298 K assuming equal pre-exponential factors; not measured values
03

Catalytic power and specificity combine several principles

  • 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
Figure 6.2-26Very short-lived high-energy arrangement of the transition state, which cannot be isolated in a bottle
Figure 6.2-27Concept model showing an intermediate between two transition states
Figure 6.2-28Catalytic cycle showing transient intermediates and regeneration of the free enzyme
Figure 6.2-29Lock-and-key and induced-fit models compared; atomic coordinates of a specific enzyme are not reproduced
04

Weak enzyme-substrate interactions matter most at the transition state

  • 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
Figure 6.2-30Simplified diagram of the chemical environment of an active site
Figure 6.2-31Comparison illustrating relative stabilisation of the substrate ground state and the transition state
Figure 6.2-32Conceptual binding of a transition-state analogue to an enzyme; the analogue does not correspond to a real drug structure
05

Binding energy is used for specificity and catalysis

  • 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
표 6.2-2Contributions of binding energy and their limits
Figure 6.2-33Arbitrary contributions to binding free energy in kJ/mol; not measured values for a real protein
06

Specific catalytic groups contribute directly

  • 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
Figure 6.2-34Simplified view of an enzyme histidine accepting a proton; the full charge balance is not shown
Figure 6.2-35Abstract scheme of transient covalent bond formation and regeneration by hydrolysis
Figure 6.2-36Simplified coordination environment of Zn2+ with water and histidine; not the coordinates of carbonic anhydrase
Figure 6.2-37Productive and unproductive collisions compared inside an enzyme
Figure 6.2-38Hydrogen bonding provided by backbone N-H groups of the oxyanion hole
Figure 6.2-39Simple catalytic triad diagram; bond lengths and angles are not shown
Figure 6.2-40Model bell-shaped pH-activity curve from two ionisation steps; not an observed curve of a specific enzyme
2027 High School Specialised Subject · Biochemistry · Sangil Park (Asan High School) · Reference material is printed as an appendix.
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