Enzymes

• Enzymes are globular proteins with a precise tertiary (3D) structure
• The active site is a small region on the enzyme's surface with a specific shape determined by the amino acid sequence
• The active site is complementary to the substrate — the molecule the enzyme acts on
• The precise shape depends on hydrogen bonds, ionic bonds, disulfide bridges, and hydrophobic interactions between R-groups

Lock-and-Key Model (Fischer, 1894)

• The active site has a rigid, fixed shape that is exactly complementary to the substrate
• The substrate fits into the active site like a key into a lock
• Limitation: Does not explain how some enzymes can act on multiple similar substrates, or why the enzyme sometimes changes shape slightly

Induced-Fit Model (Koshland, 1958)

• The active site is flexible and changes shape slightly when the substrate binds
• The substrate induces a conformational change in the enzyme, creating a tighter fit
• This "moulding" of the enzyme around the substrate helps to lower the activation energy more effectively
• The induced-fit model is the currently accepted model

Lowering Activation Energy

Enzymes work by lowering the activation energy ($E_a$) — the minimum energy required for a reaction to occur.

They do this by:

• Holding substrates in the correct orientation for the reaction
• Putting strain on bonds in the substrate
• Providing a suitable microenvironment (e.g., local pH) in the active site

$\text{Rate of reaction} \propto \frac{1}{E_a}$

Effect of Substrate Concentration

• At low substrate concentration: many active sites are empty → increasing substrate concentration increases the rate
• As concentration rises: more active sites are occupied
• At high substrate concentration: all active sites are occupied → the enzyme is saturated → rate reaches a maximum ($V_{max}$)
• To increase rate beyond $V_{max}$: need to add more enzyme

Michaelis-Menten Kinetics

The relationship between substrate concentration $[S]$ and reaction rate $v$ is:

$v = \frac{V_{max} \cdot [S]}{K_m + [S]}$

Where:

• $V_{max}$ = maximum rate when all active sites are saturated
• $K_m$ = Michaelis constant — the substrate concentration at which the reaction rate is $\frac{V_{max}}{2}$
• A low $K_m$ means high affinity (enzyme binds substrate easily)
• A high $K_m$ means low affinity (needs more substrate to reach half max rate)

Effect of Enzyme Concentration

• More enzyme = more active sites available
• Rate increases linearly with enzyme concentration (assuming excess substrate)

Effect of Temperature

• Increasing temperature increases kinetic energy of molecules → more frequent and energetic collisions
• Rate increases up to the optimum temperature (typically ~37°C for human enzymes)
• Above the optimum: the enzyme denatures — hydrogen bonds and other weak bonds break → active site changes shape → substrate can no longer fit
• $Q_{10}$ (temperature coefficient): the factor by which rate increases for every 10°C rise (typically ~2 for enzyme reactions)

$Q_{10} = \frac{\text{Rate at } (T + 10)°C}{\text{Rate at } T°C}$

Effect of pH

• Each enzyme has an optimum pH (e.g., pepsin ~2, trypsin ~8, catalase ~7)
• Changing pH alters the ionisation of R-groups → disrupts ionic bonds and hydrogen bonds → active site shape changes → denaturation
• pH changes can be reversible (if mild) or irreversible (if extreme)

Competitive Inhibition

• The inhibitor has a similar shape to the substrate
• It competes with the substrate for the active site
• Blocks the active site, preventing the substrate from binding
• Effect: Increases apparent $K_m$ (needs more substrate to reach half max rate), but $V_{max}$ is unchanged (adding excess substrate can outcompete the inhibitor)
• Example: Malonate inhibits succinate dehydrogenase (competes with succinate)

Non-competitive Inhibition

• The inhibitor binds to an allosteric site (a site OTHER than the active site)
• Binding causes a conformational change in the enzyme, altering the shape of the active site
• The substrate can still bind, but the enzyme cannot catalyse the reaction effectively
• Effect: $V_{max}$ is reduced, but $K_m$ is unchanged
• Adding more substrate does NOT overcome the inhibition
• Example: Cyanide inhibits cytochrome oxidase in the electron transport chain

Reversible vs Irreversible Inhibition

• Reversible: Inhibitor binds temporarily (can dissociate); competitive and most non-competitive inhibitors are reversible
• Irreversible: Inhibitor binds permanently (covalently) to the enzyme, permanently destroying its function
• Example of irreversible: Organophosphate nerve agents permanently bind to acetylcholinesterase

Summary Table

• Cofactors are non-protein molecules or ions required for enzyme activity
  • Inorganic cofactors: Metal ions (e.g., $Zn^{2+}$ in carbonic anhydrase, $Fe^{2+}$ in catalase)
  • They often help the substrate bind or stabilise the enzyme-substrate complex
• Coenzymes are organic cofactors (often vitamins or derived from vitamins)
  • They carry chemical groups or electrons between enzymes
  • Examples: NAD⁺ (carries hydrogen in respiration), coenzyme A (carries acetyl groups)
• Prosthetic groups are cofactors permanently bound to the enzyme
  • Example: Haem group in catalase (contains $Fe^{2+}$)

• Enzymes work in metabolic pathways — sequences of enzyme-catalysed reactions
• End-product inhibition (feedback inhibition): the final product inhibits an earlier enzyme in the pathway
  • This is a form of non-competitive inhibition
  • Prevents overproduction of the product
  • Example: In the pathway A → B → C → D, product D inhibits the enzyme catalysing A → B

Question: Explain the difference between competitive and non-competitive inhibition. Include the effect on $K_m$ and $V_{max}$. (6 marks)

Solution:

In competitive inhibition, the inhibitor has a similar shape to the substrate and binds to the active site of the enzyme, competing with the substrate. This means a higher substrate concentration is needed to achieve the same rate, so the apparent $K_m$ increases. However, $V_{max}$ remains unchanged because adding sufficient substrate can outcompete the inhibitor for all active sites.

In non-competitive inhibition, the inhibitor binds to an allosteric site (different from the active site), causing a conformational change that distorts the active site. The substrate can still bind but the reaction is not catalysed effectively. $V_{max}$ is reduced because some enzyme molecules are always inhibited regardless of substrate concentration. $K_m$ remains unchanged because the affinity of the unaffected enzyme molecules for the substrate is not altered.

• Enzymes are globular proteins that lower activation energy; the induced-fit model is the accepted mechanism.
• Enzyme rate depends on substrate concentration, temperature, pH, and enzyme concentration.
• $V_{max}$ = maximum rate at saturation; $K_m$ = substrate concentration at half $V_{max}$.
• Competitive inhibitors bind the active site (↑$K_m$, same $V_{max}$); non-competitive inhibitors bind allosteric sites (same $K_m$, ↓$V_{max}$).
• Cofactors (metal ions), coenzymes (organic), and prosthetic groups assist enzyme function.