7. Enzyme Inhibition
Reading time: ~40 minutes | Key topics: Competitive, uncompetitive, non-competitive, mixed, and irreversible inhibition
Overview of Enzyme Inhibition
Enzyme inhibitors are molecules that reduce or abolish enzyme activity. They are central to pharmacology, toxicology, and metabolic regulation. Over 50% of pharmaceutical drugs act as enzyme inhibitors.
Two Major Classes
- Reversible inhibitors: Bind non-covalently (hydrogen bonds, hydrophobic/ionic interactions). Includes competitive, uncompetitive, non-competitive, and mixed inhibition.
- Irreversible inhibitors: Form covalent bonds, permanently inactivating the enzyme. Activity is restored only by new enzyme synthesis. Includes mechanism-based (suicide) inhibitors.
Competitive Inhibition
In competitive inhibition, the inhibitor resembles the substrate and binds directly to the active site of the free enzyme (E), forming an EI complex instead of ES. The apparent $K_m$ increases:
where $K_i = [E][I]/[EI]$ is the inhibitor dissociation constant. Crucially, $V_{\max}$ remains unchanged because saturating [S] outcompetes the inhibitor. The modified Michaelis-Menten equation is:
On a Lineweaver-Burk plot, competitive inhibition produces lines that intersect on the y-axis ($1/V_{\max}$ unchanged, $-1/K_m^{\text{app}}$ shifts right with increasing [I]).
Clinical Examples
- Methotrexate inhibits dihydrofolate reductase (DHFR) by mimicking dihydrofolate, blocking thymidylate synthesis in rapidly dividing cancer cells.
- Statins (e.g., atorvastatin) competitively inhibit HMG-CoA reductase, the rate-limiting enzyme in cholesterol biosynthesis.
- Malonate competitively inhibits succinate dehydrogenase (Complex II) by mimicking succinate in the citric acid cycle.
Uncompetitive Inhibition
In uncompetitive inhibition, the inhibitor binds only to the ES complex, creating a dead-end ESI complex. This is rare in single-substrate reactions but common in multi-substrate systems. Both apparent $K_m$ and $V_{\max}$ decrease by the same factor:
where $K_i'$ is the dissociation constant for the inhibitor from the ESI complex. Defining the factor $\alpha' = 1 + [I]/K_i'$, both $V_{\max}$ and $K_m$ are divided by $\alpha'$:
On a Lineweaver-Burk plot, uncompetitive inhibition produces parallel lines — the slope ($K_m/V_{\max}$) remains constant, while both intercepts change. This distinctive parallel-line pattern is the hallmark of uncompetitive inhibition.
Why Parallel Lines?
Since both $K_m$ and $V_{\max}$ decrease by the same factor $\alpha'$, their ratio $K_m/V_{\max}$ (the slope of the Lineweaver-Burk line) is unchanged. Only the intercepts shift, producing parallel lines offset from the uninhibited line.
Non-competitive Inhibition
In non-competitive inhibition, the inhibitor binds with equal affinity to both E and ES ($K_i = K_i'$) at an allosteric site. The $K_m$ is unchanged, but $V_{\max}$ decreases:
On a Lineweaver-Burk plot, lines intersect on the x-axis (same $-1/K_m$), confirming that $K_m$ is unchanged. Increasing [S] cannot overcome non-competitive inhibition.
Examples
- Heavy metal ions (Pb$^{2+}$, Hg$^{2+}$, Cd$^{2+}$) bind to cysteine sulfhydryl groups at allosteric sites, distorting enzyme conformation.
- Doxycycline acts as a non-competitive inhibitor of matrix metalloproteinases (MMPs).
- EDTA chelates essential metal cofactors, effectively acting as a non-competitive inhibitor of metalloenzymes.
Mixed Inhibition
Mixed inhibition is the most general form: the inhibitor binds both E and ES with different affinities ($K_i \neq K_i'$). Defining $\alpha = 1 + [I]/K_i$ and $\alpha' = 1 + [I]/K_i'$:
The apparent parameters are $K_m^{\text{app}} = (\alpha/\alpha')K_m$ and $V_{\max}^{\text{app}} = V_{\max}/\alpha'$. On a Lineweaver-Burk plot, lines intersect left of the y-axis (second or third quadrant).
Special Cases of Mixed Inhibition
- If $K_i' \to \infty$ (inhibitor cannot bind ES): $\alpha' = 1$, reduces to competitive inhibition.
- If $K_i \to \infty$ (inhibitor cannot bind E): $\alpha = 1$, reduces to uncompetitive inhibition.
- If $K_i = K_i'$: $\alpha = \alpha'$, reduces to non-competitive inhibition.
Irreversible Inhibition
Irreversible inhibitors form stable covalent bonds with active-site residues, permanently inactivating the enzyme. Mechanism-based (suicide) inhibitors are processed by the enzyme's own catalytic mechanism into a reactive species that covalently modifies the active site. The kinetics are time-dependent:
where $k_{\text{inact}}$ is the first-order rate constant for inactivation and $[E]_0$ is the initial enzyme concentration. The half-life of enzyme inactivation is:
Important Examples
- Aspirin (acetylsalicylic acid) acetylates Ser-530 of cyclooxygenase (COX-1/COX-2), irreversibly blocking prostaglandin synthesis and platelet aggregation.
- Penicillin acylates the active-site serine of DD-transpeptidase, preventing bacterial cell wall cross-linking and causing cell lysis.
- DIFP (diisopropyl fluorophosphate) covalently modifies the active-site serine of serine proteases (trypsin, chymotrypsin, elastase) and acetylcholinesterase, acting as a nerve agent.
- Allopurinol is oxidized by xanthine oxidase to alloxanthine, which remains tightly bound to the enzyme's molybdenum center (suicide inhibitor used to treat gout).
Comparison of Inhibition Types
The following table summarizes the key features of each reversible inhibition type, providing a quick reference for distinguishing between them in kinetic experiments.
| Property | Competitive | Uncompetitive | Non-competitive | Mixed |
|---|---|---|---|---|
| Inhibitor binds | E only | ES only | E and ES equally | E and ES differently |
| Binding site | Active site | Allosteric (ES) | Allosteric | Allosteric |
| $K_m^{\text{app}}$ | Increases | Decreases | Unchanged | Increases or decreases |
| $V_{\max}^{\text{app}}$ | Unchanged | Decreases | Decreases | Decreases |
| LB plot pattern | Intersect y-axis | Parallel lines | Intersect x-axis | Intersect left of y-axis |
| Overcome by [S]? | Yes | No | No | Partially |
Key Concepts
1. Enzyme inhibitors are classified as reversible (non-covalent, equilibrium-based) or irreversible (covalent, permanent inactivation).
2. Competitive inhibitors increase apparent $K_m$ without affecting $V_{\max}$. They can be overcome by high [S].
3. Uncompetitive inhibitors decrease both $K_m$ and $V_{\max}$ by the same factor, producing parallel lines on a Lineweaver-Burk plot.
4. Non-competitive inhibitors decrease $V_{\max}$ without changing $K_m$, as they bind equally well to E and ES.
5. Mixed inhibition is the general case ($K_i \neq K_i'$), affecting both $K_m$ and $V_{\max}$. It reduces to the other types as special cases.
6. Irreversible (suicide) inhibitors are activated by the enzyme's own mechanism, then covalently modify the active site. They show time-dependent, exponential loss of activity.
7. Lineweaver-Burk plots remain the classic graphical method for distinguishing inhibition types, though non-linear regression is preferred for accurate parameter estimation.