Enzyme Kinetics: Vmax Km and Inhibitors
Enzyme Kinetics
Enzyme kinetics is the quantitative study of how enzymes catalyse reactions, focusing on reaction rates and the factors that influence them. At A-Level, you need to understand the Michaelis-Menten model, the significance of Vmax and Km, and how different types of inhibition alter these parameters.
The Michaelis-Menten Model
The Michaelis-Menten equation describes how reaction velocity (v) relates to substrate concentration [S] for a simple enzyme-catalysed reaction:
v = Vmax × [S] / (Km + [S])
This model assumes:
- The reaction involves a single substrate binding to a single active site
- An enzyme-substrate complex (ES) forms as an intermediate
- The rate-limiting step is the conversion of ES to product (E + P)
- Steady state conditions apply — the rate of ES formation equals the rate of ES breakdown
The Michaelis-Menten Curve
When you plot reaction velocity (v) against substrate concentration [S], you get a characteristic rectangular hyperbola:
- At low [S]: the rate increases approximately linearly because many active sites are unoccupied. Substrate concentration is the limiting factor.
- At intermediate [S]: the rate of increase begins to slow as fewer free active sites are available.
- At high [S]: the curve plateaus and approaches Vmax asymptotically. All active sites are saturated with substrate. Adding more substrate has no further effect on rate.
Vmax and Km
Vmax (Maximum Velocity)
Vmax is the theoretical maximum rate of reaction when all enzyme active sites are saturated with substrate. It is never quite reached experimentally — the curve approaches Vmax asymptotically. Vmax is directly proportional to enzyme concentration: doubling the amount of enzyme doubles Vmax, because there are twice as many active sites available.
Km (Michaelis Constant)
Km is defined as the substrate concentration at which the reaction rate is exactly half of Vmax (½Vmax). It is a measure of the enzyme's affinity for its substrate:
- A low Km means the enzyme reaches ½Vmax at a low substrate concentration — it has high affinity for the substrate and binds it tightly
- A high Km means a higher substrate concentration is needed to reach ½Vmax — the enzyme has low affinity for the substrate
Km is a characteristic constant for a given enzyme-substrate pair under defined conditions. It is independent of enzyme concentration.
| Parameter | Definition | Depends on enzyme concentration? |
|---|---|---|
| Vmax | Maximum rate at full saturation | Yes — proportional to [E] |
| Km | [S] at ½Vmax; inversely related to affinity | No — intrinsic to the enzyme |
Enzyme Inhibition
Inhibitors are molecules that reduce the rate of an enzyme-catalysed reaction. They are classified as competitive or non-competitive (and at A-Level you may also encounter reversible vs irreversible).
Competitive Inhibition
A competitive inhibitor has a similar shape to the substrate and binds to the active site of the enzyme. It competes directly with substrate molecules for access to the active site.
Effects on kinetics:
- Vmax is unchanged — at very high substrate concentrations, the substrate outcompetes the inhibitor, so the maximum rate can still be achieved
- Km is increased (apparent Km rises) — a higher substrate concentration is needed to reach ½Vmax because the inhibitor occupies some active sites
- The inhibition can be overcome by increasing substrate concentration
Example: Malonate is a competitive inhibitor of succinate dehydrogenase in the Krebs cycle. Malonate resembles succinate in structure and binds to the active site, blocking the conversion of succinate to fumarate.
On a Michaelis-Menten plot, the curve with a competitive inhibitor is shifted to the right but reaches the same Vmax.
Non-Competitive Inhibition
A non-competitive inhibitor binds to a site other than the active site — an allosteric site. Binding causes a conformational change in the enzyme that distorts the active site, reducing its ability to form enzyme-substrate complexes or to catalyse the reaction.
Effects on kinetics:
- Vmax is decreased — even at saturating substrate concentrations, some enzyme molecules are inhibited and cannot function
- Km is unchanged — the inhibitor does not affect substrate binding to free enzyme, so the affinity is unaltered
- The inhibition cannot be overcome by adding more substrate
Example: Heavy metal ions (e.g. Hg²⁺, Pb²⁺) can act as non-competitive inhibitors by binding to -SH groups on the enzyme, disrupting its tertiary structure.
On a Michaelis-Menten plot, the curve with a non-competitive inhibitor has a lower plateau (reduced Vmax) but the same Km.
Summary Table
| Feature | Competitive | Non-competitive |
|---|---|---|
| Binding site | Active site | Allosteric site |
| Resembles substrate? | Yes | No |
| Effect on Vmax | Unchanged | Decreased |
| Effect on Km | Increased (apparent) | Unchanged |
| Overcome by excess substrate? | Yes | No |
Reversible vs Irreversible Inhibition
Most competitive and non-competitive inhibitors are reversible — they bind temporarily through weak bonds (hydrogen bonds, ionic interactions) and can dissociate from the enzyme.
Irreversible inhibitors form strong covalent bonds with the enzyme, permanently inactivating it. Examples include:
- DFP (diisopropyl fluorophosphate) — irreversibly inhibits acetylcholinesterase by binding to a serine residue in the active site. This is the mechanism of nerve agents.
- Aspirin — irreversibly inhibits cyclooxygenase (COX) by acetylating a serine residue, blocking prostaglandin synthesis.
- Penicillin — irreversibly inhibits transpeptidase, preventing bacterial cell wall synthesis.
Clinical and Industrial Applications
Drug design frequently exploits enzyme inhibition:
- Statins are competitive inhibitors of HMG-CoA reductase, reducing cholesterol synthesis
- ACE inhibitors block angiotensin-converting enzyme, lowering blood pressure
- Protease inhibitors used in HIV treatment block viral protease enzymes
Metabolic poisons such as cyanide (inhibits cytochrome c oxidase in the electron transport chain) and arsenic (inhibits pyruvate dehydrogenase) are irreversible or tightly-binding inhibitors.
End-Product Inhibition and Allosteric Regulation
In metabolic pathways, the end product often acts as a non-competitive inhibitor of an early enzyme in the pathway. This is called end-product inhibition or feedback inhibition. For example:
- In the synthesis of isoleucine from threonine, isoleucine inhibits threonine deaminase (the first enzyme in the pathway)
- ATP inhibits phosphofructokinase (PFK) in glycolysis when cellular energy levels are high
This provides negative feedback regulation, preventing wasteful overproduction of metabolites.
Exam Tips
- Always state both the effect on Vmax AND Km when describing inhibitor type — marks are allocated for both
- On graph questions, be able to sketch two curves (with and without inhibitor) on the same axes and label Vmax, Km, and ½Vmax
- AQA commonly asks you to identify inhibitor type from experimental data — look for whether increasing [S] restores the rate (competitive) or not (non-competitive)
- Remember that Km is read from the x-axis (it is a concentration), while Vmax is read from the y-axis (it is a rate)