Enzyme Kinetics

Enzymes are biological catalysts — proteins (with some RNA exceptions) that speed up metabolic reactions by lowering the activation energy without being consumed in the reaction. Understanding enzyme kinetics means understanding how the rate of an enzyme-catalysed reaction changes in response to substrate concentration, temperature, pH, and the presence of inhibitors.

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Enzyme–Substrate Interaction

The Lock-and-Key Model

Proposed by Emil Fischer in 1894, this model suggests that the active site of an enzyme has a rigid, fixed shape that is exactly complementary to the shape of its substrate — much like a key fitting into a lock.

• Explains enzyme specificity: only substrates with the correct shape can bind.
• Limitation: does not explain how the active site can change shape during catalysis or how some enzymes can act on a range of structurally similar substrates.

The Induced-Fit Model

Proposed by Daniel Koshland in 1958, this model proposes that the active site is flexible. When the substrate enters the active site, the enzyme undergoes a conformational change, moulding around the substrate to form the enzyme–substrate complex more precisely.

• The conformational change may also place strain on the substrate, helping to break specific bonds and lower activation energy.
• Better explains why some molecules that are similar in shape to the substrate can bind but are not catalysed (they do not induce the correct conformational change).
• The induced-fit model is the currently accepted model at A-Level.

Exam Tip: When describing enzyme action, always refer to the induced-fit model unless specifically asked about lock-and-key. Use precise language: "the active site changes shape slightly to become complementary to the substrate, forming the enzyme–substrate complex."

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The Effect of Substrate Concentration on Reaction Rate

At low substrate concentration, the rate of reaction increases approximately proportionally with substrate concentration — there are many unoccupied active sites, so increasing substrate concentration increases the frequency of successful enzyme–substrate collisions.

At higher substrate concentrations, the rate of increase slows because fewer active sites are available. Eventually, all active sites are occupied at any given moment — the enzyme is saturated — and the reaction reaches its maximum rate (Vmax). Further increases in substrate concentration have no effect because there are no free active sites.

A graph of initial rate (V₀) against substrate concentration [S] gives a rectangular hyperbola that plateaus at Vmax.

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Michaelis–Menten Kinetics

The relationship between reaction rate and substrate concentration is described by the Michaelis–Menten equation:

V₀ = (Vmax × [S]) / (Km + [S])

Where:

• V₀ = initial rate of reaction
• Vmax = maximum rate when all active sites are saturated
• [S] = substrate concentration
• Km = the Michaelis constant — the substrate concentration at which the reaction rate is exactly half of Vmax (V₀ = Vmax / 2)

Interpreting Km

• A low Km means the enzyme reaches half its maximum rate at a low substrate concentration — it has a high affinity for its substrate (the enzyme binds substrate tightly and efficiently).
• A high Km means a higher substrate concentration is needed to reach half Vmax — the enzyme has a lower affinity for its substrate.
• Km is a characteristic constant for a given enzyme–substrate pair under specific conditions.

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Lineweaver–Burk Plot (Double Reciprocal Plot)

The Michaelis–Menten curve is a hyperbola, which makes it difficult to determine Vmax and Km accurately by eye. The Lineweaver–Burk plot transforms the data by plotting 1/V₀ against 1/[S], producing a straight line:

1/V₀ = (Km / Vmax) × (1/[S]) + 1/Vmax

• The y-intercept = 1/Vmax
• The x-intercept = −1/Km
• The gradient = Km/Vmax

This linear transformation allows precise determination of Vmax and Km from experimental data and makes it easier to identify the type of inhibition from graphical analysis.

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Effects of Temperature