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.
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."
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.
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.
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.
Effects of Temperature
- At low temperatures, molecules have low kinetic energy. The frequency of successful enzyme–substrate collisions is low, so the rate of reaction is slow.
- As temperature increases, kinetic energy increases, leading to more frequent collisions and a higher rate of reaction.
- The rate increases up to the optimum temperature (typically 37–40 °C for human enzymes). The temperature coefficient (Q₁₀) describes the factor by which the rate increases for every 10 °C rise; for most enzyme reactions Q₁₀ ≈ 2 below the optimum.
- Above the optimum temperature, the increased molecular vibrations disrupt the weak bonds (hydrogen bonds, ionic bonds, hydrophobic interactions) that maintain the enzyme's tertiary structure. The active site changes shape — the enzyme is denatured — and can no longer bind substrate. The rate decreases rapidly.
- Denaturation is usually irreversible for most enzymes.
Exam Tip: Never say the enzyme is "killed" by high temperature — enzymes are not alive. Say the enzyme is denatured: its tertiary structure is disrupted and its active site is no longer complementary to the substrate.
Effects of pH
- Each enzyme has an optimum pH at which its rate of reaction is highest.
- Changes in pH alter the ionisation of R groups (e.g., –NH₃⁺ loses H⁺ to become –NH₂; –COO⁻ gains H⁺ to become –COOH).
- This disrupts ionic bonds and hydrogen bonds within the tertiary structure, altering the shape of the active site.
- Extreme pH values cause denaturation.
- Some enzymes have unusual pH optima that reflect their working environment: pepsin (stomach) has an optimum pH of approximately 2; trypsin (small intestine) has an optimum pH of approximately 8.
Enzyme Inhibition
An inhibitor is a molecule that reduces the rate of an enzyme-catalysed reaction. Inhibitors can be reversible or irreversible.
Competitive Inhibition
- The inhibitor has a shape similar to the substrate and binds to the active site, blocking the substrate from entering.
- The inhibitor competes directly with the substrate for the active site.
- Effect on kinetics:
- Vmax is unchanged — at sufficiently high substrate concentrations, the substrate outcompetes the inhibitor and all active sites are occupied by substrate.
- Km is increased — a higher substrate concentration is needed to reach half Vmax because the inhibitor is occupying some active sites.
- Example: malonate competitively inhibits succinate dehydrogenase (an enzyme in the Krebs cycle) because malonate has a similar shape to succinate.
On a Lineweaver–Burk plot: the line has a steeper gradient but the same y-intercept (same 1/Vmax). The x-intercept moves closer to zero (−1/Km becomes less negative, reflecting increased Km).
Non-Competitive Inhibition
- The inhibitor binds to an allosteric site (a site other than the active site) on the enzyme.
- Binding causes a conformational change in the enzyme that alters the shape of the active site, reducing the enzyme's catalytic ability.
- The inhibitor does not compete with the substrate — both can be bound simultaneously.
- Effect on kinetics:
- Vmax is decreased — even at high substrate concentrations, some enzyme molecules are inhibited and cannot function, so the overall maximum rate is reduced.
- Km is unchanged — the affinity of the uninhibited enzyme molecules for the substrate is not affected.
- Example: cyanide inhibits cytochrome c oxidase (Complex IV of the electron transport chain) by binding to the iron in the enzyme's haem group at a non-active-site location.
On a Lineweaver–Burk plot: the line has a steeper gradient and a higher y-intercept (1/Vmax is larger). The x-intercept remains the same (−1/Km is unchanged).
Irreversible Inhibition
- The inhibitor binds permanently to the enzyme (often via a covalent bond), permanently disabling it.
- Example: aspirin irreversibly inhibits cyclooxygenase (COX) by acetylating a serine residue in the active site, preventing the synthesis of prostaglandins.
- Example: organophosphate nerve agents (e.g., sarin) irreversibly inhibit acetylcholinesterase.
End-Product Inhibition and Metabolic Pathways
In metabolic pathways, the final product often acts as a non-competitive inhibitor of an enzyme early in the pathway. This is a form of negative feedback:
A → B → C → D (where D inhibits the enzyme catalysing A → B)
- When [D] is high, the pathway slows down, preventing wasteful overproduction.
- When [D] is low (because it is being used), inhibition is released and the pathway speeds up.
- This allows cells to regulate metabolic flux efficiently.
Summary
- The induced-fit model is the accepted model of enzyme action: the active site changes shape to bind the substrate.
- Reaction rate increases with substrate concentration until Vmax is reached (enzyme saturation).
- Km is the substrate concentration at half Vmax; low Km = high affinity.
- The Lineweaver–Burk plot (1/V₀ vs 1/[S]) linearises the Michaelis–Menten curve for accurate determination of Vmax and Km.
- Temperature and pH affect rate by altering enzyme shape; extremes cause denaturation.
- Competitive inhibitors bind the active site (Vmax unchanged, Km increased); non-competitive inhibitors bind allosteric sites (Vmax decreased, Km unchanged).
- End-product inhibition provides negative feedback regulation of metabolic pathways.
A-Level Deep Dive
Spec mapping
This lesson is mapped to AQA 7402 Section 3.1.4.2 — Enzyme action and the kinetic-analysis extensions implicit in the spec's reference to factors affecting enzyme activity (refer to the official AQA specification document for exact wording). It covers the induced-fit model of catalysis, the Michaelis–Menten relationship between substrate concentration and rate, the Lineweaver–Burk linearisation, the effects of temperature and pH, competitive vs non-competitive vs irreversible inhibition, and end-product (feedback) inhibition. This lesson is the anchor for AQA 7402 Required Practical 1 — Investigation into the effect of a named variable on the rate of an enzyme-controlled reaction.
Historical context: the kinetic framework is associated with Leonor Michaelis and Maud Menten (1913), whose mathematical treatment (paraphrased — never quoted verbatim) reduced enzyme kinetics to a steady-state assumption yielding V₀ = (Vmax × [S]) / (Km + [S]). Hans Lineweaver and Dean Burk (1934) reformulated this as a double-reciprocal plot that is still examined as the canonical visualisation of inhibitor type at A* depth.
Required Practical 1 — Investigating Enzyme Rate (full anchor)
This is the central practical for the lesson. AQA 7402 RP1 typically uses catalase (decomposition of H₂O₂ to H₂O + O₂, gas-syringe collection), amylase (hydrolysis of starch, monitored by iodine spot tests), or trypsin (hydrolysis of casein, monitored by clearance of milk turbidity).
Generic method (catalase / H₂O₂ example):
- Prepare a serial dilution of hydrogen peroxide (e.g. 0, 1, 2, 3, 4, 5% v/v) — this becomes the independent variable (substrate concentration).
- Place a fixed volume of substrate solution in a conical flask connected by tubing to a gas syringe.
- Add a fixed volume of catalase (e.g. 1 cm³ of 1% yeast suspension) — keeping enzyme concentration constant (control variable).
- Immediately start a stopwatch. Record the volume of O₂ collected at fixed time intervals (e.g. every 10 s for 60 s).
- Repeat each substrate concentration at least three times to allow mean and standard deviation calculation.
- Control variables: temperature (use a thermostatted water bath at 25 °C or 37 °C), pH (buffer the substrate at pH 7), enzyme concentration, volume of solutions, time of measurement.
- Dependent variable: initial rate of reaction, calculated as the gradient of the tangent at t = 0 of a graph of cumulative O₂ volume against time.
Why initial rate? As the reaction proceeds, substrate concentration falls and product accumulates (potentially inhibiting the reaction or shifting the equilibrium). Taking the gradient at t = 0 captures the rate when [S] is at its maximum and product concentration is zero — the only point at which substrate concentration unambiguously equals the value set by the investigator.
Data analysis: