Describe the effect of substrate concentration on enzyme activity. Explain the Michaelis–Menten equation, the significance of Km and the Lineweaver–Burk plot.

Effect of Substrate Concentration

• At low [S] the reaction is first order — rate is proportional to [S]
• At high [S] it becomes zero order — rate is independent of [S], because all active sites are saturated
• The curve is a rectangular hyperbola

Michaelis–menten Equation

Assumptions

• Only the initial velocity is measured, so the reverse reaction is negligible
• A steady state exists — ES is formed and broken down at equal rates
• [S] is far greater than [E]

Significance of KM

• Km is a measure of the affinity of the enzyme for its substrate
• Low Km = high affinity (saturated at low substrate)
• High Km = low affinity
• It is a constant for a given enzyme and substrate, independent of enzyme concentration
• Units are those of concentration (mol/L)
• Helps identify which isoenzyme is present, and predicts behaviour at physiological substrate levels

Lineweaver–burk Plot

• Advantage — gives accurate values of Km and Vmax without needing very high substrate concentrations, and distinguishes types of inhibition at a glance
• Other plots — Eadie–Hofstee, Hanes–Woolf

Allosteric Enzymes Do Not Obey Michaelis–menten

• They give a sigmoid curve, not hyperbolic
• Because of co-operativity between subunits — binding at one site alters affinity at the others
• The measure used is K0.5 or S0.5, not Km
• Examples — phosphofructokinase-1, aspartate transcarbamoylase; haemoglobin behaves the same way though it is not an enzyme

Enzyme Units

Measurement of Enzyme Activity

• Enzymes are measured by their activity, not their mass — they are present in far too small an amount to weigh
• Conditions must be standardised — optimum pH, 37 °C, saturating substrate, so that the rate depends on enzyme concentration alone
• Zero-order conditions are used deliberately: with substrate in excess, velocity is proportional to the amount of enzyme
• Only the initial velocity is measured, before product accumulates
• Coupled assays are used when the product is not directly measurable — the reaction is linked to one that changes NADH absorbance at 340 nm

Applied Aspects

• Glucokinase mutations cause MODY-2 (maturity onset diabetes of the young) — a raised Km resets the glucose sensor of the β cell to a higher threshold
• Alcohol dehydrogenase has a low Km and is saturated at low blood alcohol → alcohol is cleared by zero-order kinetics, at a constant rate irrespective of concentration
• Phenytoin, aspirin and ethanol all show zero-order elimination at therapeutic doses → small dose increases cause large rises in plasma level and toxicity
• Knowing Km guides the design of competitive inhibitors as drugs
• Enzyme deficiency states may be due to a raised Km rather than an absent enzyme — some respond to large doses of the vitamin coenzyme, as in vitamin-responsive homocystinuria