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Biology · University

Enzyme kinetics and biological rate models

Enzymes catalyse reactions without being consumed in the net reaction. They alter rates but not the equilibrium constant for a given reaction and conditions.

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Prerequisites

Relevant school subject foundations and careful reasoning.

Study notes

Catalysis

Enzymes catalyse reactions without being consumed in the net reaction. They alter rates but not the equilibrium constant for a given reaction and conditions.

Saturation

The Michaelis-Menten model gives v=Vmax[S]/(Km+[S]) under its assumptions. Saturation arises when increasing substrate gives diminishing rate increases.

Parameters

At [S]=Km, the model rate is Vmax/2. Km is not universally equal to a dissociation constant or a direct affinity measure in every mechanism.

Data

Estimate kinetic parameters from appropriate data with uncertainty. A fitted curve does not establish that every mechanistic assumption is true.

Worked examples

For Vmax=10, Km=2 and substrate concentration 2 in consistent units, find rate.

v=10×2/(2+2)=5.

5

At [S]=Km, the Michaelis-Menten rate is what fraction of Vmax?

Substitute [S]=Km into the model.

1/2

Check your understanding

  1. Does an enzyme change the equilibrium constant of the same reaction at the same conditions?

    1. Only when substrate is absent
    2. No
    3. Only when it is large
    4. Yes, always doubles it

  2. With Vmax=12,Km=3,[S]=9 in consistent units, find rate.

  3. Why can increasing substrate eventually produce only a small rate increase?

  4. Which statement about Km is appropriately qualified?

    1. It must be negative
    2. It is always dimensionless
    3. Its interpretation depends on the kinetic mechanism
    4. It is always exactly a binding dissociation constant

Answers and marking guidance

Answers and marking notes
  1. No

    Catalysis changes rates, not the thermodynamic equilibrium constant.

  2. 9

    12×9/(3+9)=9.

  3. In the model, the rate approaches Vmax as substrate greatly exceeds Km, reflecting saturation behaviour.

    Credit asymptotic saturation under the model.

  4. Its interpretation depends on the kinetic mechanism

    Mechanistic assumptions determine how Km relates to other constants.

Further reading and review references

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