Enzyme Kinetics: Understanding the Rate of Enzyme-Catalyzed Reactions



The mechanism of an enzyme-catalyzed reaction is to determine the rate of the reaction and how it changes in response to changes in experimental parameters, a discipline known as enzyme kinetics. This is the oldest approach to understanding enzyme mechanisms and remains the most important.

TURNOVER NUMBERTurnover number of an enzyme is the number of substrate molecules converted into a product by an active enzyme molecule per second when the enzyme is fully saturated with the substrate. Turnover is equal to the kinetic constant (in this case it is K2), also called kcat. The maximal rate “Vmax” reveals the turnover number of an enzyme if the concentrations of the active sites of an enzyme are known, then it will be written as- Vmax=K2[E]T

Therefore, it can be written as, K2=Vmax/[E]T

The turnover numbers of most of the enzymes with their physiological substrates fall in the range of 1-104 per second.

Enzyme Turnover numbers (per second)
Carbonic anhydrase 600,000
3-Ketosteroid isomerase 280,000
Acetylcholinesterase 25,000
Penicillinase 2,0000
Lactate dehydrogenase 1,0000
Chymotrypsin 100
DNA polymerase 1 15
Tryptophan synthetase 2
Lysozyme 0.5


The key factor affecting the rate of the reaction catalyzed by an enzyme is the substrate concentration [S]. One simplified approach in studying Enzyme kinetics is to first measure the initial rate/initial velocity [V0] when substrate concentration[S] is greater than enzyme[E]. But at low concentrations of [S], V0 increases linearly with an increase of [S]. Whereas, at high concentrations, V0 increases in smaller amounts as compared to [S] until a point comes where V0 has its increment vanishingly small. This plateau-like region of V0 is close to the maximum velocity of Vmax.

Plot between [S] vs V0

Here, Vmax is extrapolated because V0 does not reach Vmax. The [S] where V0 is half of its maximal, known as Km also known as Michaelis constant. Here, the ES complex is the key feature to understand the kinetics of the enzyme. Victor and Henri proposed in 1903 that the relationship between enzyme and substrate in the form of ES is a necessary step in enzymatic analysis. This idea was further explained in a form of an equation by Leonor Michaelis and Maud Menten in 1913.

  • The enzyme first binds to the substrate in a fast reversible manner:
  • Enzyme first binds to the substrate in a fast reversible mannerThe ES complex advances to a slower second step to yield a free enzyme and the product [P]:

Free enzyme and the product

The slower second reaction is the rate-limiting step; therefore, the overall rate reaction is proportional to the concentration of enzyme-substrate complex [ES]. The maximum initial rate (Vmax) is observed theoretically when all the enzymes are present in ES and  where E is negligibly small.. Under these conditions, [E=ES], the enzyme is said to be saturated, that is, with an increase in the substrate concentration [S] the enzyme will not have any effect on the reaction. The saturation is the characteristic feature of enzyme catalysis and is observed as the plateau-like figure in Fig-1.

Steady state kinetics

The concept of steady-state was introduced by G. E Briggs and Haldane in 1925. When the enzyme is first added along with an excess of substrate, there is an initial short period called the pre-steady state. This reaction quickly reaches the steady-state in which [ES] remains approximately constant over time. The V0 is measured by analyzing the steady-state even though it is limited to the early part of a reaction. This analysis is called steady-state kinetics.

The curve expressing the relationship between S and V0 is the same for most of the enzymes and is expressed algebraically by the Michaelis-Menten equation.

Michaelis Menten equation
Where, Km is considered to be the Michaelis constant

Now, we will introduce another term [Et] representing total enzyme concentration. The rates of formation and breakdown of ES are in detail explained by rate constants k1(formation) and k1+k2 (breakdown).

  • Rate of ES formation = k1([Et-[ES]) [S] – Equation 3
  • Rate of ES breakdown= k-1[ES]+k2[ES] – Equation 4

Dividing equation 1 and 2 and further simplifying, we get,

Rate of ES formation The term (k2+k-1)/k1 is the Michaelis constant Km, therefore, it can further be simplified as,

Rate of ES breakdownSignificance of Km

  • The Km can vary from enzyme to enzyme, and even for different substrates of the same enzyme.
  • The term Km is an indicator of the affinity of an enzyme for its substrate.
  • Higher is the value of Km; lower is the affinity of the enzyme towards the substrate.
  • Lower is the value of Km; higher is the affinity of the enzyme towards the substrate.

Also, transforming the equation into a double reciprocal plot. First, taking the reciprocal of the Michaelis- Menten equation:

the reciprocal of the Michaelis- Menten equationFurther simplifying the equation by separating the components,

Michaelis- Menten equation

This form of equation is known as Lineweaver-Burk equation.

Lineweaver-Burk equation

References and Sources:

  • https://bionumbers.hms.harvard.edu/bionumber.aspx?id=105086&ver=1#:~:text=The
    turnover number of an enzyme, is the,from 1 to 10^4 per second (Table link).
  • https://chem.libretexts.org/Bookshelves/Biological_Chemistry/Supplemental_Modules_(Biological_Chemistry)/Enzymes/Enzymatic_Kinetics/Michaelis-Menten_Kinetics
  • https://alevelbiology.co.uk/notes/michaelis-menten-constant/
  • https://bio.libretexts.org/Under_Construction/Cell_and_Molecular_Biology_(Bergtrom)/05:_Enzyme_Catalysis_and_Kinetics/5.04:_Enzyme_Kinetics
  • https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7756376/
  • https://faculty.ksu.edu.sa/sites/default/files/lab6_11.pdf
  • https://www.inf.ed.ac.uk/teaching/courses/csb/CSB_lecture_enzyme_kinetics.pdf
  • http://physics.bu.edu/~pankajm/PY571/Notes/Lecture4.pdf
  • https://link.springer.com/chapter/10.1007/978-981-13-0785-0_15
  • https://bio.libretexts.org/Courses/Wheaton_College_Massachusetts/Principles_of_Biochemistry/07:_Enzymes_catalysis_and_kinetics/7.02:_Derivation_of_Michaelis-Menten_equation

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