The substrate concentration of the enzyme operating at one‑quarter of its maximum rate is = 0.333.
Relationship between Km and substrate concentration is -
Km is the concentration of substrate.It allows the enzyme to achieve half Vmax. High Km enzyme requires a higher concentration of substrate to get Vmax. Since, Km is a constant. If the substrate concentration is increased, it has no effect on it.
An enzyme with a high Km has a low affinity for its substrate. The substrate concentration Km corresponds to the substrate concentration.
The substrate concentration at which the reaction rate of the enzyme-catalyzed reaction is half of the maximum reaction rate Vmax.
The equation is:
<em>V₀ = </em><u><em>Vmax [S] </em></u>
<em> [S] + Km</em>
Here,
V₀ is initial rate,
Km is the dissociation constant between the substrate and the enzyme,
Vmax is the maximum rate, and
S is the concentration of substrate.
taking fraction of V₀ and Vmax :
<u><em> V₀ </em></u><em> = </em><u><em> [S</em></u><em>]</em><u><em> </em></u><em> </em>
<em>Vmax [S] + Km</em>
<u><em> </em></u><u>V₀ </u> = <u> 0.5Km </u> = 0.333
Vmax 1.50 + Km
Therefore, the substrate concentration of this enzyme operating at one‑quarter of its maximum rate is = 0.333.
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