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An enzyme is discovered that catalyzes the chemical reaction:SAD -------->HAPPY
<-------A team of motivated researchers sets out to study the enzyme which they call Happyase. They find that the Kcat for happyase is 600s-1. They carry out several experiments. When [Et]=20 nM and [SAD]=40 \mu M, the reaction velocity, Vo is 9.6 \mu Ms^{-1} . Calculate the Km for the substrate SAD.

Respuesta :

Answer: Km = 10μM

Explanation: Michaelis-Menten constant (Km) measures the affinity a enzyme has to its substrate, so it can be known how well an enzyme is suited to the substrate being used. To determine Km another value associated to an eznyme is important: Turnover number (Kcat), which is the number of time an enzyme site converts substrate into product per unit time.

Enzyme veolcity is calculated as:

[tex]V_{0} = \frac{E_{t}.K_{cat}.[substrate]}{K_{m}+[substrate]}[/tex]

where Et is concentration of enzyme catalitic sites and has to have the same unit as velocity of enzyme, so Et = 20nM = 0.02μM;

To calculate Km:

[tex]V_{0}*K_{m} + V_{0}*[substrate] = E_{t}.K_{cat}.[substrate][/tex]

[tex]K_{m} = \frac{E_{t}.K_{cat}.[substrate]-V_{0}*[substrate]}{V_{0}}[/tex]

[tex]K_{m} = \frac{0.02*600*40-9.6*40}{9.6}[/tex]

Km = 10μM

The Michaelis-Menten for the substrate SAD is 10μM.

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