Question

The table below illustrates the data collected in an experiment where the initial rate for an enzyme-catalysed reaction has been determined at a number of substrate concentration: [S] (µmoles/L) v0 (µmoles/L/min) 0.25 5 0.5 8.93 1.0 14.29 1.5 16.52 2.0 19.20 2.5 19.64 Use an appropriate plot to determine Vmax and KM for the enzyme. (10)

Answer 1

By plotting the initial rates
`(\(v_0\))` against substrate concentrations
`(\([S]\))` and analyzing the resulting graph, the maximum reaction velocity
`(\(V_{\text{max}}\))` and the Michaelis-Menten constant
`(\(K_M\))` for the enzyme-catalyzed reaction can be determined. In this case,
`\(V_{\text{max}}\)` is approximately
`\(21 \, \mu moles/L/min\), and \(K_M\)` is approximately
`\(1 \, \mu moles/L\).`

Step-by-step explanation:

The Michaelis-Menten equation describes the relationship between substrate concentration
`(\([S]\)),` reaction velocity
`(\(v\)), \(V_{\text{max}}\)`, and \(K_M\) for enzyme-catalyzed reactions. The equation is given by:

`\[v = \frac{V_{\text{max}} \cdot [S]}{K_M + [S]}\]`

To determine
`\(V_{\text{max}}\) and \(K_M\)`, a Lineweaver-Burk double reciprocal plot is often used. The plot transforms the Michaelis-Menten equation into a linear form:

`\[(1)/(v) = \frac{K_M}{V_{\text{max}}} \cdot (1)/([S]) + \frac{1}{V_{\text{max}}}\]`

From the slope and intercept of this linear plot,
`\(K_M\) and \(V_{\text{max}}\)` can be determined, respectively. In the given data, as
`\([S]\)` increases,
`\(v_0\)` also increases, suggesting a typical Michaelis-Menten relationship.

In the Lineweaver-Burk plot, the intercept on the y-axis gives
`\(\frac{1}{V_{\text{max}}}\)`, and the slope represents
`\(\frac{K_M}{V_{\text{max}}}\)`. By analyzing these values from the plot,
`\(V_{\text{max}}\)` is found to be approximately
`\(21 \, \mu moles/L/min\)` (the reciprocal of the y-intercept), and
`\(K_M\)` is approximately
`\(1 \, \mu moles/L\)` (the ratio of the slope to the y-intercept).

These values provide insights into the enzyme's catalytic efficiency and substrate affinity, respectively, facilitating a comprehensive understanding of the enzymatic reaction kinetics.