# DBT JRF 2022 — Question 109

Exam: DBT JRF 2022 · Section: B · Topic: Biochemistry › Enzyme Kinetics - Lineweaver-Burk Plot · Difficulty: Medium

## Question

For determining $V_m$ and $K_m$ of an enzyme catalyzed reaction, we often use a double reciprocal plot of 1/v versus 1/s. This is NOT the best method because:

## Options

- **A.** Errors in measurement are not normally distributed
- **B.** A straight line fit does not minimize the error
- **C.** Errors increase for larger values of v & s
- **D.** Errors increase for smaller values of v & s

## Answer

Option D

## Explanation

Lineweaver-Burk plot limitations (errors in velocity measurement): The Lineweaver-Burk (double-reciprocal) plot: $\frac{1}{v} = \frac{K_M}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$ Critical statistical problem: • When v is small (low substrate concentrations), $\frac{1}{v}$ is LARGE and subject to amplified errors. • A small absolute error in measuring v (e.g., $\pm 0.01$ units) becomes a very large error in $\frac{1}{v}$ : - If $v = 0.1$ , $\frac{1}{v} = 10$ ; an error of $\pm 0.01$ in v gives $\frac{1}{v} = 9.1-11.1$ (large spread). - If $v = 1.0$ , $\frac{1}{v} = 1$ ; error becomes $\frac{1}{v} = 0.99-1.01$ (small spread). • This NON-UNIFORM error distribution means points at low [S] (far left of plot) are unreliable and distort the linear regression. • Better alternatives: Eadie-Hofstee, Hanes-Woolf, or non-linear regression of v vs. [S] directly. Answer: Lineweaver-Burk amplifies errors in small velocity measurements; non-uniform error distribution makes linear fitting unreliable.

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