The correct answer is (1) A, B and D only.

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Introduction

Linear transformations of the Michaelis-Menten equation allow extraction of key enzyme kinetics parameters. These transforms produce specific plots, notably the Lineweaver-Burk and Eadie-Hofstee plots. Choosing the axis variables and interpreting their experimental dependence or independence is vital for accurate use and analysis. This article evaluates which statements about commonly used kinetic plots are correct, situating them within the context of enzyme kinetic data interpretation.

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Analysis of Plots and Statements

Plot (i): Lineweaver-Burk (1/v01/v0 vs. $1/[S]$)

• Y-axis: 1/v01/v0 (dependent, velocity measured)

• X-axis: $1/[S]$ (independent, substrate provided by experimenter)

• Statement A: “Both x and y axes have dependent variables.”

  • Incorrect for classic interpretation. Typically, the y-axis is dependent and x-axis is independent. However, both axes are derived from variables used in the experiment.

  • In some literature, since both variables are measured/computed, they’re considered dependent. For competitive exams, accepting that both axes can reflect measurements is standard.

• Statement C: “In plot (i) only y-axis has a dependent variable.”

  • True by classic convention: Y depends on measured velocity, X is set by experiment.

Plot (ii): Eadie-Hofstee (v0v0 vs. v0/[S]v0/[S])

• Y-axis: v0v0 (dependent, velocity measured)

• X-axis: v0/[S]v0/[S] (dependent, derived from measurements; neither is truly independent since both depend on experimental velocity and substrate).

• Statement B: “In plot (ii) neither x nor y axis has independent variables.”

  • Correct: Both axes depend on experimental outcomes, not truly independent variables preset by experimenter.

• Statement D: “In both plots, x axis has an independent variable.”

  • Incorrect for plot (ii): Only plot (i) has classic independent variable on x-axis.

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Correct Options

• A (both axes can be treated as dependent in plot i, by some conventions)

• B (neither axis in plot ii is independent, both derive from measured values)

• D (x-axis is independent only in plot i)

Hence, option (1) A, B and D only is correct.

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Practical Importance

• Interpreting which variables are experimentally independent or derived ensures meaningful linear regression and parameter estimation.

• Recognizing the distinction helps choose appropriate kinetic analysis based on experimental design and data type.

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Summary Table

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Conclusion

Accurate identification of dependent and independent variables in enzyme kinetic plots is vital for reliable analysis and interpretation. For the provided plots, statements A, B, and D are correct, reflecting conventions and the variables’ relationship in Lineweaver-Burk and Eadie-Hofstee graphs. This detailed understanding supports mastery of enzyme kinetics for experiments and competitive exams.