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GATE BT: GATE Biotechnology (BT): Quantitative Core and High-Yield Calculations

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GATE Biotechnology (BT): Quantitative Core and High-Yield Calculations

GATE Biotechnology (BT) tests breadth across biochemistry, molecular biology, bioprocess engineering, genetics, and bioinformatics, but the marks that separate candidates often come from quantitative items. This section targets recurring calculation patterns: enzyme kinetics, inhibition, microbial growth, bioreactor yield, nucleic-acid quantification, and centrifugation. The exam expects you to apply standard equations with correct units and to recognize which assumption each model makes.

Core rules and concepts

  • Michaelis–Menten: v = Vmax[S]/(Km + [S]). Km is the substrate concentration at half Vmax; it is not a direct measure of affinity unless the mechanism is stated.
  • Reversible inhibition: competitive inhibition raises apparent Km and leaves Vmax unchanged; noncompetitive inhibition lowers Vmax and leaves Km unchanged; uncompetitive inhibition lowers both apparent Km and Vmax.
  • Exponential growth: specific growth rate µ = ln(X2/X1)/(t2 − t1); doubling time = ln2/µ.
  • Yield: YX/S = ΔX/ΔS. Ignore maintenance only when the question states it is negligible.
  • Nucleic-acid A260: 1 A260 unit = 50 µg/mL double-stranded DNA, 40 µg/mL RNA, or 33 µg/mL single-stranded DNA.
  • Centrifugation: sedimentation depends on particle size, shape, and density difference; Svedberg values are not additive.

Worked example

An enzyme has Km = 2 mM and Vmax = 100 µmol/min. At [S] = 2 mM, v = 100 × 2/(2 + 2) = 50 µmol/min. Add a competitive inhibitor at I = 1 mM with Ki = 1 mM: apparent Km = Km(1 + I/Ki) = 2 × (1 + 1) = 4 mM. Then v = 100 × 2/(4 + 2) = 33.3 µmol/min. Reasoning: the competitive inhibitor raises apparent Km without changing Vmax, so velocity falls at fixed [S] but can be restored at sufficiently high [S].

Traps that cost marks

  • Treating Vmax as the velocity at any substrate concentration.
  • Mixing inhibition patterns: noncompetitive inhibition does not change Km.
  • Forgetting blank correction or using A260 outside the linear range.
  • Confusing optical density with dry cell weight; OD is not linear at high values.
  • Mixing units such as mM and µM or minutes and hours without conversion.