IIT JAM Biotechnology (BT): the quantitative core
The Biotechnology (BT) domain covers the whole BT paper of IIT JAM: general biology and biomolecules, genetics and molecular biology, microbiology and immunology, bioprocess and biochemical engineering, and recombinant DNA technology with bioinformatics. MCQs carry 1/3 negative marking; multiple-select and numerical-answer (NAT) items carry none. Recall questions exist, but ranks are decided on quantitative items - enzyme kinetics, growth and yield calculations, plasmid and restriction mapping, and genetics probabilities.
Core rules to hold exactly
- Michaelis–Menten: v = Vmax[S]/(Km + [S]). Km is the substrate concentration giving half-maximal velocity and is an inverse index of affinity; Vmax is a rate (e.g. µmol min⁻¹ mg⁻¹), never a concentration.
- Lineweaver–Burk: 1/v = (Km/Vmax)(1/[S]) + 1/Vmax, so the y-intercept is 1/Vmax, the x-intercept is −1/Km and the slope is Km/Vmax.
- Inhibition signatures: competitive - Km increases, Vmax unchanged; pure noncompetitive - Vmax falls, Km unchanged; uncompetitive - both fall by the same factor.
- Batch growth: µ = ln2/td, valid only in exponential phase; Monod links it to substrate as µ = µmax·S/(Ks + S).
- Yields: YX/S = ΔX/ΔS, and the observed yield falls when maintenance energy matters.
- Oxygen supply at steady state: kLa(C* − CL) = qO2·X.
Worked example
An uninhibited enzyme gives a double-reciprocal y-intercept of 0.02 (µmol min⁻¹)⁻¹ and an x-intercept of −0.20 mM⁻¹. With a fixed inhibitor concentration the y-intercept is unchanged but the x-intercept moves to −0.05 mM⁻¹. Reasoning: Vmax = 1/0.02 = 50 µmol min⁻¹ and Km = 1/0.20 = 5 mM without inhibitor; with inhibitor Vmax stays 50 (y-intercept fixed) while the apparent Km = 1/0.05 = 20 mM, a four-fold rise. That is competitive inhibition, with α = 4.
Traps that cost marks
Mixing mM and µM between [S] and Km; treating Km as a maximum rate; using ln2 where log2 belongs, or vice versa, in doubling-time conversions; assuming µ is constant in lag phase; reporting an apparent Km without saying it is inhibitor-dependent; and leaving a NAT question blank, which is a guaranteed loss since nothing is deducted.