GATE BT cheat sheet

Biotechnology (GATE BT) - Core Principles and Quantitative Relations

• Michaelis–Menten: v = Vmax·S/(Km + S). Km is the substrate concentration at v = Vmax/2 and equals (k-1 + k2)/k1 for E + S ⇌ ES → E + P; a low Km indicates high enzyme affinity.

• Lineweaver–Burk: 1/v = (Km/Vmax)(1/S) + 1/Vmax. Slope = Km/Vmax, y-intercept = 1/Vmax, x-intercept = −1/Km. Competitive inhibition raises apparent Km (Vmax unchanged); non-competitive lowers Vmax (Km unchanged); uncompetitive lowers both Vmax and Km.

• Monod growth kinetics: μ = μmax·S/(Ks + S). At steady state in continuous culture, D = μ, and cell washout occurs when D > μmax·S0/(Ks + S0). Biomass yield Yx/s = ΔX/ΔS; product yield Yp/s = ΔP/ΔS.

• Batch growth phases: lag, exponential (X = X0·e^μt, doubling time td = ln2/μ ≈ 0.693/μ), stationary, decline. In exponential phase, specific growth rate μ = (ln X2 − ln X1)/(t2 − t1).

• Sterilization: first-order thermal death, N = N0·e^(−kt), and decimal reduction time D = 2.303/k. For a temperature change, D2/D1 = 10^((T1 − T2)/z), where z is the temperature rise giving a 10-fold D reduction; F0 integrates lethality at 121 °C with z = 10 °C.

• Oxygen transfer: OTR = kLa·(C* − CL). At steady state OTR equals OUR = qO2·X, so kLa = qO2·X/(C* − CL). The sulphite oxidation method estimates kLa; dynamic gassing-out method uses the re-aeration slope after nitrogen sparging.

• Molecular biology central rules: DNA replication is semiconservative and bidirectional; PCR doubling after n cycles gives copies ≈ N0·2^n; Tm of a duplex rises with G+C content and salt, and falls with mismatches. Restriction enzymes: Type II cleave within palindromic recognition sites; a 6-bp cutter (e.g., 4-cutter vs 6-cutter) gives average fragment lengths of 4^n bp for an n-base recognition site.

• Chromatography and separation: resolution Rs = 2(tR2 − tR1)/(w1 + w2); retention factor k = (tR − t0)/t0; selectivity α = k2/k1; plate number N = 16(tR/w)^2 and HETP = L/N. In gel filtration, Kav = (Ve − V0)/(Vt − V0), and larger molecules elute earlier.

• Mass and energy balances: degree of reduction γ (γ = 4C + H − 2O − 3N for C, H, O, N formulas) is conserved in balanced growth; respiratory quotient RQ = CO2 produced/O2 consumed (RQ ≈ 1 for carbohydrate, >1 for lipid-rich or organic acid substrates, <1 for highly reduced substrates).