Biotechnology — applied biology at the genetic-engineering / industrial-application grain. Foundations: (1) Polymerase Chain Reaction (PCR) exponential amplification (Mullis 1983, Saiki et al. 1985/1988): N(c) = N_0 · (1 + e)^c where N_0…
biotechnology
PCR exponential amplification: N(c) = N_0·(1+e)^c; e ∈ [0,1]
Polymerase Chain Reaction (PCR; Mullis 1983 Nobel Prize 1993; Saiki et al. 1985/1988) is the foundational in-vitro DNA amplification…
CRISPR-Cas9: sgRNA-directed DNA cleavage; 20-nt protospacer + 5'-NGG-3' PAM
CRISPR-Cas9 (Jinek et al. 2012, Cong et al. 2013, Mali et al. 2013, Doudna & Charpentier Nobel 2020) is the reprogrammable RNA-guided…
Hardy-Weinberg: p² + 2pq + q² = (p+q)² = 1; F2 3:1 and 9:3:3:1
Hardy-Weinberg equilibrium (Hardy 1908 / Weinberg 1908): for a single-locus diploid trait in a large randomly-mating population under no…
PCR at e=1, c=30: 2^30 = 1,073,741,824 ≈ 10^9-fold amplification
Sympy-exact witness of the PCR amplification identity at canonical anchor values. Setup: N(c; N_0, e) = N_0·(1+e)^c; specialise to e = 1…
Hardy-Weinberg identity: p²+2pq+q² = (p+q)²; at p=q=1/2 → {1/4, 1/2, 1/4}
Sympy-exact witness of the Hardy-Weinberg binomial identity and its evaluation at the symmetric-allele anchor p = q = 1/2. Setup:…
Mendel dihybrid: F2 ratio 9:3:3:1 sums to 16 = 2^4; fractions sum to 1
Sympy-exact witness of the Mendelian F2 dihybrid ratio 9:3:3:1 arithmetic invariants. Setup: monohybrid F2 = {AA, Aa, aa} with 1:2:1…