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…
Monod chemostat kinetics: μ(S)=μ_max·S/(K_s+S); dS/dt, dX/dt ODE system with dilution D
Monod chemostat kinetics — the canonical continuous-culture bioreactor framework (Monod 1949; Herbert-Elsworth-Telling 1956 chemostat…
Plasmid-loss exponential decay: fraction retained = e^{−λn}; binary-fission dilution Markov chain
Plasmid-loss exponential-decay framework — the canonical population model for segregational plasmid instability in bacterial/yeast…
CRISPR NHEJ indel yield: p_cut=1−e^{−μt}; Poisson-process per-cell-cycle cut-rate framework
CRISPR NHEJ indel-yield Poisson framework — the canonical stochastic model for Cas9-mediated gene editing efficiency at a target locus per…
Monod: S_ss=K_s·D/(μ_max−D); D_crit=μ_max·S_feed/(K_s+S_feed); at D=μ_max/4,K_s=S_feed: S_ss=S_feed/3
Sympy-exact symbolic witness of the Monod chemostat steady-state canonical forms and washout threshold. Setup: S, K_s, μ_max, Y, S_feed, D…
Plasmid-loss: f(n)=exp(−λn); n_half=log(2)/λ; at λ=ln2 → n_half=1; retained@2gen = 1/4
Sympy-exact symbolic witness of plasmid-loss exponential decay canonical form and generation-half-loss anchors. Setup: P_0, λ, t, n — all…
CRISPR indel: p_cut=1−e^{−μt}; t_half=log(2)/μ; at μt=1: p_cut=1−1/e; at μt=ln2: p_cut=1/2
Sympy-exact symbolic witness of the CRISPR NHEJ indel-yield Poisson canonical form and cut-rate anchors. Setup: μ_cut, t — both positive…
mAb (Köhler-Milstein 1975)
Köhler-Milstein 1975 (Nobel 1984) hybridoma; modern humanized + fully-human + bispecific mAbs $200B/yr market.
rDNA (Cohen-Boyer 1973)
Cohen-Boyer 1973 first recombinant DNA; modern genetic-engineering + Bayh-Dole 1980 transformed biotech industry.
PCR (Mullis 1983)
K Mullis 1983 (Nobel 1993) PCR; modern qPCR + digital-droplet-PCR + ddPCR; foundation of molecular-diagnostics.
CRISPR-Cas9 (2012)
Jinek-Charpentier-Doudna 2012 (Nobel 2020) CRISPR-Cas9; modern Casgevy 2023 + CRISPR-IL Sherkow review.
Synthetic genome (Venter 2010)
Venter-JCVI 2010 'Synthetic Cell' Mycoplasma; modern JCVI-syn3.0 473 genes minimal; foundation of synthetic-biology.
Biomanufacturing scale-up
Modern biopharmaceutical industry $400B; CHO + HEK293 + yeast Pichia; perfusion + intensified processes.
Recombinant DNA (Cohen-Boyer 1973)
S Cohen-H Boyer 1973 recombinant-DNA; modern modern foundational text + Genentech 1976 + insulin Humulin 1982 + biotech-revolution.
Monoclonal Ab (Köhler-Milstein 1975)
G Köhler-C Milstein 1975 (Nobel 1984) hybridoma; modern modern foundational text + therapeutic-mAb + 2024 100+ FDA-approved + bispecific…
CRISPR-Cas9 (Doudna-Charpentier 2012)
J Doudna-E Charpentier 2012 (Nobel 2020) CRISPR-Cas9 in-vitro; modern modern foundational + base / prime-editing 2017-2019 + 2023…
Phage display (Smith 1985)
G Smith 1985 + Winter 1990 (Nobel 2018) phage-display; modern modern foundational text + adalimumab Humira + biopharmaceutical engineering.
Directed evolution (Arnold 1993)
F Arnold 1993 (Nobel 2018) directed-evolution; modern modern foundational text + MLDE 2020 ML-driven + 2024 enzyme-engineering generative.
CAR-T (Kymriah 2017)
Carl June-FDA 2017 Kymriah-Yescarta CAR-T-CD19; modern modern foundational + bispecific BiTE blinatumomab + 2024 in-vivo CAR-T mRNA Pfizer.