Lab calculations for biology

Cells — cells/mL = mean count per large square × dilution × 10⁴ (each large Neubauer square holds 0.1 µL); viability is live ÷ (live + dead). Seeding uses typical growth areas and working volumes per vessel; check yours. Doubling time = t × ln 2 ÷ ln(N₂/N₁).
Centrifuge — RCF = 1.118 × 10⁻⁵ × r × rpm², with r in cm (use the rotor’s maximum radius).
PCR master mix — volume per reaction = final ÷ stock × reaction volume; water fills the rest after the template. Edit, add, or remove components; overage covers pipetting loss. Copy the recipe as text for a lab notebook.
DNA and RNA — A260 of 1 (1 cm) ≈ 50 ng/µL dsDNA, 33 ssDNA or oligo, 40 RNA. A260/280 ≈ 1.8 (DNA) or 2.0 (RNA) and A260/230 ≈ 2.0–2.2 indicate clean samples. Copy number uses 650 g/mol per base pair (330 per nt ssDNA, 340 RNA). Ligation insert mass = vector ng × insert bp ÷ vector bp × ratio. Oligo volume (µL) = nmol ÷ µM × 1000.
OD and units — OD600 conversion factors (E. coli ≈ 8 × 10⁸ cells/mL per OD unit, yeast ≈ 3 × 10⁷) are rough and instrument-dependent; calibrate against plate counts. Unit conversions for volume, mass, molar concentration, and amount, and mass ↔ molar concentration.
Growth, PCR, kill — see below.

For learning and planning. Check critical work against authoritative references and your lab’s validated protocols.

Growth, PCR and kill

Companion to chapters 2, 4, 11 and 13 of Human Biology for the Medical Maker: Basic chemistry (first-order kinetics and the D-value), Cell biology (doubling and PCR), Disease mechanisms (exponential growth of a tumour) and Infection control (sterility assurance level).

Educational — not a medical device, and not a process validation. Not for diagnosis, treatment, monitoring or dosing.

PCR amplification — copies = N₀ × (1 + E)ⁿ for efficiency E over n cycles, for two efficiencies side by side on a log plot. The book’s cases are one click away: 30 cycles at 90 % against 100 % (1.9³⁰ ≈ 2 × 10⁸ against 2³⁰ ≈ 10⁹, about five times less) and the chapter 4 question, 35 cycles at 95 % (≈ 1.4 × 10¹⁰ copies per starting molecule). The lesson: a small loss per cycle compounds, so quantitative PCR measures efficiency with a standard curve instead of assuming it. Efficiency must be 0–100 % and cycles a whole number up to 60; other input is rejected, not clamped.
Exponential growth — N = N₀ × 2^(t/T). One bacterium doubling every 20 minutes becomes 2³⁰ ≈ 10⁹ in 10 hours.
Size → doublings — the chapter 11 exercise: doublings = 3 × log₂(D/d) for a sphere of cells of constant size. A 10 µm cell needs about 30 doublings to reach 1 cm (about 10⁹ cells): ≈ 4.9 years at 60 days per doubling, ≈ 16 years at 200 days. Most of a tumour’s doublings happen before it is detectable.
Log reduction, D-value, SAL — first-order kill: survivors = N₀ × 10^(−t/D), where the D-value is the time for a tenfold reduction at a stated condition. Twelve D-values take 10⁶ organisms to a sterility assurance level of 10⁻⁶ — a one-in-a-million chance that an item carries a survivor. Run backwards, the same arithmetic shows that a 99 % (2-log) kill regrows in under seven doublings. D-values depend on the organism, the process and the load: the inputs are illustrations, and real sterilisation is validated on the real process, not calculated.

Limits

Real growth is exponential only for a while: nutrients, space and the immune system bend the curve; real PCR plateaus as reagents run out. The tool draws the ideal curves on purpose.
First-order kill is a model; real survival curves can have shoulders and tails.

Related: ODE solver (growth and kinetics as differential equations), solutions and dilutions, DNA and protein sequences.

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Growth, PCR and kill

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