M = image size ÷ actual size
Rearrange: actual = image ÷ M. Units: 1 mm = 1 000 µm = 10⁶ nm — always convert first.
Course Sheet · BIO/100 · Expanded Study Edition SHEET Nº 002
Formulæ & field notes — twenty chapters of life with 12 labelled plates, exam traps, mnemonics, quick questions and a flash-card review. Click any equation to copy it; tick chapters as you master them.
PLATE 0HELIX · CELL
Unit One · Chapters 01–04
Microscopes, molecules, membranes — and the two engines that power every living thing.
Unit I · Cells & Chemistry
Everything alive is cells. Measure one correctly and the rest of biology scales from there.
M = image size ÷ actual size
Rearrange: actual = image ÷ M. Units: 1 mm = 1 000 µm = 10⁶ nm — always convert first.
SA ∝ L² · V ∝ L³ ⇒ SA/V falls as a cell grows
Why cells stay microscopic: diffusion can't service a growing volume. Big organisms add cells, not cell size.
PLATE Ithe generalized animal cell
Field Notes
Unit I · Cells & Chemistry
Water, four families of molecules, and the catalysts that make life fast enough.
pH = −log₁₀[H⁺]
pH 7 ⇒ [H⁺] = 10⁻⁷ M. One unit = ×10 change. Blood is buffered to 7.35–7.45 — no negotiation.
v = Vmax[S] ÷ (Km + [S])
Rate rises with substrate then plateaus when every active site is busy. Km = [S] at ½Vmax; low Km = tight binding.
Field Notes
Unit I · Cells & Chemistry
What crosses, what can't, and the physics deciding where water goes.
ψ = ψs + ψp
Water moves high ψ → low ψ. Pure water ψ = 0; solutes make ψs negative; turgor makes ψp positive.
rate ∝ (SA × ΔC) ÷ distance
Big area + steep gradient + thin barrier = fast exchange. Explains alveoli, villi, gills, root hairs.
PLATE IIplant cells in three solutions
Field Notes
Unit I · Cells & Chemistry
Two equations that are each other's mirror — the whole carbon–oxygen economy of Earth.
6CO₂ + 6H₂O light · chlorophyll→ C₆H₁₂O₆ + 6O₂
In chloroplasts. The O₂ released comes from split water, not CO₂ — proven with isotope tracers.
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ≈30–32 ATP
Reverse the arrow and you get photosynthesis — inputs of one are outputs of the other.
Table 04·C — The ATP Ledger
| Stage | Where | Net yield / glucose |
|---|---|---|
| Glycolysis | Cytoplasm | 2 ATP + 2 NADH |
| Pyruvate oxidation | Matrix | 2 NADH + 2 CO₂ |
| Krebs cycle ×2 | Matrix | 2 ATP + 6 NADH + 2 FADH₂ |
| Electron transport | Inner membrane | ≈ 26–28 ATP |
Field Notes
Unit Two · Chapters 05–08
From dividing cells to pedigrees: how information is copied, shuffled, read and occasionally broken.
Unit II · Genetics & DNA
One genome, two strategies: photocopy exactly (mitosis) or shuffle and halve (meiosis).
gamete variety = 2n ⇒ humans: 2²³ ≈ 8.4 × 10⁶
Per parent — before crossing over and random fertilization. Variation is effectively inexhaustible.
Mitosis: 2n → 2 × 2n · Meiosis: 2n → 4 × n
Humans: 2n = 46, n = 23. Mitosis for growth & repair; meiosis only in gonads.
PLATE IIIPMAT — mitosis at a glance
Field Notes
Unit II · Genetics & DNA
A monk, some peas, and the ratios that let you predict the next generation.
Aa × Aa → 1 AA : 2 Aa : 1 aa ⇒ 3 : 1
Test cross (Aa × aa) gives 1 : 1 and reveals an unknown genotype. Incomplete dominance → 1 : 2 : 1 phenotype.
AaBb × AaBb → 9 : 3 : 3 : 1 · P(A∧B) = P(A)·P(B)
Only for unlinked genes. “AND” multiplies, “OR” adds — the two rules that solve every genetics problem.
Field Notes
Unit II · Genetics & DNA
Structure explains mechanism: the double helix suggests exactly how it copies itself.
A = T · G = C ⇒ purines (A+G) = pyrimidines (C+T)
A=T holds 2 H-bonds, G≡C holds 3 — GC-rich DNA is harder to melt.
width 2 nm · 0.34 nm/bp · ≈10 bp per turn (3.4 nm)
Watson–Crick 1953, from Franklin's Photo 51. Antiparallel strands: 5′→3′ against 3′→5′.
PLATE IVthe replication fork
Field Notes
Unit II · Genetics & DNA
The gene is a sentence; transcription photocopies it, translation reads it three letters at a time.
DNA →transcription→ mRNA →translation→ protein
RNA pairs A–U, G–C. Information flows outward; reverse transcriptase (viruses) is the rare exception.
4³ = 64 codons → 20 amino acids + 3 stops
Start = AUG (methionine); stops = UAA, UAG, UGA. Degenerate but unambiguous.
Field Notes
Unit Three · Chapters 09–11
Tissues, plumbing and hormones: how a rooted organism solves every problem it can't walk away from.
Unit III · Botany
Three organs, three tissue systems, and one very useful monocot/dicot cheat table.
Table 09·A — Monocot vs Eudicot
| Feature | Monocot | Eudicot |
|---|---|---|
| Cotyledons | 1 | 2 |
| Leaf venation | Parallel | Net-like |
| Vascular bundles | Scattered | Ring |
| Floral parts | × 3 | × 4 or × 5 |
| Examples | Grasses, lilies, palms | Beans, roses, oaks |
xylem = water ↑ (dead) · phloem = sugar ⇅ (alive)
Xylem vessels are hollow dead tracheids; phloem sieve tubes are living, with companion cells.
PLATE Vcross-section of a leaf
Field Notes
Unit III · Botany
A 90-metre redwood lifts water with no heart and no pump — only physics.
ψ = ψs + ψp · ψs = −iCRT
Soil (≈ −0.03 MPa) → root → leaf (≈ −1.5) → air (very negative). Water falls down the ψ gradient.
evaporation → tension → cohesion ⇒ column rises
Hydrogen bonds hold the column together; transpiration at the leaf pulls it up — zero ATP.
PLATE VIthe stem's two pipelines
Field Notes
Unit III · Botany
No nerves, no muscles — plants steer with five chemicals and a light switch.
Table 11·A — The Big Five Hormones
| Hormone | Made in | Key jobs |
|---|---|---|
| Auxin | Shoot tips | Elongation, phototropism, apical dominance |
| Gibberellin | Young leaves, seeds | Stem elongation, germination |
| Cytokinin | Roots | Cell division, delays ageing |
| Ethylene (gas) | Ripening tissue | Fruit ripening, leaf fall |
| Abscisic acid | Leaves, stems | Closes stomata, dormancy |
flowering ⇐ night length · Pr ⇌ Pfr
“Long-day” plants are really short-night (spinach); “short-day” = long-night (poinsettia). A night-flash of light flips the switch.
Field Notes
Unit Four · Chapters 12–18
Seven systems, one theme: every organ is an exchange surface, a pump, or a feedback loop.
Unit IV · Human Physiology
A nine-metre disassembly line where pH decides which enzyme works where.
Table 12·A — Stations, Juices & pH
| Station | Enzyme / juice | Substrate → product | pH |
|---|---|---|---|
| Mouth | Salivary amylase | Starch → maltose | ≈ 6.8 |
| Stomach | Pepsin + HCl | Protein → peptides | ≈ 2.0 |
| Small intestine | Amylase, trypsin, lipase | Starch / protein / fat | ≈ 8.0 |
digestion = mechanical + enzymatic · absorption ∝ SA
Every adaptation — teeth, churning, villi, microvilli — exists to multiply surface area.
PLATE VIIthe alimentary canal, schematically
Field Notes
Unit IV · Human Physiology
Four chambers, two circuits, and a pump that turns over its own volume every minute.
CO = HR × SV ≈ 70 bpm × 70 mL ≈ 4.9 L/min
Your ≈ 5 L blood volume completes one lap per minute at rest — ×5 during hard exercise.
BP = CO × TPR · MAP ≈ DBP + ⅓(SBP − DBP)
120/80 mmHg: systolic = contraction, diastolic = filling.
PLATE VIIIthe heart · oxygenated side shaded red
Field Notes
Unit IV · Human Physiology
You breathe because of CO₂, not oxygen — and gases only ever move downhill.
V̇ = tidal volume × rate ≈ 500 mL × 14 ≈ 7 L/min
Only ~350 mL of each breath reaches alveoli; the rest fills airway “dead space”.
O₂: 104 → 40 mmHg · CO₂: 45 → 40 mmHg
No pumps for gases — pure diffusion across ~0.5 µm of tissue, in under a second.
Field Notes
Unit IV · Human Physiology
The kidneys filter a bathtub of fluid every day and take back 99% of it.
urine = filtrate − reabsorbed + secreted
GFR ≈ 125 mL/min → ≈ 180 L/day filtered, only ≈ 1.5 L excreted. ~99% reclaimed.
PLATE IXthe nephron — one of ~1 million
Field Notes
Unit IV · Human Physiology
An electrical alphabet written in millivolts — same voltage every time, meaning carried by frequency.
stimulus ≥ threshold → Na⁺ in → K⁺ out → refractory
All-or-nothing: a stronger stimulus fires more often, never harder. Na⁺/K⁺-ATPase restores rest.
PLATE Xthe motor neuron
Field Notes
Unit IV · Human Physiology
Slow mail, precise addresses: hormones in the blood, receptors only where they matter.
Table 17·A — Core Hormones
| Hormone | Source | Effect |
|---|---|---|
| Insulin | Pancreas β | Glucose → glycogen; sugar ↓ |
| Glucagon | Pancreas α | Glycogen → glucose; sugar ↑ |
| Adrenaline | Adrenal medulla | Fight-or-flight: HR ↑, bronchi dilate |
| Thyroxine | Thyroid | Metabolic rate |
| Growth hormone | Anterior pituitary | Growth, protein synthesis |
| ADH | Posterior pituitary | Kidney retains water (ch. 15) |
deviation → receptor → control → effector → reversal
Thermostat logic: the response always opposes the change. Positive feedback is rare (birth contractions).
Field Notes
Unit IV · Human Physiology
Three lines of defence: a wall, a patrol, and an intelligence service with a memory.
1°: slow (~1 wk) → memory cells ⇒ 2°: fast & huge
Vaccines are the first exposure, rehearsed safely. This curve is why you (mostly) get measles once.
self vs non-self ⇐ MHC markers
Every nucleated cell displays MHC “ID tags”; cytotoxic T cells check them. Transplant rejection is this system working.
Field Notes
Unit Five · Chapters 19–20
Populations change over generations; energy flows and matter cycles through everything they touch.
Unit V · Evolution & Ecology
Darwin supplied the mechanism; Hardy and Weinberg supplied the null hypothesis to detect it.
p + q = 1 · p² + 2pq + q² = 1
Holds only with huge population, random mating, no mutation/migration/selection — i.e. never. Deviation = evolution detected.
q² = 0.09 → q = 0.30 → p = 0.70
carriers = 2pq = 2(0.7)(0.3) = 0.42
A recessive condition affecting 9% means 42% are carriers. Always start from q².
PLATE XIthree shapes of natural selection
Field Notes
Unit V · Evolution & Ecology
Energy flows one way and is lost as heat; matter goes round forever. Everything else follows.
dN/dt = rN(K − N)/K
Exponential (J) while N ≪ K; flattens to an S at carrying capacity K. r = intrinsic growth rate.
~10% transfer per level · NPP = GPP − R
Why food chains rarely exceed 4–5 links, and why eating lower on the chain feeds more people per hectare.
PLATE XIIenergy shrinks ~10× at every step
Field Notes
M = image ÷ actual
pH = −log₁₀[H⁺]
ψ = ψs + ψp
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ≈30–32 ATP
gamete variety = 2n
3 : 1 · 9 : 3 : 3 : 1
A = T · G = C
4³ = 64 codons
CO = HR × SV ≈ 5 L/min
BP = CO × TPR
V̇ = TV × rate ≈ 7 L/min
urine = filt − reabs + sec
p² + 2pq + q² = 1
dN/dt = rN(K − N)/K
NPP = GPP − R