Biology

All living things are made of cells, and every cell comes from a cell. A cell feeds through its surface, which grows as r² while its needs grow with its volume, r³: double the radius and each unit of volume gets half as much surface. A large organism is therefore many small cells, not one big one.

Use: Explains why the agents of infection went unseen until lenses of 200× and more, and why germ theory had to wait for the microscope.

First: Hooke named the cell in Micrographia, 1665 (Gutenberg). Schleiden (plants, 1838) and Schwann (animals, 1839) made all life cellular, and Virchow added omnis cellula e cellula, 1855 (Mazzarello, 1999).

A dissolved substance moves down its concentration gradient: the flux J is the diffusion coefficient D times the gradient. The time to cover a distance x grows as x². Oxygen in water at body temperature crosses 1 µm in under a millisecond, 1 mm in about 3 minutes and 1 cm in about 5 hours.

Use: Diffusion alone serves no tissue more than about a millimetre from its supply. That is why the body needs a heart and a branching network of vessels, and why the lungs and the gut are built from huge, thin surfaces.

First: Adolf Fick, 1855 (Annalen der Physik).

Green plants, algae and some bacteria build sugar from carbon dioxide and water using light, storing about 2,870 kJ in each mole of glucose and giving off oxygen. At most 4.6 % of the sunlight falling on a C₃ crop (wheat, rice, potatoes) can end up as biomass, and 6 % for a C₄ crop (maize, sorghum, sugarcane); fields over a season get well below that.

Use: Sets the ceiling on food from land. A field's yield is the sunlight it receives times this efficiency, and water, nutrients and the length of the season decide how near the ceiling it gets (holding fertility).

First: Ingenhousz showed in 1779 that plants restore air only in light. Calvin, Benson and Bassham traced the path of carbon with ¹⁴C, 1946–1954 (Nobel Prize 1961). The limits: Zhu, Long and Ort, 2008.

Cells burn glucose back to carbon dioxide and water and capture the energy as about 30 molecules of ATP per glucose (older books say 36–38). Without oxygen, yeast turns glucose into ethanol and muscle into lactate, for 2 ATP.

Use: Food energy follows from it: 1 g of carbohydrate or protein gives about 17 kJ (4 kcal), 1 g of fat about 37 kJ (9 kcal). The oxygen-free route makes bread, beer, yoghurt and silage (fermentation).

First: Mitchell's chemiosmotic theory, 1961, explained how the energy is captured (Nature; Nobel Prize 1978). The yield of about 30 follows from the measured ratios of ATP made per oxygen used (Hinkle, 2005).

An enzyme speeds one reaction by millions of times at body temperature. Its rate v rises with the concentration of its substrate [S] until every enzyme molecule is busy, at Vₘₐₓ; Kₘ is the concentration that gives half that rate. Each enzyme works fastest over a narrow range of temperature and pH, and most are destroyed by heating above about 60 °C.

Use: Why vegetables are blanched before freezing (to stop their own enzymes), why a mash for brewing is held at a set temperature (fermentation), and why a body temperature above 40 °C is an emergency.

First: Michaelis and Menten, 1913 (English translation, Johnson and Goody, 2011).

The heart's output Q is its rate f times the volume V of each beat. At rest the whole blood volume goes round about once a minute; in hard exercise the output rises four- to fivefold.

Use: A fast, weak pulse means a small volume per beat, from bleeding or dehydration, being made up by rate: lay the person flat, keep them warm and look for the loss (shock). Harvey's arithmetic proved the circulation: the heart sends out more blood in half an hour than the body holds, so the same blood must go round.

First: William Harvey, De motu cordis, 1628, chapter 9 (English translation, Gutenberg).

Steady flow Q through a tube rises with the fourth power of its radius r and falls with its length L and the viscosity η of the fluid. At the same pressure difference ΔP, halving the radius cuts the flow sixteenfold.

Use: Why a partly blocked artery starves the muscle beyond it, and why fluid or blood is given fast through a short, wide cannula, never a long thin one.

First: Hagen, 1839, and Poiseuille, 1840–1846 (Sutera and Skalak, 1993).

The gut wall carries sodium and glucose across together, and water follows them. That carrier keeps working in cholera and the other diarrhoeas that make the gut pour water out, so a drink of the right salt and sugar strength replaces losses that would otherwise kill within hours. The WHO formula, in millimoles per litre, totals 245.

Use: Treats the dehydration of diarrhoea without a drip. The home recipe is 1 litre of safe water, 6 level teaspoons of sugar, ½ level teaspoon of salt (wound care and first aid). Measure, never guess: too much salt is dangerous in small children.

First: Crane described the sodium–glucose carrier in 1960–1961; trials in Dhaka and Calcutta proved oral rehydration between 1968 and 1971; the reduced-osmolarity formula has been recommended by WHO and UNICEF since 2003 (WHO).

A day's energy need E is the basal metabolic rate (the body at rest) times a physical activity level. For adults aged 18–30, BMR in kilocalories a day from weight W in kilograms is given above; older adults have their own lines. PAL is 1.40–1.69 for a sedentary life, 1.70–1.99 for an active one and 2.00–2.40 for hard physical work. A 60 kg man doing farm work needs about (15.1 × 60 + 692) × 2.1 ≈ 3,350 kcal (14 MJ) a day.

Use: Ration planning: multiply by people and days, and turn it into food at about 3,500 kcal per kg of dry grain, so about 1 kg of grain a day for that farm worker.

First: FAO, WHO and UNU, Human energy requirements, 2004, tables 5.2 and 5.3 (FAO).

Mass in kilograms divided by the square of height in metres. For adults WHO counts under 18.5 as underweight, 18.5–24.9 as normal, 25 or more as overweight and 30 or more as obese; under 16 is severe thinness.

Use: Screens adults for hunger or excess with a scale and a tape. It misleads in very muscular people, in pregnancy and in children. For a child from 6 months to 5 years, measure the mid-upper-arm circumference instead: under 115 mm is severe acute malnutrition.

First: Quetelet proposed the ratio in 1835 (MacTutor); Keys named it the body mass index in 1972 (Journal of Chronic Diseases).

Growing bacteria divide at a steady doubling time g: about 20 minutes for E. coli at 37 °C with food. Ten doublings make a thousandfold increase; one cell becomes a million in under 7 hours.

Use: Behind the food-safety rules: keep cooked food out of 5–60 °C, eat or chill it within 2 hours, and reheat it until steaming hot (WHO Five keys to safer food; preserving the harvest).

First: Monod measured and described bacterial growth, 1949 (Annual Review of Microbiology).

At a fixed temperature every D minutes of heating kills 90 % of the organisms still alive. Each organism, and each kind of spore, has its own D. Spores of Clostridium botulinum survive boiling and have a D of about 0.2 minutes at 121 °C, so canning is designed for 12 tenfold reductions: the 'botulinum cook' of about 3 minutes at 121 °C at the centre of the can.

Use: Why low-acid food needs a pressure canner at 116–121 °C while acid food (pH below 4.6) needs only boiling water (preservation guide), and why surgical instruments are sterilised in steam at 121 °C for at least 15 minutes: boiling kills bacteria and viruses but not spores.

First: Bigelow showed that heat kills at a logarithmic rate, 1921 (Journal of Infectious Diseases); Esty and Meyer measured the botulinum spores that the 12-reduction rule is built on, 1922 (Journal of Infectious Diseases).

Each parent passes on one of its two copies of a gene, at random. Crossing two carriers gives 1 : 2 : 1 by gene and 3 : 1 by appearance when A is dominant. Genes on different chromosomes sort independently, so two traits together give 9 : 3 : 3 : 1. Mendel's peas: 5,474 round seeds to 1,850 wrinkled, 2.96 : 1.

Use: Predicts what a cross will give and how many generations it takes to fix a trait, and explains why a hidden defect appears when relatives breed (securing seed and breeding stock).

First: Gregor Mendel, Versuche über Pflanzen-Hybriden, read 1865, published 1866 (English translation, Wellcome Collection).

DNA is two strands wound in a helix and held together by base pairs: adenine with thymine, guanine with cytosine. Each strand therefore fixes the other, so a cell copies its DNA by separating the strands and building a new partner for each.

Use: The basis of every genetic test, of paternity and forensic matching, and of PCR and sequencing.

First: Chargaff found the equal ratios, 1950 (Experientia). In 1953 came Franklin and Gosling's X-ray evidence (Nature) and Watson and Crick's model (Nature).

Each three letters of messenger RNA, a codon, names one amino acid or 'stop'. Four letters in threes give 64 codons for 20 amino acids, so most amino acids have several. Nearly every living thing uses the same code, which is why a bacterium given the human gene can make human insulin.

Use: Lets a gene be read as the protein it makes; behind insulin, vaccines and enzymes made by microbes (biology as engineering).

First: Crick, Barnett, Brenner and Watts-Tobin showed the code is read in threes, 1961 (Nature); Nirenberg and Matthaei read the first word the same year, UUU for phenylalanine (PNAS).

If a gene has two forms with frequencies p and q, so p + q = 1, and mating is random, the population holds p² of one type, 2pq carriers and q² of the other, unchanged from one generation to the next.

Use: Counts the carriers nobody can see: if 1 child in 2,500 is born with a recessive disease, q = 1/50 and about 1 person in 25 carries it. Marriage between cousins raises the risk because both parents are more likely to carry the same rare gene.

First: G. H. Hardy (Science, 1908) and, independently, the physician Wilhelm Weinberg, 1908.

A breeding group of M males and F females loses variation like an ideal group of size Nₑ, which is set mostly by the scarcer sex. Each generation it becomes ΔF more inbred. One bull with 25 cows gives Nₑ ≈ 3.8: about 13 % more inbreeding every generation.

Use: FAO's minimum for keeping a breed is Nₑ = 50, ΔF = 1 % a generation: for example 25 males and 25 females, or 14 males and 116 females (FAO, 2013). Use several sires, bring in unrelated ones, and save seed of cross-pollinated crops from many plants (livestock, seeds).

First: Sewall Wright, Evolution in Mendelian populations, 1931 (Genetics).

The gain R in the next generation is the selection differential S (how far the chosen parents are above the average) times the heritability h², the share of the trait's variation that is inherited. Milk yield and growth rate have h² of about 0.2–0.4; fertility and resistance to disease often under 0.1.

Use: If the animals kept for breeding average 10 kg heavier at a year old than the flock, and h² = 0.3, their offspring will average about 3 kg heavier. A trait with low heritability improves faster through better feed and care than through selection.

First: Jay Lush, Animal Breeding Plans, 1937 (Hill, 2014).

A form of a gene at frequency p whose carriers leave a fraction s more offspring rises by about s p (1 − p) a generation: slowly while it is rare, fastest at 50 %, slowly again near 100 %. Bacteria can divide every hour, so their resistance evolves thousands of times faster than any change in us.

Use: Antibiotic resistance is selection: each course kills the susceptible bacteria and leaves the resistant. Resistant infections directly caused about 1.14 million deaths in 2021 (GRAM, 2024). Give antibiotics only for bacterial infection, at the full dose, and never to make livestock grow (antibiotics).

First: Darwin and Wallace, 1858 (Linnean Society); Darwin, On the Origin of Species, 1859 (Gutenberg). The arithmetic: Haldane, Fisher and Wright, 1924–1932 (Wright, 1931).

Growth is fastest at half the carrying capacity, so the most that can be taken year after year, the maximum sustainable yield, is rK/4, from a stock held near K/2. Take more and the stock shrinks, its growth falls and the catch collapses.

Use: Sets the take from a fish pond, a fishery, a hunted herd or a woodlot. A lake that holds at most 10,000 fish, growing at r = 0.5 a year when sparse, yields at most about 1,250 a year from a stock kept near 5,000. Because r and K are never known exactly, take less than that (fish ponds).

First: Verhulst, 1838 (MacTutor); the maximum sustainable yield, Schaefer, 1954.

About a tenth of the energy at one feeding level reaches the next; the rest is spent on living. After n steps up a food chain, a tenth to the nth power is left.

Use: A field feeds far more people as grain than as meat from animals fed that grain. Livestock add food rather than cost it where they eat what people cannot: grass on land that cannot be cropped, and kitchen and crop waste.

First: Lindeman, 1942 (Ecology); a mean of 10 % from 48 aquatic food webs, Pauly and Christensen, 1995 (Nature).

R₀ is the number of people one case infects where nobody is immune. Immunising a fraction v cuts it to R₀(1 − v). Once v passes the critical fraction 1 − 1/R₀, each case infects fewer than one and outbreaks die out.

Use: Measles, with up to 18 infections per case (WHO), needs about 95 % of people immune: two doses for nearly everyone. A disease with R₀ = 2 is stopped at 50 %. Babies too young to vaccinate are protected only by the immunity around them.

First: The threshold, Kermack and McKendrick, 1927; R₀ in Ross's and Macdonald's work on malaria, 1911–1952 (Heesterbeek, 2002).

A population of N people is split into susceptible S, infectious I and recovered R. β is the rate of infecting contacts, 1/γ the time a case stays infectious, and R₀ = β/γ. The epidemic peaks when the susceptible share falls to 1/R₀ and ends with some people never infected.

Use: Shows why early action counts: halving contacts halves R₀ and can turn a growing outbreak into a shrinking one, and isolating cases sooner does the same by shortening 1/γ. It can be stepped forward a day at a time on paper (the derivative).

First: Kermack and McKendrick, 1927 (Proceedings of the Royal Society A; MacTutor).

The polymerase chain reaction heats DNA to about 95 °C to part its strands, cools it to 50–65 °C so short primers bind on either side of the target, then lets a heat-proof polymerase copy it at 72 °C. Each cycle doubles the target: 30 cycles, about an hour, make a billion copies from one.

Use: Detects a germ from a few copies of its DNA or RNA (the COVID-19 test), matches a person or an animal, and supplies DNA for sequencing.

First: Kary Mullis's method, first published by Saiki and colleagues, 1985 (Science); Nobel Prize 1993.