DNA & Genetics

The instruction manual inside every cell!

Junior level — plain language, no maths

Tucked inside almost every one of your 37 trillion cells is a complete set of instructions for building and running an entire human being. They're written on a twisted, ladder-shaped molecule called DNA. Unspool the DNA from a single cell and it stretches about two metres - yet it's so impossibly thin that it folds up inside a space smaller than the full stop ending this sentence.

The whole manual is written in an alphabet of just four letters - A, T, C and G - and yours runs to about 3.2 billion of them. Meaningful stretches of that text are called genes, and most genes are the recipe for one protein. Proteins are the body's workforce: they build your muscles, ferry oxygen through your blood, digest your lunch, and fight off disease.

The wildest part is the copying. Every time a cell divides, all 3.2 billion letters get transcribed - accurately - in a few hours, with only about one slip per billion letters. That's like hand-copying three thousand books and making a grand total of three typos. In the simulation below, watch the double helix unzip and replicate in real time.

DNA replication, transcription, translation, and Mendelian genetics

Student level — the core equations

DNA's double helix (Watson & Crick, 1953) is two antiparallel strands zipped together by complementary bases: A with T (two hydrogen bonds), C with G (three). Each strand runs \(5'\!\to\!3'\), and that pairing is the whole trick of copying - each strand is a template for rebuilding the other. Replication is semi-conservative: helicase unwinds the ladder, primase lays down starters, and DNA polymerase builds the new strand \(5'\!\to\!3'\), giving one smooth leading strand and a stitched-together lagging one. Fidelity hits \(\sim\!10^{-9}\) errors per base, because the polymerase proofreads its own work and mismatch repair mops up the rest.

The central dogma (Crick, 1958) fixes the flow of information: \(\text{DNA} \to \text{RNA} \to \text{protein}\). In transcription, RNA polymerase reads a gene into messenger RNA, introns are spliced out, and the message is capped and tailed. In translation, ribosomes crawl along the mRNA reading three-letter codons, each one calling for a particular amino acid through the genetic code - 64 codons covering 20 amino acids plus three "stop" signals - while tRNAs shuttle the building blocks in.

Long before any of this molecular machinery was known, Mendel (1866) reasoned out the logic from pea plants alone. Genes come in two copies (alleles), one from each parent, and dominant alleles hide recessive ones. Cross two carriers, \(Aa \times Aa\), and the offspring fall into \(1\!:\!2\!:\!1\) by genotype and \(3\!:\!1\) by appearance - ratios you can check against real counts with a chi-squared statistic \(\chi^2 = \sum (O-E)^2/E\). Real inheritance then heaps on the wrinkles the peas conveniently hid: codominance, blending, and traits nudged by hundreds of genes at once.

Population genetics, Hardy-Weinberg equilibrium, and molecular evolution

Scholar level — full mathematical depth

01Hardy–Weinberg: evolution's null hypothesis

Population genetics starts by asking what happens when nothing happens. In an idealised population - infinite, randomly mating, with no selection, mutation or migration - allele frequencies \(p\) and \(q = 1-p\) settle into genotype frequencies \(p^2 : 2pq : q^2\) and stay put forever. That's the Hardy–Weinberg equilibrium, and its real value is as a baseline: any population that departs from it is being pushed by an evolutionary force, so the deviation itself becomes the measurement.

02Measuring how far populations have drifted apart

Split a species into subpopulations and they diverge. The fixation index \(F_{ST} = (H_T - H_S)/H_T\) captures how much, comparing the genetic diversity within groups to that of the whole: \(F_{ST} = 0\) means everyone's interbreeding freely, \(F_{ST} = 1\) means complete isolation. It's the standard yardstick for questions from human ancestry to conservation genetics - and, notably, human \(F_{ST}\) is strikingly small, a genetic echo of how recently and how thoroughly our species mixed.

03The neutral theory: most change is just noise

Kimura's neutral theory (1968) made a startling claim: at the molecular level, most variants that spread do so not because they help, but because they're invisible to selection and rise by pure chance - genetic drift. Its cleanest result is that the fixation rate of neutral mutations equals the mutation rate itself, \(k = \mu\), independent of population size. Adaptation is real, but against a vast background of molecular churn signifying nothing, the default explanation for change became "drift", not "advantage".

04Reading selection in the code

You can catch selection red-handed by comparing two kinds of DNA change: synonymous substitutions that leave the protein untouched, and nonsynonymous ones that alter it. Their ratio \(\omega = dN/dS\) is a verdict: \(\omega < 1\) means purifying selection is weeding out harmful changes, \(\omega > 1\) means positive selection is actively driving them, and \(\omega \approx 1\) means drift alone. And because neutral changes tick over at a roughly steady pace, they double as a molecular clock for dating when two lineages last shared an ancestor.

05Splitting a trait into its causes

For traits shaped by many genes, quantitative genetics partitions the total variation: \(V_P = V_A + V_D + V_I + V_E\), separating additive genetic effects from dominance, epistasis, and the environment. The ratio that matters for evolution is narrow-sense heritability \(h^2 = V_A/V_P\) - only the additive part \(V_A\) is what selection can reliably act on, which is why \(h^2\), not the vaguer notion of "genetic", predicts how fast a population responds to breeding or selection.

06The missing heritability puzzle

Modern genome-wide association studies scan millions of DNA markers across huge cohorts, and for complex traits like height they find hundreds of real hits - that together explain only a fraction of the heritability twin studies say is there. This missing heritability is one of the field's live puzzles, blamed on rare variants the scans miss, tangled gene-environment interactions, and epistasis too intricate for additive models to see. We can read the whole genome now; we still can't fully read a person from it.