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A cell lineage follows descent of biological cells through successive divisions. DNA replication can transmit a mutation to descendant biological cells.

In 1943, Salvador Luria and Max Delbrück grew separate Escherichia coli B cell cultures from small equal inocula, without the challenging bacteriophage. They used nutrient broth or an asparagine–glucose cell culture medium. On nutrient agar plates, they first spread excess bacteriophage and then the bacterial sample centrally, leaving an outer margin. After incubation, resistant biological colonies provided the readout; counts were usually made at 24 and 48 hours. Their control plated repeated samples from one shared culture. Independently grown cultures varied much more than this sampling comparison. That contrast supported resistant lineages arising before challenge: early mutations could produce many resistant descendants before natural selection revealed them.^[ref]

This was evidence about the timing of heritable resistance, not DNA sequencing of the responsible genes. It does not establish uniform mutation rates or exclude environmentally induced mutations; the paper itself discusses physiological dependence and delayed expression.^[ref]

Now construct a deliberately small mathematical model of the timing effect. Start with one sensitive biological cell at generation $g=0$. Every biological cell divides into two in each of five synchronous rounds, with no death or growth difference. There are $N_g=2^g$ biological cells immediately after round $g$, ending with $N_5=32$. In each scenario, exactly one newly formed daughter changes to resistance immediately after round $g$; its descendants inherit resistance without reversion or further mutations. Resistance is expressed immediately, and the final challenge allows every resistant biological cell, and no sensitive one, to form one separate biological colony.

The descendant count obeysAt the moment of the event there is one resistant biological cell; each remaining round doubles its descendants. This proves the formula by repeated multiplication, with terminal case $R_5=1$. An event after round 1 gives $R_1=16$ resistant and 16 sensitive biological cells; an event after round 4 gives $R_4=2$ resistant and 30 sensitive biological cells. Both scenarios contain one mutation event. A culture with no event gives zero resistant biological colonies under these assumptions. The difference is family size, rather than the number of events.

For comparison, suppose each of the 32 final sensitive biological cells independently acquires resistance only on challenge, with probability $p=1/16$ and no subsequent multiplication before counting. Then the resistant count has a binomial distribution, with expected value $32p=2$ and variance $32p(1-p)=15/8$. This alternative mathematical model has no pre-challenge resistant family to amplify. Its independent trials are an assumption of the comparison, not a consequence of using physically distinct biological cells. The clonal scenarios explain how a jackpot can occur; they do not assign probabilities to the event times or estimate a real mutation rate.

// Target: biology.bigb

A mutation changes inherited genetic sequence. Under an infinite sites mutation model, every mutation occurs at a previously unmutated position, so mutations below the sample's common ancestor correspond to segregating sites.

More precisely, a mutation changes a genetic nucleotide sequence; in cellular organisms this is a DNA sequence. An altered sequence can be copied by DNA replication into descendant biological cells, changing their genotype whether or not an observable phenotype changes. Inheritance along a cell lineage does not require transmission to an offspring organism. In animals, germline mutations can enter offspring through gametes, whereas somatic mutations remain in body-cell lineages.^[ref]

A DNA lesion is damage to the physical DNA molecule, such as a damaged nucleobase or a broken strand. It need not become a lasting mutation: DNA repair can restore the original sequence. Conversely, a copied nucleotide substitution can leave an ordinary, correctly paired DNA duplex whose sequence differs from the ancestor. The distinction is between a damaged template and a changed inherited message, not simply between harmful and harmless effects.^[ref]

Small mutations include nucleotide substitutions and indels. Larger changes can remove a gene, duplicate a chromosome region or rearrange its order. Genetic recombination can bring existing alleles together without creating a new nucleobase at the exchanged positions; the mechanism and the resulting sequence change are different questions. A molecular description of a mutation, its effect on a gene product and its effect on a phenotype are likewise three separate statements.

For an original consequence ledger, choose the coding strand segment $5^{\prime }\text{-}\mathrm{ATG}\mathrm{TTT}\mathrm{GAA}\mathrm{TAA}\text{-}{3}^{\prime }$ with initiation at the first displayed codon. Use the standard genetic code, the same reading frame and suitable gene expression context throughout. Its messenger RNA has U in place of T, and the predicted amino acid chain is methionine–phenylalanine–glutamic acid residue, followed by a stop codon. This is a constructed coding segment, not an experimentally measured gene.

In the second row, position 6 changes from T to C, replacing TTT by TTC. Both corresponding RNA codons specify phenylalanine, so the predicted chain is unchanged. Changing position 5 from T to C instead gives TCT, whose RNA codon specifies serine. Changing position 7 from G to T gives TAA and therefore a stop codon before the original glutamic acid residue. Each is one nucleotide substitution, but their coding consequences differ. Even preservation of the amino acid chain does not guarantee unchanged gene expression or phenotype.

Insert GGA after ATG to add a glycine codon, or remove the complete TTT codon to remove phenylalanine. Both indels preserve the downstream reading frame because their lengths are three nucleotides. A one-nucleotide insertion at that location instead produces a frameshift mutation; the positional explanation and a worked regrouping appear under frameshift mutation. The ledger illustrates why interpreting a genetic variant requires its position and context, rather than just the label mutation.

Mutation supplies new inherited variation on which natural selection can act. The Luria-Delbrück experiment makes the distinction unusually visible: natural selection reveals resistant descendants, while the timing of a prior mutation determines how many descendants are available to reveal. This connects an invisible change in one biological cell to a visible pattern across cell cultures.

A somatic mutation occurs in a body-cell lineage outside the germline mutation route. Its descendant biological cells can inherit it through DNA replication, even though it is not transmitted through gametes. Thus heritability within a cell lineage differs from inheritance between sexually reproducing organisms.