= Maxam-Gilbert sequencing
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\b[Maxam-Gilbert sequencing] determines a <DNA> <nucleotide sequence> by base-selective chemical cleavage of end-labelled molecules, followed by <polyacrylamide gel electrophoresis> and <autoradiography>. <Allan M. Maxam> and <Walter Gilbert>'s 1977 paper uses fragment lengths to locate attacked bases along the labelled strand. <Sanger sequencing> instead creates endpoints during <DNA> synthesis; the chemical method starts with the strand whose sequence is wanted.<A new method for sequencing DNA by Allan M. Maxam and Walter Gilbert>[Printedp.560, Abstract and opening description]{ref}
The label is crucial: each visible fragment shares one identifiable end, making its length a positional ruler. The paper allows either a 5′ or a 3′ terminal label and demonstrates separately resolved, 5′-labelled strands. Chemical modification must be partial, so that many molecules retain different cleavage positions. Destroying every susceptible site on every molecule would erase much of the distant sequence from the labelled fragments.<A new method for sequencing DNA by Allan M. Maxam and Walter Gilbert>[Printedp.560, terminal labelling and partial base modification]{ref}
The original four displays preferentially reveal <guanine>, preferentially reveal <adenine>, reveal <cytosine> and <thymine> together, and reveal <cytosine> alone. The purine displays use unequal reactivity rather than four perfectly exclusive reactions. Comparing parallel lanes supplies redundant information: a signal in the cytosine/thymine display but not the cytosine display identifies <thymine>. A sequence of four interior cleavage positions assigned A, C, T and G in order of increasing distance from a 5′ label identifies $5'\text{-ACTG-}3'$ at those positions. The <nucleotide sequence> of the opposite strand requires the <reverse complement> and its orientation.
A subtle experimental point prevents an off-by-one interpretation: the observed fragment ends immediately before the base destroyed by the chemical attack. The base assigned to a band is the attacked base, not an intact last base carried by that fragment. The 1977 example used a 64-base-pair <lac operon> fragment and denaturing gels; the authors read 62 bases of each strand and cross-checked the complementary sequences.<A new method for sequencing DNA by Allan M. Maxam and Walter Gilbert>[Printedpp.560–561, An Example and Figure2 interpretation]{ref}
An original <Poisson distribution> model illustrates why partial cleavage matters. If the number of attacks on a molecule has mean $\lambda$, then
$$
\Pr(N=0)=e^{-\lambda},\quad \Pr(N=1)=\lambda e^{-\lambda},\quad
\Pr(N\geq2)=1-e^{-\lambda}(1+\lambda).
$$
At $\lambda=0.1$, about $90.48\%$ are unhit, $9.05\%$ singly hit and $0.47\%$ multiply hit. At $\lambda=1$, the multiply-hit fraction rises to $26.42\%$. This independent-site model is an illustration, not a fitted description of the paper's sequence-dependent reaction rates. Gel resolution, incomplete specificity and multiple hits can all limit the recovered <sequencing read>.
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