Origami & Folding
what one sheet can do
Concept

Self assembly — where it appears

A structure that forms because its parts only fit together one way, with nothing directing the order they arrive in. It replaces a sequence of operations with a set of local specificities, so what a designer writes is not a procedure but a collection of pieces whose only stable arrangement is the wanted one.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

a route the search found123456121110987131415161718242322212019helices 24colours 12 : 12a route is not forbiddenscaffold used 21%48 staples of 3224 helices · 1536 bases · 48 staples · colours 12 : 12

A sheet that routes itself

DNA origami folds one long strand into a shape by holding it against itself with a few hundred short ones. There is no sheet and no crease — what has to be designed is a route — and the first thing that can go wrong is a counting argument crease patterns already know under another name.

biology · Molecular folding the two things a domain has to be long enough forthe bar starts where the demand is first met and runs to the rightunique in the whole design11 bases and upstill paired at 45 degrees17 bases and upwhere a honeycomb crossover may sitfirst one inside both bands: 21 baseswhere a square-lattice crossover may sitfirst one inside both bands: 24 bases4812162024283236a domain runs between two crossovers, so its length is a whole multiple of the period

A domain too short to be unique

A staple holds the scaffold by pairing with a stretch of it, and two arguments decide how long that stretch has to be. One is combinatorics — a stretch of seven bases has about four hundred other places in a 7,249-base strand it would also match. The other is thermodynamics, and it is the one that binds: a duplex that is unique at eleven base pairs still comes apart at the temperature the design is held at, and staying paired takes seventeen. Rounded up to the crossover period, that is three periods on both lattices, and the lattice the helix prefers is the one whose three-period domain leaves some of its staples unattached.

biology · Molecular folding

Named alongside it

The objects these essays reach for when they reach for this one.

DNA origamiIdealisationNecessary conditionParityPeriodicityRoutingScaffoldThreshold

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