Origami & Folding
what one sheet can do
Concept

Scaffold — where it appears

The single long strand a DNA origami is folded from, held in shape by the short ones stapled across it. It is a borrowed molecule rather than a designed one — a viral genome of about seven thousand bases — so both its length and its sequence are constraints nobody chose for the purpose.

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

a strand of 7249 bases at 64 to a helixthe bar is the largest member of the family that is still buildablea square blockstopped by the strand's length100 helices · 88% of the stranda single rowstopped by the strand's length113 helices · 100% of the stranda comb of teethstopped by the routing5 helices · 4% of the stranda plusstopped by the routingno size works at allan L with equal armsstopped by the strand's length113 helices · 100% of the strand

Two ceilings

A DNA origami is limited by the length of one viral strand and by whether its helices can be visited once each in a single pass. Grown one step at a time, a square block runs into the first at a hundred helices and a plus runs into the second at five — so which limit a shape meets is decided by the shape and not by the chemistry.

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 origamiDesign constraintHamiltonian pathIdealisationParityPeriodicityRoutingSelf assemblyThreshold

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