Circumsembly
Circumsembly (or redundant access self-assembly) is selfassembly where
different parts A and B of the product-to-self-assemble are reachable by n (n being at least two) possible pathways, such that
if up to (n-1) paths between A & B are blocked by irreversible assembly errors, self-assembly can still proceed from A all the way to B.
In practice much less than (n-1) paths should ever be blocked and the wole product assembled.
Minus the few irreversible assembly errors which can be tolerated in a good design.
(wiki-TODO: add a sketch)
(Choice of name: "circum" from circumventing assembly errors.)
Contents
Relation to yield in the synthesis of chain molecules
artificial synthesis of chain molecules by iterative addition of monomers to the reactive end
suffers from exponential/geometric drop-off in yield.
With every added monomer a probability smaller one of failure is multiplied.
An artificial selfassembled rod of de-novo proteins can suffer the same.
But a stiff rod made from several parallel sub-strands can circumvent irreversible errors.
Prerequisites for circumsembly
- selfassembly at multiple spots simultaneously
- sideward assembly crossing sub-strands is possible
- sufficient stiffness of selfassemblies such that the same spot can be reached via multiple (at least two) pathways
Benefits of circumsembly
- A much reduced dropoff in yield of product.
Especially for 2d and 3D structures where the number of paths for circumvention grows quadratically/cubically respectively.
The math for how the drop-off in yield is reduced exactly in not entirely nontrivial.
(wiki-TODO: check out the math more closely)
Minimal problem:
- Given A rod of n parallel rows of 2D-squares starting out empty adding to the right only.
- Successive addition at the growth front – this needs to accounting for sideward additions – nontrivial
- What is the average blocknumber till all paths are blocked
This is likely easy for n=2 analytically.
For bigger n this might be easiest answered with a simulation.
