Difference between revisions of "Circumsembly"
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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.<br> | 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.<br> | ||
In practice much less than (n-1) paths should ever be blocked and the wole product assembled. | 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. | + | Minus the few irreversible assembly errors which can be tolerated in a good design.<br> |
| + | {{wikitodo|add a sketch}} | ||
== Relation to yield in the synthesis of chain molecules == | == Relation to yield in the synthesis of chain molecules == | ||
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But a stiff rod made from several parallel sub-strands can circumvent irreversible errors. | But a stiff rod made from several parallel sub-strands can circumvent irreversible errors. | ||
| − | == Prerequisites == | + | == Prerequisites for circumsembly == |
* selfassembly at multiple spots simultaneously | * selfassembly at multiple spots simultaneously | ||
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* sufficient stiffness of selfassemblies such that the same spot can be reached via multiple (at least two) pathways | * sufficient stiffness of selfassemblies such that the same spot can be reached via multiple (at least two) pathways | ||
| − | == Benefits == | + | == Benefits of circumsembly == |
* A much reduced dropoff in yield of product. <br>Especially for 2d and 3D structures where the number of paths for circumvention grows quadratically/cubically respectively. | * A much reduced dropoff in yield of product. <br>Especially for 2d and 3D structures where the number of paths for circumvention grows quadratically/cubically respectively. | ||
Revision as of 16:39, 13 May 2022
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)
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.
