Chemical concrete machine, short list of gates and moves

Continuing from  Local FAN-IN eliminates GLOBAL FAN-OUT (II)  and   Local FAN-IN eliminates global FAN-OUT (I)  I propose the following list of gates and moves, which are taken from graphic lambda calculus, with the FAN-IN and DIST moves added. (So this could be called the “chemical concrete machine sector”, and it has Turing universality, via the fact that it contains the combinatory logic.)

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Principle: each gate is a molecule, each move is an enzyme.

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Dictionary:  we need four trivalent gates, which can be distinguished one from another by looking at the number of inputs/outputs and from a choice of colour between red and green. To these add the arrows, loops and the termination gate. The translation from graphic lambda calculus notation to this new coloured notation is the following.

convention_1

Each of these gates is a molecule.  [Speculations: (1) by looking at DNA backbones, could be the 5′-3′ phosphate-deoxyribose backbone be used as \rightarrow? ]

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The moves, translated. Each move is made possible by an enzyme (hence move = enzyme). Here is the list, with the names taken from graphic lambda calculus, by using the dictionary for translation.

convention_2

convention_3

convention_6

convention_4

  • Elimination of loops:

convention_5

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Implementation needed, but this is out of my competence.  I was thinking that could be possible by using DNA origami techniques, but it might turn out that the schema here is even more close to the structure of DNA. This is an outrageous speculation, but I can’t stop to remark that there are 4 trivalent gates, making two pairs of duality (seen in the graphic beta move and in the FAN-IN move), and this resembles to the A-T, G-C pairing (but it might be a coincidence).

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