EncEnc

If you see this then share with attribution. The genetic code is cracked, up to 4! alternatives. As I suspected, is a version between chemlambda v2 and this chemSKI.

Chora is a mask. Two masks make a node, two nodes make a mask, rewrite is mask eversion.

This is so elegant that I can’t believe when I see it.

Based initially on the encoding tried in this picture

which is different from the permutation cube.

UPDATE: Up to transposition (A and U are inversed), it seems the same as the table 2 (biperiodic table) from M X He, S V Petoukhov, P E Ricci, Genetic code, Hamming distance and stochastic matrices, which I found from searching for the relations between Hamming [8,4] and genetic code. (Hamming [8,4] code matches perfectly with an encoding of the 8 nodes I use, built from geometric reasons.)

SNK is sink (with sign is the S or South combinator) and SOU is source (with sign is the N or North combinator).

G = ++

C = −−

A = +−

U = −+

Arg, R

CGG	CGU	AGG	CGA	CGC	AGA
−++ 231 FI	−+− 213 L	+++ 000 SNK	−++ 231 FI	−+− 213 L	+++ 000 SNK
−++ 231 FI	−++ 231 FI	−++ 231 FI	−+− 213 L	−+− 213 L	−+− 213 L

Ser, S

UCU	UCG	UCC	UCA	AGU	AGC
−−− 111 SOU	−−+ 321 FOX	−−− 111 SOU	−−+ 321 FOX	++− 123 D	++− 123 D
+−+ 312 A	+−+ 312 A	+−− 132 FOE	+−− 132 FOE	−++ 231 FI	−+− 213 L

Leu, L

CUU	CUC	UUA	CUA	UUG (START)	CUG (START)
−−− 111 SOU	−−− 111 SOU	−−+ 321 FOX	−−+ 321 FOX	−−+ 321 FOX	−−+ 321 FOX
−++ 231 FI	−+− 213 L	++− 123 D	−+− 213 L	+++ 000 SNK	−++ 231 FI

Ala, A
GCA	GCU	GCC	GCG
+−+ 312 A	+−− 132 FOE	+−− 132 FOE	+−+ 312 A
+−− 132 FOE	+−+ 312 A	+−− 132 FOE	+−+ 312 A

Gly, G

GGU	GGA	GGG	GGC
++− 123 D	+++ 000 SNK	+++ 000 SNK	++− 123 D
+++ 000 SNK	++− 123 D	+++ 000 SNK	++− 123 D

Pro, P

CCA	CCU	CCC	CCG
−−+ 321 FOX	−−− 111 SOU	−−− 111 SOU	−−+ 321 FOX
−−− 111 SOU	−−+ 321 FOX	−−− 111 SOU	−−+ 321 FOX

Val, V

GUU	GUG	GUC	GUA
+−− 132 FOE	+−+ 312 A	+−− 132 FOE	+−+ 312 A
+++ 000 SNK	+++ 000 SNK	++− 123 D	++− 123 D

Thr, T

ACU	ACG	ACC	ACA
+−− 132 FOE	+−+ 312 A	+−− 132 FOE	+−+ 312 A
−−+ 321 FOX	−−+ 321 FOX	−−− 111 SOU	−−− 111 SOU

START

AUG (MET)	CUG (LEU)	UUG (LEU)
+−+ 312 A	−−+ 321 FOX	−−+ 321 FOX
−++ 231 FI	−++ 231 FI	+++ 000 SNK

STOP

UAA	UGA	UAG
−++ 231 FI	−++ 231 FI	−++ 231 FI
+−− 132 FOE	++− 123 D	+−+ 312 A

Ile, I

AUU	AUC	AUA
+−− 132 FOE	+−− 132 FOE	+−+ 312 A
−++ 231 FI	−+− 213 L	−+− 213 L

Asn, N

AAU

AAC

++− 123 D	++− 123 D
−−+ 321 FOX	−−− 111 SOU

Asp, D

GAU	GAC
++− 123 D	++− 123 D
+−+ 312 A	+−− 132 FOE

Cys, C

UGU	UGC
−+− 213 L	−+− 213 L
+++ 000 SNK	++− 123 D

Gln, Q

CAA	CAG
−++ 231 FI	−++ 231 FI
−−− 111 SOU	−−+ 321 FOX

Glu, E

GAA	GAG
+++ 000 SNK	+++ 000 SNK
+−− 132 FOE	+−+ 312 A

His, H

CAU	CAC
−+− 213 L	−+− 213 L
−−+ 321 FOX	−−− 111 SOU

Tyr, Y

UAU	UAC
−+− 213 L	−+− 213 L
+−+ 312 A	+−− 132 FOE

Lys, K

AAA	AAG
+++ 000 SNK	+++ 000 SNK
−−− 111 SOU	−−+ 321 FOX

Phe, F

UUU	UUC
−−− 111 SOU	−−− 111 SOU
+++ 000 SNK	++− 123 D

Met, M

AUG (START)

+−+ 312 A

−++ 231 FI

Trp, W

UGG

−++ 231 FI

+++ 000 SNK

RNA based combinators

Thank you for noticing me about arXiv:2008.08814 An RNA-Based Theory of Natural Universal Computation.

The author proposes to partially use combinators which are RNA encoded, in such a way that the combinatory logic rewrites are implemented by pervasive RNA editing rules. The idea is like in Molecular computers, namely that for any rewrite there is an enzyme which detects the rewrite pattern and then does the rewrite using a small repertoire of cleavage and ligation.

The author concentrates on the BCKW system, which works well until the rewrite for W combinator. At this point the problem of duplication appears, which makes the author to propose the following replacement of duplications:

• use RNA pseudoknots for term representation, in the sense that parantheses matching correspond to double-stranded portions of the pseudoknot
• instead of duplication, tag a term with a label and use the same double strand matching idea to reference the term in another or the same term (pseudoknot)

This is very interesting to pursue, perhaps in combination with chemSKI with tokens which somehow proposes another mechanism for duplication, or with Combinatory Chemistry: Towards a Simple Model of Emergent Evolution arXiv:2003.07916 where duplication is delegated to the environment.

Partially explored also in Chemlambda strings, Zipper logic, as well as here in Zipper Logic and RNA pseudoknots. The idea is different though, look how I and K combinators look:

See also the first, apparently, project which proposes the use of combinators in chemistry, UPIM, mentioned locally here.

Numerics with the permutation cube and some amino acids

Read Summer numerics: permutation cube, first. I’ll reproduce here the image from that post:

Now, code the RNA bases A, G, C, U as

A = 00

C = 11

G = 01

U = 10

so when you flip the first bit you get the Watson-Crick duality

A–U , G–C

and when you flip the second bit you get a purine-pyrimidine symmetry justified by Chargaff’s second parity rule.

A–G, U–C

A codon is one of the 64 triplets with letters A, C, U, G.

Now, look at the permutation cube, which uses 3 bits to code the 6 nodes of Pure See and the degenerate fanout FO (111) and the degenerate fanin FIN (000).

Each of these nodes are trivalent, ie they have 3 ports and each port is of type “in” or “out”, therefore we need 1 bit/port to describe this.

All in all we can distribute the 3 bits which describe the type of node to the 3 ports, each port having also a bit which describes if it’s “in” or “out”, so in conclusion each port has a 2 bits description…. which we code with the four letters of the RNA code.

Then each node has a codon associated. And each codon codes for an amino acid.

What gives? This:

What is mildly remarkable is that the 6 main nodes fall over different amino acids!

The degeneracy of FO and FIN is partially respected, in the sense that indeed FIN is a degenerate D (but also is a degenerate FI and A) and FO is a degenerate L (but also is a degenerate FOE and FOX).

Hmm. Is fun.

Zipper logic and RNA pseudoknots

UPDATE: compare with the recent Chemlambda strings (working version).

Zipper logic is a variant of chemlambda, enhanced a bit with a pattern identification move called CLICK.

Or, chemlambda is an artificial chemistry.  Does it have a natural, real counterpart?

It should. Finding one is part of the other arm of the research thread presented here, which aims to unite (the computational part of) the real world with the virtual world, moved by the same artificial life/real life basic bricks. The other arm is distributed GLC.

A lot of help is needed for this, from specialists!Thank you for pointing to the relevant references, which I shall add as I receive them.

Further is a speculation, showing that zipper graphs can be turned into something which resembles very much with RNA pseudoknots.

(The fact that one can do universal computation with RNA pseudoknots is not at all surprising, maybe with the exception that one can do functional style programming with these.)

It is a matter of notation changes. Instead of using oriented crossings for denoting zippers, like in the thread called “curious crossings” — the last  post is Distributivity move as a transposition (curious crossings II) — let’s use another, RNA inspired one.

So:

• arrows (1st row) are single stranded RNA pieces. They have a natural 5′-3′ orientation
• termination node (2nd row) is a single strand RNA with a “termination word on it”, figured by a magenta rectangle
• half-zippers are double strands of RNA (3rd and 4th rows). The red rectangle is (a pair of antiparallel conjugate) word(s) and the yellow rectangle is a tag word.

Remark that any (n) half-zipper can be transformed into a sequence of (1) half-zippers, by repeated applications if the TOWER moves, therefore (n) half-zippers appear in this notation like strings of repeated words.

Another interesting thing is that on the 3rd row of the figure we have a notation for the lambda abstraction node and on the 4th row we have one of the application  node form chemlambda. This invites us to transform the other two nodes — fanin and fanout — of chemlambda into double stranded RNA. It can be done like this.

On the first two rows of this picture we see the encoding of the (1) half-zippers, i.e. the encoding of the lambda abstraction and application, as previously.

On the 3rd row is the encoding of the fanout node and on the 4th row the one of the fanin.

In this way, we arrived into the world of RNA. The moves transform as well into manipulations of RNA strings, under the action of (invisible and to be discovered) enzymes.

But why RNA pseudoknots? It is obvious, as an exercise look how the zipper I and K combinators look in this notation.

We see hairpins.

___________________________________

Conclusion:  help needed for chemistry experts. Low hanging fruits here.

___________________________________