A*B/C^2 Design For Both DEC and INC

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Andrew Kaechele

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Posted 1 year ago

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Photo of Andrew Kaechele

Andrew Kaechele

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A while back I was asked how I designed my A*B/C^2 puzzles, and at the time I couldn't remember. A few days working on round 4 seems to have refreshed my memory and I think I can answer now.

This time around my paper designs did serve as a good starting point, and this one in particular resulted in a INC solution for me and a DEC solution for Astromon.

A little disclaimer here, when putting together these "paper" designs, I don't use exact math. I write the oligos down on paper and see where they could share lanes. And I don't want them sharing to big or to small of a lane. And by "lane" I mean reverse complements in the design sequence. And of course the shared lanes are not perfect matches, this is where I have to ballpark, or estimate. If I come to a point where there is no complementary sequence for both oligos sharing a lane, I know one or the other states is going to have a bulge or an internal loop. And I've found these bulges and loops come in very handy later on when it's time to "balance" the oligos. So if in a shared lane the [C] oligo will be missing a bond, further down the line I will chose to match [C] over matching [A] or [B], maintaining a rough balance.

Another thing I am shooting for in my paper design is a scheme for part of the reverse complements of each [A] and [B] to be able to form a static stem, or crash together in states 1-3. In the diagram I labeled them Magnets.

Photo of Andrew Kaechele

Andrew Kaechele

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So I have it where I wanted it. At this point Astromon started on a DEC design and I continued on with the INC design. Looking at what I had, I saw that it was possible to match the reporter to the unpaired bases at the beginning of the design in state 4.



After grafting some extra nts from the end of the design back to the beginning, and completing the complementary reporter sequence I got this. (Below)

AAAAAAAAGUCAGAACUUAGUCUUGUCUCAGUAUGUACCUGUAUCUGGAAAAGCAGAUAAUCCGCCACCGUGCUCUCAGUGAGAA



This would appear to have broken the design, but it was expected. The reporter is now bonding strongly to what are the first nts of the [C] oligo complementary sequence. Nothing else has changed. All I need to do is balance the reporter sequence so it only forms with the unpaired end of [C]s complement in state 4.

An easy way to do this is to add a "tail" magnet. The tail magnet will fold back on the reporter sequence and form a hairpin in states 1-3.

AUGACAAAGUCAGAACUUAGUCUUGUCUCAGUAUGUACCUGUAUCUGGAAAAGCAGAUAAUCCGCCACCGUGCUCUCAGUGAGAA



This gives a lot of added flexibility when working with the reporter. The reporter is shorter and therefore more sensitive than the other oligos.

Some more mutations resulted in this. (Below)

AUGACAAAGUCAGUAUUUAGUCUUGUCUCAGUAUGUACCUGUAUCUGGAAAAGCAGAUAAUCCGCCACCGUGCUCUCAGUGAGAA



Almost there. Now the tail magnet is too strong, and pairing in an unexpected way with part of the unpaired [C] complement. (Above) A single mutation, base 7 from an (A) to a (U) results in this, a solution.

AUGACAUAGUCAGUAUUUAGUCUUGUCUCAGUAUGUACCUGUAUCUGGAAAAGCAGAUAAUCCGCCACCGUGCUCUCAGUGAGAA



And shortly after Astromon solved the DEC version starting with the same #neutral design. (Below)

http://www.eternagame.org/game/browse/8489874/?filter1=Id&filter1_arg2=8526453&filter1_arg1=...



I thought I might have to put the reporter in between [A] and [B], but he made it work at the beginning.

This is the second example this week of starting from neutral and getting a DEC and INC solution from the same design.

These two solutions came from the same base or #neutral design.

http://www.eternagame.org/game/browse/8489874/?filter1=Id&filter1_arg2=8523202&filter1_arg1=...




http://www.eternagame.org/game/browse/8489875/?filter1=Id&filter1_arg2=8524687&filter1_arg1=...



I spent considerable time on the "diagram" at the beginning of this thread, so that it would be readable for others. But paper designs don't have to be for anyone but yourself. Here is the actual paper design that I used for this post. It was drawn on the back of some old homework.



For me, making these paper designs has led to a better understanding of the parts of this problem. All of my successful designs have started this way. I would encourage players who are struggling with these puzzles to give it a try.
(Edited)