The GU-challenge or The watch theory

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PART I - Theory

Jonasz asked in the chat, how he could get one more GU-pair into this puzzle. He had then gotten 26 GU-pairs in. Only one player had got one more GU-pair into this puzzle than him, so we couldn't help him. He got one more in than I did originally, and Brourd had 26 GU-pairs just as him.

Instead of getting help, he ended up helped us. After he left, I suddenly realized there was a color pattern in the picture he had posted in the chat. A pattern that may be a step on the road to find out how to raise the GU content more in GU-challenges puzzles. The way the blue nucleotide is facing in each GU-pair might be important.



If you imagine your puzzle is a watch, the blue is on the one side of the needle, no matter what time it is. Center of puzzle multiloop, center of the watch

I later asked Jonasz if I could post his picture. When he heard about that analogy, and the idea, he named it The watch theory.

I tried reverse the direction of GU-pair. This way I got two GU's less in.



Just like there is a right direction for GC-pairs in multi loops normally, there appear to be a right side for placing of GU-pairs in a GU-challenge puzzle. That is if one want's most in. :) As Brourd said: With GU placement, it has to be very precise. Even one wrong placed GU, puzzle falls apart.

When discussing the idea with Brourd, he said about the direction pattern: Helps prevent mispairing when all the U's are going the same way. I agreed. Later Jonasz said: I think it is because this structure lower the possibility of misparing on a makro scale.

I think this pattern will arise in puzzles centered around multiloops with 3 or more arms. If we know a rule for which direction GU-pairs have to turn in, then we can get much more in.

Edited chat with the most important points pulled out:
Brourd: But, there are a few other things
Brourd: like the placement of nucleotides in loops
Eli Fisker: Boostpoint opposite red in end basepair
Eli Fisker: Preventing slide
Eli Fisker: Is that it?
Brourd: Yes, and the placement of nt's in loops to prevent yellow-blue mispairing
...
Brourd: The best example would be my puzzle Spiral Triangle, with the U in the GU pair being across from the yellow loop and making the bulge blue to prevent mispairing.
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Eli Fisker

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Posted 8 years ago

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PART II - Testing

To find out how this work, I have made some test puzzles.

If you have the GU-pairs in the both of the two strings in this puzzle, it does not matter which way the GU-pairs turn – as long as all turn the same way.





If you switch side so the GU-pairs turn opposite each other between the upper and the bottom string, then you can't get in as much GU-pairs.

If the puzzle is bend a little like below, there is still no difference in number of pairs you can get in, depending on if the blue nucleotide is to the left or right side of the string.





The more it bends, the less GU-pairs you can get in. And GC-pairs will be needed to get a hold on the structure.

If I let the GU-pairs switch side for each string, I get less in. This tendency continues, if I bend the shape more. So in a GU-challenge that is like a long string and not too bent, direction of GU-pairs does not matter much, as long as they all turn the same way.



If you want to play with the puzzle yourself, copy this dot bracket sequence into the puzzlemaker:

.....(((((..(((((.....)))))..))))).....

If I cange structure I can get the same number of GU-pairs in no matter which way the GU-pairs turn, as long as I don't use GC-pairs.





For further play, here is dot bracket structure:

.....(((((..(((((....)))))...(((((....)))))..))))).....

The pattern from Jonasz puzzle get more clear, when GC-pairs get involved. Then the following happens. The first puzzle with blue nucleotide to the right side of the arm, 16 GU-pairs can be placed.



When blue nucleotide is to the left like below, only 12 GU-pairs can get in, and one of them is turned opposite of the others, to get it in.



I think it comes down to direction of GC-pairs in multiloops.

Here is a partial from the right arm in the puzzle. Notice the two red nucleotides beside each other.



I think two red nucleotides in line, when in connection with a multi loop weakens the puzzle. Brourd said the C wants to pair up else where. I think this will be the case when this pattern shows up in connections to hairpin loops and internal loops too.

Dot bracket structure for puzzle:

.....(((((..(((((....)))))..(((((....)))))..(((((....)))))..))))).....

Using this knowledge off cause will be much harder in a GU-challenge puzzle with more complex shapes, but this should give you an idea about how the challenges can be approached.
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PART III - The missing GU-link or watch theory in lab

After finding out about the pattern in GU-challenges, I went to check if this got any implications for our lab designs. To my surprise there was a very clear pattern with only few exceptions. Not the same pattern as in Jonasz puzzle, but a mirrored one.

Starting the reading in the neck, and go counter clockwise like I demonstrated in this picture. This is Mat's winning design from The one bulged cross lab. Name of the design: Mat – Mod of D9 Design.



Check the left side of the string - going in reading direction and note if it is a blue or red nucleotide you meet in the GU-pair.

The first to the left should be a blue, if there is more so should they, unless it is in the last GU-pair. In the last GU-pair the nucleotide to the left should be red. If there is only one GU-pair, the one to the left can be both blue or red as it is both the last and first.

So Mat's design would be read like: L,L,L,R or if you count in colors, B,B,B,R.

Here is a spreadsheet with data for past labs. I have included data for designs with GU-pairs and a score on 94% and over. Notice for understanding of data: Small letters means that the GU pair broke the area apart, according to prediction mode and shapedata.

Here is a design with a GU-pair in the neck. Here is a better explanation of how designs should be read in relation to The watch theory. Only read the color of nucleotide in a GU-pair on the left side on the strand, the area marked with black. So this one is read like, efter nucleotid letter U,U,U,U,G, after side of Blue nucleotide L,L,L,L,R or after color B,B,B.B,R.

Dimension9 One bulged cross puzzle (97%) JewelOfTheMoon


As Starryjess nicely summed up things: Most of the U's should be on the left, except the last pair.

And if there is just one GU pair in the whole puzzle, the U could be to the left as it is the first, or the right as it is also the last.

Thanks to Starryjess for looking through all this, comming with great ideas for improving clarity and correcting my worst errors.
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Edward Lane

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no I still don't know what you mean by right and left - despite trying to get this a few times.

you say "Check the left side of the string - going in reading direction and note if it is a blue or red nucleotide you meet in the GU-pair. "

looking at Mat – Mod of D9 Design, nucleotide 16, I see red but you say that's blue, I'm sure it makes sense, but think you need to define your terms a bit more :)
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Hi Edward!

I understand why you are asking. Starry suggested that I put other terms on than left and right on. Sorry for the confusion

Yes, nucleotide 16 in Mat - Mood of D9 Design is red.



I made a picture with marking of the reading area, the part marked by the orange marking. This should explain a bit better. You should only read on the left side of the strand. The arrows shows the reading direction in the orange marked area.
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Eli Fisker: Left side of a strand is the anticlockwise from within the multiloop
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The overall reading start in nucleotide 6 (the basepair closing the hook) and continues in reading direction of the arrows.
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TLdicey

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I find the watch idea (or windmill) not bad, but given the alignment can always be mirrored as well I propose a different "read":

Imagine all the stacks/arms are little rivers flowing into the centre "hole". As you follow the count of bases from 1 to end, you only read the side of pairs where you head "downriver", and you expect the GU pairs to have the same orientation of 1 nucleotide for the entire trip (i.e. you either encounter only G's or if mirrored, only U's).

I'd say there are a few exceptions though, for example if in Mat's "Mood of D9.." you placed a GU at 42-49, the G would be in optimal position at 49, against expectations, just because of adjacent pairs.

To test this in strategy market, and technical terms for the counting, counting and according/penalising points by how GU pairs fare in same orientation: only count check at every first base of a pair, or only every 2nd (as you can imagine in the editor, only every open bracket to half of the puzzle, after which only every closed - excluding free bases at start and end). Exclude GU pairs in a 2nd run of crunching numbers (regardless of conformity or non-conformity to the rule to exclude bias) that are (or are not) in optimal energetic positions in relation to the stronger bond close to them (and the side of the starting point) according to: http://getsatisfaction.com/eternagame... - compare quads 15-16 with 74-75 for an example of what I mean.
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Thanks, Dicey! Thinks this will help clarifying the strategy.

Also I should include this picture for reading direction in more complicated designs, that Edward Lane wished for earlier.

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Thanks for that diagram Eli, it means the leftness is not quite the correct terminology for puzzles with more than one multiloop

in my opinion the leftness rule means that stacks that join 2 multiloops would be read both ways around and thus cancel each other out.

So I'd read this as saying "don't count any bases in the stacks that join a multiloop at each end when applying this rule". I guess that might also apply if there are multiple stacks leading to multiloops off the the Hook.

but I guess that would be the Ed variant of the Eli watch rule :)

oh and incidentally feel free to call me Ed or Edward - you don't need to say Edward Lane all the time - it makes me feel very formal, that's just the Facebook login giving my whole name :)
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Eli Fisker

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Ed, thanks for your comment. As you rightly suspected earlier, the more complex shape changed the rules about left.

Now it has become clear that what I mean, is that the left is depending on the reading direction of RNA. That means for all other places than the neck, "left" will be the second strand in the string one passes through, if one goes through in the reading direction. From nucleotide 1 to the last one.
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now that is a definition that I can't poke holes in - even if there are multiple necks that seems to still make sense :)
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Now it has become clear that what I mean, is that the left is depending on the reading direction of RNA.


I don't think left and right are precise enough to explain which strand and which pair is meant, especially seeing how these can be mirrored (if you imagine standing on the other side of the image it would mess with your head; even the natural mode sometime swaps/mirrors in mispairing-motion). Also keeping in mind about that these are actual 3D strings and loops, "left" and "right" would prove disastrous for description.
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Eli's "left" appears to be defined thusly

The second strand of nucleotides in the stack one passes through, if one goes through in the reading direction. From nucleotide 1 to the last one. Except in any neck (a stack or series of stacks off the hook prior to any multiloop) where it's the first strand.

(I think)
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Thx, Ed, didn't see your comment before I posted mine below, sometimes my net freeze.
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I will go with what Starryjess originally suggested. She suggested I used the term strand to explain this.

Strand means nucleotides in a row – like strawberries on a straw. It takes two strands to make a string.

So in a string there are two strands. Here if following the RNA reading direction through the design, this means:

Read only color of base in GU-pair, when going through the second strand in a string. Except in the neck – there read first strand.
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That's much better. After 2 hours of debating where left and right is, lets put it in editor sequence terms =p

Starting with the first open bracket (exclude all free bases) count only for the open brackets until n (n being the number of pairs i.e. "()"'s ) after which count only closed brackets to end. Test if GU, see if U or G and so on. I'm still for excluding GU pairs that seem to have turned for energy circumstances (towards optimal quad orientation) =P
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I think you might get slightly confused using that definition if you have a structure that looks like ...((((...))))..((((...))))... - which is why I went for my definition above - It probably can be written in terms of open and closed brackets but I think it gets complex
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TLdicey

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You blocked me from updating my post:

That's much better. After 2 hours of debating where left and right is, lets put it in editor sequence terms =p (I'm sure if paramodic was here he'd explain it with the help of Eli's arrows as vectorial towards the "centre of gravity")

Starting with the first open bracket (exclude all free bases) count only for the open brackets until n (n being the number of pairs i.e. "()"-s or total "("-s or total ")"-s) after which count only closed brackets to end. Test if GU, see if U or G and so on. I'm still for excluding GU pairs that seem to have turned for energy circumstances (towards optimal quad orientation) =P

I just meant it would be easier to think it that way (sequence) for proposing it to the strategy market with penalizations ideas.
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Eli Fisker

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Dicey, I loved your imagined response from Paramodic: ...he'd explain it with the help of Eli's arrows as vectorial towards the "centre of gravity".

That is actually a quite accurate one and easy to remember.
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Eli Fisker

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Ok, now I don't understand. :)

Thanks Dicey, for making me clarify the theory.
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Sometime back in late november, we had a small player competition on getting most GU-pairs into TLDiceys design Crop circles. Brourd won that competition with 23 pairs based on design with 21 done by Freywa. TLDicey, Flashback, Edward and I, got 20 in.

Dicey sent me Brourds solution. That made me see following pattern in the 3-3 loop. A a way to get more GU-pairs in, is to swich side with the GU-pairs and let boost side switch side too. My gu-challenge post have notning about 3-3 loops, and mostly is useful in designs with long arms. Blue to the right, will mostly work in multiloops, where the stacks are not adjacent as here. I starting to think like this with GU-challenges, the red really wants to avoid itself. And it sort have a habit of wanting to be on the "outside" of the puzzle. I'm starting to think there is more than the one pattern I found so far. It will depend on the shape of the puzzle and of how pressured it's multiloops are.