Energy, structure and symmetric colors

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I been talking with Chaen and Mat about D9's puzzle Cinq de Mélange which was made out of elements from 5 successful puzzels.

It actually synthesised better than the individual parts it was made from. But it's arms(strings) does not look totally foreign. Most of them are in the same ”mood” of color.

I think I noticed a tendency in player and robot puzzles.

In the robot designs something totally different can be going on in each individial arm. The robots don't seem to be aware, that this might be a problem. I've been seeing this strategy among players too, but not to the same extend.

We tend to make our RNA-puzzles arms more similar to each other. It's a general player tendency, at least for the good ones. Maybe it's a thing called aestetics :)

Similar that is in color and patterns, so you don't have an arm with mostly green-red, one with mostly yellow-blue arm and blue-red. (Or where the main impression is green, blue or red)

The good players tend to make their arms/string similar, but give the patterns in the arms a unique twist, as an arm have a nasty habit to pair up with an other if totally identical.

In a good design the individual arm is not a copy of another one, rather a bit like mirroring one of it's neighbours. (This might be the reason the GC pairs in the innerloop in the bulged star ended up pointing in different directions. But because of the small loops stabilizing the general structure, there weren't a severe punishment for doing so.)

One thing I also think I noticed is in a puzzle with four arms, that it seem to be okay if arm 1 and 3 are identical to each other, and arm 2 and 4 are identical, if 1and 3 are a little different from 2 and 4.

If the arms are too different, the puzzle tend to do bad. Why does too different arms seems to cause a problem? What is the cause of this?

I think it might have something to do with the different energy levels in the arms, creating an unbalance in the puzzle as a whole.

An arm with mostly green-red pattern have a very different energy level from a blue-yellow arm
That causes the energetic unbalance in the puzzle. A strong string one place have a tencency to make a week spot crack open another place.

Even in a really good design, if you have 2 weak spots and strengthen just one of them, it can crack in another place. That is what I think happened in Mats Branches V 1.1, 85% design. (the two GC basepair 34-45 and 60-71 are turning in a different direction than the others) The strengthening of one arm is visible in the higher energy level (lower negative number) in arm 34-45

I put both Mats 85% and 90% design through RNA secondary structure prediction, the picture displays the energy of the different strings. I played with this tool before, but dumped it til now, because it didn't make sense – made the correct structuredrawing of the highest scoring candidates in The star and the bulged star. Maybe it doesn't like the big inner loops. It don't like One bulged cross either. But its been doing better with the branches, and what I needed it to do here was display my point with even distribution of energy.

Mats Branches V1.1, 85%

In these two pictures compare arm 60-71 and 34-45)

Below is Mats Branches V1, 90%. Here the energy is more evenly distrubuted. I predict that the energy level in the neck, might need to go a bit down.

For a design to be succesful, I think there need to be some sort of energy balance.
so if one arm has a energy of -8, then its symentrical oposite shall have around the same energy level. (At least in these symetrical puzzles, where the arms are of the same length)

Let me hear what you think about this.
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Eli Fisker

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Posted 9 years ago

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Jeehyung Lee, Alum

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This is an incredible hypothesis - thanks for sharing this Eli!

Just forwarded this to dev & synthesis team members.
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Matt Baumgartner [mpb21], Alum

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Wow, this is a great analysis! We will definitely be looking in to this.
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Adrien Treuille, Alum

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Hmm... This is very interesting. I wonder how we can test this hypothesis, or apply it to the latest lab puzzle?
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Eli Fisker

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I mentioned this post Energy, structure and symmetric colors to Stlnegril9 today and he later mentioned it in chat. And it got picked up that the score I mentioned on the designs, didn't match the score that is in lab now. Turns out there has been a later update on the labscores, as the lab was re-synthesized. This is great for Mat's designs as they did even better, but it reverse the order of the designs compared to what I did say. Now the designs are both winners and they are both in very close range of each other.

Score before: Mat – Branches V1.1 (85%), Mat – Branches V1 (90%)
Score now: Mat – Branches V1.1 (97%), Mat – Branches V1 (95%)

Comment on the design score reversal. I don't think this means the main thing I said is wrong. I just went with the evidence, for what I already saw. I think even energy distribution still holds on average, though my evidence for it is propably flawed.

Thanks to Brourd and Mat for picking up the scoring differences between past and precent.
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I thought this document was very helpful. Beyond Eli's concept on symmetry, it helped me learn some tools and think about total energy across 'structures'. Reading the document and then playing with the designs in EteRNA and GeneBee helped think through the concepts. However a newer player (like me) may find it difficult to follow for a few reasons that I wrote down:

(Note all of this is likely very obvious to experienced persons, and, being new to this, may include some incorrect guesses on my part.)

1- It wasn't obvious that the images in the document came from GeneBEE, although Eli had a link and referenced GeneBEE. Anyone who had generated an image in GeneBEE would recognize it as such. If the links to the puzzles worked, simply 'Copying the current Sequence' in EteRNA and pasting to GeneBee to Submit would create the same image. A few issue made that harder to follow.
2- The URL Links to the 2 example puzzles don't work (the website at time of publishing Eli's document has changed)
3 - One could guess the puzzle/lab design from the IDs in the URL of Eli's document, but the 2 names in the document ("Mats Branches V1.1, 85%" and "Mats Branches V1, 90%") don't match the lab. The "%" numbers are lab synthesis results and because they re-ran those labs the % changed slightly.
4 - Even after finding the correct puzzle/lab designs, a few minor notes on why EteRNA won't quite match Eli's images from GeneBEE:
a) GeneBEE flips the model mirror-image and also rotates the orientation of the puzzle
b) GeneBEE energy calc's are slightly different

# 3 is what Eli just explained above.
"Mats Branches V1.1, 85%"

"Mats Branches V1, 90%"
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Eli Fisker

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Thanks for your additions, Stlnegril9. I think it added value to the post.

By the way, I should have mentioned that I first later found about the energy differences between Eterna and Genebee, but I should have linked the article to this one. So thanks for pointing it out. Here it comes:

Something loopy

Another post have relevance to Energy, structure and symmetric colors too. I predicted that neckarea probably would need a lower energy concentration. And this post has a comment on that.

Energy in neck area
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Eli Fisker

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Even energy distribution - energy equilibrium in the RNA structure

I was watching a Khan Academy video on an unrelated topic, when it got me thinking about Even energy distribution in RNA’s.

Quote from the video:

“If you stress an equilibrium in any way, the equilibrium moves in such a way to relieve the stress.

I think an RNA sequence when folding, seeks towards an equilibrium of a fairly even energy distribution across the design.

And when highly uneven energy distribution is introduced in one place of the design, it puts stress on the system. And when stress is added, the RNA seeks to regain its equilibrium of an even energy distribution by regrouping its stems - which results in a structure that is different from the wanted target structure that one was attempting to form.

If overall energy in the whole design gets too negative per base pair content, the RNA will restructure itself to a less pressured conformation = avoiding too many short stems with too many GC pairs, by regrouping and forming less GC intensive stacks elsewhere. So if there are A’s and U’s present in loop areas, those will get involved in stem area. (Pressured designs are hard to solve)

Similar if the overall energy for the whole design is too far moved towards positive, the RNA will restructure itself if possible = avoiding too many stems with too much AU, by regrouping and forming more. So if there are G’s and C bases present in what was supposed to be loop area, the design will regroup itself to make them appear in stem area. If there isn’t it will make very long stems of AU’s or not bind up at all. (Weak designs are hard to fold)

However there may be some kind of sections in RNA that may be less affected by an uneven energy distribution. The hook area between main design and barcode, seems to act as a buffer zone at times. While it is generally not recommendable, it is very well possible solving a design and then attach an all GC or all AU base pair barcode.

RNA seems to dislike uneven energy distribution at local spots like stem, uneven energy distribution between stems themselves, uneven energy distributions between stems of similar length, and too much negative energy overall in the whole design or too little.

I think RNA designs have an optimal equilibrium when it comes to free energy. They have an optimal range for a specific structure with stems of a particular length. And if that energy level is either too high or too low, in relation to that particular structure, one is not going to get the target structure one is aiming for.

Background posts

Even energy distribution in RNA designs

Energetic Pressured designs