Area to discuss Switch puzzle analysis and its relation to lab

Eli_Fisker · January 16, 2018, 9:13am

This is a forum area to discuss switch puzzles and their relation to lab.

This discussion sprang out of a discussion between Cynwulf and I on switch puzzles that I shared the other day. I put it up at the OpenTB lab while it didn’t really belong there. Omei suggested it getting an area on its own. So in the style of Gerry Smith I hereby name and start the discussion.

Here are what fine insights Cynwulf allowed me to share on his behalf on making of switches.

Switch puzzles relation to switch lab

Cynwulf, switches and repeat sequence

Get your switch game on!

Eli_Fisker · January 16, 2018, 6:50pm

Number of potential states for a switch puzzle

Cynwulfs puzzles and question got me inspired.

He asked the following question:

“I would imagine that there is a proportional correspondence between the number of possible states and the number of shapes you can make with a sequence of length=N. But HOW MANY could you have AT ONCE? I am not sure how to answer that.”

Cynwulf earlier wrote this answer to Astromons question about if real RNA could have 6 states:

Including the standard modified RNA bases and REAL RNA has potentially N^10 states where N is the length of the sequence.

Thus for the puzzle above there could be ~374^10 =53544642343907161646949376 states the RNA has a chance of being in at any time.

For the more standard simplified 4-base RNA model the equation becomes N^4, or 374^4= 19565295376 states the RNA has a chance of being in.

These States are similar to the distribution of electrons about an atom. That is, there are very many potential states, but there are only a few states which the system inhabits most of the time.

Because there are certain states which are more favorable and thus occupied more of the time than not, we speak of states. In the case of electrons these states are realized through the electron orbital models and for RNA secondary structure prediction we refer to Folded States.

In both cases these states do not represent absolutes, but rather model the probabilistic nature of the system being considered.

When we use algorithms to model RNA folding, what the shape folds into is calculated to be the most favorable state and thus the one in which we would expect the RNA to be found most of the time, but the RNA itself is constantly changing between states, only spending nanoseconds at a time in most of them.

The Ligand also does not bind and stay bound (unless specifically designed to do so), but rather forms a bound complex with the RNA that again persists based on the probability of this interaction occurring. While bound the ligand increases the probability that the RNA will be in certain states.

If without the ligand the RNA would be in the State-1 conformation 80% and in the State-2 conformation 15% of the time, then perhaps the ligand would (when bound to the RNA) attenuate this ratio to 55% for State-1 and 35% for State-2.

14 Mar 2017

Eli_Fisker · January 16, 2018, 6:55pm

Multiloops and internal loops as switch junktions

I have been thinking about if Cynwulfs question may get easier to answer if it gets reformulated or simplified.

jandersonlee mentioned the multiloop as a potential structure in relation to get a structure switch.

“Extrapolating more from the paper might suggest that using a multiloop as part of a switching juncture (hinge) could be useful.”

I suspect it may be easier to answer this question, if more limits are put on the question. Eg. to what amount of states are possible when given the following limits:

The structure gets repeated
The sequence overall gets repeated
The sequence and the structure are of the same length

Switch puzzles counts as answers. Hint for Cynwulf.

Number of switching stems in multiloops and potential amount of states

I have found myself wondering about the relation between numbers of multiloops and numbers of states, for switch puzzles that have both repetitive sections of structure and repetive sequence.

Here I’m thinking about puzzles made out of pure repeat structures. And solved with repeat sequence for those repeat structures.

Basically what are the relation between stems in internal/multiloops and number of possible states?

Here are some rough guesses. They are by no means final. I would love to see more puzzles like Cynwulfs, looking into things like that.

Internal loop - two switching stems - two states
Multiloop - three stems - two switching stems - two states
Multiloop - four stems - three switching stems - two/three states
Multiloop - five stems - four switching stems - three/four states
Multiloop - six stems - five switching stems - four/five?

For now there seems to be a limit to how many states a puzzle can have and still use repeat structure and sequence.

Eli_Fisker · January 16, 2018, 6:58pm

Different state limits with different switch elements?

Now switches can switch over less than a multiloop. They can switch over an internal loop. Similar, just because there are multiloops in switches, don’t mean that all their stems are taking part in the switch. Hence it is useful separating the stems counted into switching stems and static stems.

Different amount of switching stems per multiloop may vary when there are many loops. As in the below puzzle, the multiloops closest to the center has the largest amount of stems and switching stems.

Cynwulf puzzle example. The red numbers in the multiloops accounts for the number of switching stems in the multiloops.

Switchiest Switch V

The function of static stems in switches

There are limits to how many stems can be in a multiloop before the multiloop will rather form some other structure. At least for lab. I suspect that simulations will pass more. At least for single state puzzles we have been capable of making sun puzzles with an unrealistic amount of stems in a multiloop.

Example of multiloop with three stems. Two of them switching. Two states.

Now I wonder if not these 4 ornament sections - that are not involved in the switch - could be replaced by just a longer and static stem. I suspect their only function are to be domain separator between the identical structural and similar sequence domains in the switch and prevent them from pairing up with each other in an unwanted/uncomplete structural manner. (Any manner that destroys the structure repeat.)

I suspect at some point there will be a limit for how many repeat structures one can have next to each other. If they are to be of the same structure and with repeat sequence.

Number of multiloops as state limiting factor

The number of states possible may also depend on the number of multiloops present that can pair up with each other. And how they are connected to each other.

Here are a 5 state puzzle by Cynwulf made of 4 states made with 4 identical multiloops that each have 3 switching stems and 1 state where an internal loop break up one multiloop and the whole puzzle becomes a snake form. I have given each multiloop a yellow dot for highlight.

Eterna and fugue 5 state

4 different multiloops with each 3 switching stems (4 identical switch motives) gives 4 state. An internal loop added gives an extra 5 state. (And breaks the multiloop pattern)

I think there may be a limit of how high one can go in number of states while still keeping an identical structure. Now I wonder, if state 1 was made with a multiloop instead of its internal loop, could the puzzle get to 5 multiloops in 5 states?

cynwulf28 · January 16, 2018, 11:33pm

A lot of information to digest, thank you for starting this thread. I had been talking with wwei23 about switches and states at the same time that we were beginning to talk about all of this and he has created a number of puzzles which address at least one question… for an RNA sequence of length N, how many different states can you create from a single sequence? If you haven’t seem his many-state puzzles yet I’d check them out. I think that his puzzles suggest some of what we are likely to find on larger scales.

Eli_Fisker · January 17, 2018, 10:44pm

Np Cynwulf and thx for inspiring the thread into existence!

I had been out of the puzzle solving business in general for a real long time. Mainly because of lab. Just did a couple of puzzle here and there, namely switches.

However I did noticed Wwei23’s multistate puzzles. He has set new standards in Eterna for how multistate a switch can be.

I have a few observation on them so far:

Just because 9 nt two states can solve together, don’t mean they will both be legal for the 9 nt multistate puzzle with max amount of alternative states.
The more states, the smaller structure movement in space?
The more states, the more repetitive the base sequence (less base variance)

Why not all 9 nt states are solvable in one big multistate puzzle

For now Wwei23 is testing the limits of how many states there can be in one 9 nt puzzle. So far he has hit 22. (Said for the benefit of the others who may not have found the series yet).

His latest puzzle in the series got me wondering.

I found a structure not among his 22 states: (((…).). (There are several - not all of them could be made stable with the aptamer molecule in the puzzlemaker).

This one I suspected would not work in the full puzzle. So I made a two state puzzle of it. To show that the structures could be solved.

However this puzzle is not solvable in pure magnet segment style. With pure pyrimidine at the first half of the puzzle and guanine at the last. The sequence that the first state in the above puzzle crave, will not fill the full multistate puzzle of Wwei23. So not all potential 9 nt states are possible for 9 nt switch. At least not all together.

So basically I think there can be made different multistate series over the number 9, not all of them compatible. Not all of them holding the same amount of states. The more multistate, the more they need to be willing to share a repetitive sequence. The more states, the smaller structure movement in space?

Number of domains and amount of states

So far 9 nucleotides are only enough to make a single stem at a time. There are no double domain possible.

I suspect that when we get a multistate puzzle long enough to harbour two stems, that the amount of states possible between the two domains for a moment will jump down in numbers, for the shortest puzzles with a length that allows for double domain.

As the two stems would also put state limits on each other both for structure but also for potential solving sequence. Just as the two strands and the sequence in them, in a single stem 9 nt puzzle do.

Domain size and symmetry folds

Cynwulf has also been thinking about domains and the size of them. But opposite to me, from the larger end of the scale. I bring it here as I like it:

“I made this puzzle with two goals in mind. The first is to show a quirk of symmetries which arise from the sequence itself. In many of my previous Switch puzzles I used sequences which had symmetries of the order 2^n, that is, they had symmetries which were 2-fold, 4-fold, 8-fold, etc. This is why many of those puzzles were ~400 bases long, because that length allowed for ease of use for creating switches of the type just mentioned. I should say here that the symmetries I speak of are part of the sequence, but also can be seen in the way the RNA folds. This emergent symmetry of the structure rather than the sequence is something which I always try to convey in my puzzles.

While puzzles with the desired symmetries are easy to make for symmetries of the order 2^n, other orders of symmetry present challenges. I can certainly create a sequence with the desired number of symmetries, but when the RNA folds, often these symmetries fail to translate to the overall design.

I have two thoughts on why this is. Firstly, the RNA may have a natural proclivity toward lower order symmetries. That is, if I make a sequence with 12-fold symmetry, the puzzle is likely to fold into 2 or 4 structurally-symmetric domains rather than 6 or 12 such domains. Another possibility is that the number of bases I decide to use affects the ultimate symmetry of the puzzle. For instance, if I wanted to make a puzzle with 3-fold symmetry, using 90 bases for the puzzle or even 150 bases would more likely result in 3 distinct structural domains than if I were to use 360 or 480 bases as there are more factors which can divide into these larger numbers and thus allow for the greater likelihood of alternate symmetries being displayed in the structure.”

Playground department

Now it is unlikely to be realistic. But I couldn’t help but muse about a potential prime number system responsible for the amount of possible states per number of nucleotides. Given there are fractal patterns in prime numbers. And RNA is fractal in nature. I suspect in particular so for the switch kind.

Prime image list found in Wikipedia.

Actually I found something even better. An image visualization of prime numbers. It is seriously beautiful. It almost looks like the bow arc view that RNA sequences are sometimes displayed as. It also reminds me of Fibonacci structure.

Infographic: Visualizing Prime Numbers, For People Who Suck At Math

Enjoy! Hope this will inspire something. Puzzles most welcome. Even if I can’t solve them, I can still enjoy the switching view.

Eli_Fisker · January 18, 2018, 10:29pm

Cynwulf made me capable of this…

Armed with the advice Cynwulf shared on switch puzzles I managed to pull something I would never have thought myself capable of.

Those who know my puzzles, know there aren’t many switches among. I haven’t been the best of friends with the switch maker. My latest attempts are still baby steps, but I’m proud I made it this far. Thx, Cynwulf!

As I hope this will help other like me who struggles with switches, I will try show some of my steps towards getting there along with some images

Inspired by Cynwulfs source of puzzle inspiration, I picked a random viral RNA sequence.

First I looked at full viral RNA genomes. But they were way too long. The shortest sequence I could find was 230 nt. Which was also too long as I wanted something that sparked repeats.

Then I thought, perhaps a gene in a virus. Then it hit me. Viral capsid protein. I wanted the mRNA for that. Because that is a repeat structure when expressed as a protein. And it would be way shorter. I searched the internet and found small sequence that fit the bill of trying to make a switch puzzle with structural repeats.

This is the exact sequence:

GUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGG

This is the paper I lifted the sequence from:

Nucleotide sequence of 5’ terminus of alfalfa mosaic virus RNA 4 leading into Coat protein cistron

The viral capsid protein comes from this specific virus: Alfalfa mosaic virus RNA 4.

How to create a switch puzzle Cynwulf style

I picked a real long puzzle. I sorted all the puzzles after length, went to some of the last pages that didn’t have puzzles that were longer than the normal 400 nucleotide limit.

The puzzle picked was a Cynwulf one, Texture E of the gothic letter E.

I pasted in the sequence 6 times - enough for it to fill the puzzle up. I got this rather pretty structure despite it was not fully repeat structure.

http://www.eternagame.org/sites/default/files/chat_screens/8627_1516303760.png

Here follow the story of how I got to it.

Paste sequence into puzzle:

GUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUAC

Now it looks like this and have the shape of the original puzzle.

http://www.eternagame.org/sites/default/files/chat_screens/8627_1516307276.png

Switch to native state.

Beam the puzzle to the puzzlemaker (Right click in the puzzle and choose the Beam option)

Notice the puzzle is now stable in the puzzlemaker.

Actually I didn’t get it stable that easy when I first tried it out. I only figured this step by accident.

What I did earlier was beam the puzzle to the puzzle maker, while it was still unstable. So I beamed the puzzle while it was in the target shape. That meant it turned up unstable in the puzzle maker. Then I had to do these extra steps:

Switch to native state

I deleted the last base directly in the puzzle with the Ø button. (While taking note of which base went missing.)

Then I added in the missing base last in the dot bracket field.

And lastly I filled in that C base at that last base, to make the puzzle stable. Now the former native state is the target state.

Back on track with making a switch puzzle.

Now I open a new window with the same starter puzzle. I repeat the process, until I’m left with another stable target structure.
I make a weak base somewhere I want a switch. I changed the marked C to a U.

The structure goes unstable

Now how I did it first time was to do all the thing with base deletion again. Until I had made the new structure into a target structure. But the easier way to do this is to do the following.

Copy the puzzle sequence. Open a new window with the same puzzle. Dump the sequence there. Put the puzzle in native mode. Beam it to the puzzlemaker. And its stable.

Now it is time to pull the puzzlemaker. It can be find at top of the page where all our player puzzles also are.

Copy in the structures from the puzzles that holds the structure of your new switch

Structure 1:

…((((((.(…(((((…)))))…)))))))(((((((.(((((((…((((((.(…(((((…)))))…)))))))(((((((.(((((((…((((((.(…(((((…)))))…)))))))(((((…(((((…))))).)))))…((((((.(…(((((…)))))…)))))))))))))).)))))))…((((((.(…(((((…)))))…)))))))))))))).)))))))…

Structure 2:

…((((((.(…(((((…)))))…)))))))(((((((.(((((((…((((((.(…(((((…)))))…)))))))(((((((.(((((((…(((((.((((.((((.(((…))))))).)))))))))…((((((.(…(((((…)))))…)))))))))))))).)))))))…((((((.(…(((((…)))))…)))))))))))))).)))))))…

Add in the sequence of the second or first state and solve the puzzle. By adding the molecule where instabilities are and if needed changing bases also.

Sequence

GUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUUCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGGUUUUUAUUUUUAAUUUUCUUUCAAAUAC

I marked all the bases that were involved in change.

Now onto publish the puzzle.

Now I could have made this puzzlemaker tutorial showing just how things went fine all the way. However I decided to show as I actually did. This was what happened the first 4 times I attempted making a switch puzzle this for me new way. But assuming I’m not the only one getting stuck, like this I shall show exactly what happened.

Sigh!

New strategy

I took the original viral sequence. Added 1 A’s in front of it and 1 A’s after it. The hope was to get a structure that would not overlap so much,.

UUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGG

A GUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGG A

I had to try with different amounts of A’s around the original sequence. I made it with 1.

But now I have luck.

Here is the proof. I just changed one base to get the unstable structure in second state. And adding in the molecule there allowed me to revert to the original sequence.

Alfalfa mosaic virus RNA 4 - Dedicated to Cynwulf

I had tediously locked up most bases in the earlier puzzle that I thought would pass. I got an overlap message. And I forgot to lock the bases in my new version that did pass.

To make up for this I share how you can solve it. Paste in this sequence. It will give you a sense of the switch. Only thing you need to do is to stabilize base 265.

AGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGAAGUAGAAAAAAAAUAAAGAAAAAAAGAUAAUAAAAAAAAAAUACAAACAAACAAUAAUGCUGGUGGGAAAGCUGGAAGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGAAGUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUUAUGAGUUCUUCACAAAAGAAAGCUGGUUUCUGACUACGCGCUUUUUAUUUUUAAUUUUCUUUCAAAUACUUCCAUCAUGAGUUCUUCACAAAAGAAAGCUGGUGGGAAAGCUGGAAGUUUUUAUUUUUUAUUUUC

Eli_Fisker · January 19, 2018, 6:56pm

Repeat structure and repeat sequence in switches

Cynwulf has made a fine example puzzle.

Switch XLIX: Tying the Sheepshank

Here is his puzzle description:

“In this switch I take advantage of the properties of the sequence used in order to create a switch with a specific feature. In this case, a repetitious motif allows for the switch to be doubled up on itself in a style similar to the knot mentioned. I have locked the core bases which essentially means that this switch is solved for you ahead of time. In watching how this design switches, note which sections move where. Also, keep in mind that there are MANY opportunities for alternative designs due to the number of places the ligand may be placed. Feel free to play around with this switch in puzzle maker, I’d like to see what comes of such an experiment :-D”

I did play around with it and got two different and stable switches - that was untill I got bitten by the structure overlap monster…

Playing repeat sequence on repeat structure to ease solving

Here is how I solved it:

The way I went about it was putting the puzzle in second state where the core motive is on display. Then I practically repeated it on to every similar structure section and the rest was a question of filling in matching bases in state 1. I think I managed to solve the puzzle keeping all these core sequence repeats identical to the original middle motif in state 2.

Cynwulf confirmed my suspicion and even better said that this could be used for all his earlier puzzles of that type.

“All similar puzzles share the elegant simplicity of sequence you have described…though there are likely to be alternative methods of solving these puzzles, there should always be a way to solve using simple repeating patterns.”

But do the bots know?

Now I wonder. Solving repeat structure with repeat sequence is a handy shortcut, that human puzzle makers as Cynwulf has used and human puzzle solvers like me can make use off.

But I strongly suspect that the bots won’t see the pattern. That could stand for a test…

So my questions are these. Are the bots capable of solving switch puzzles like this one, and if so, are the sequence of the solves as pretty and repetitive as Cynwulf made them, and some of us solved them?

Basically are the bots capable of solving this kind of switch puzzle that:

Is 2 state+
Is a symmetric switch
Consists of repeat structure
Is made with repeat sequence

And do bots solve with repetitive sequence also?

How do the bots behave on switch puzzles?

That question I can’t really answer for now.

Back in the early Eterna days, we could see how 3 different bots fared on our single state puzzles. If they got stalled or not.

Which allowed us to make puzzles just to test if we could stall the bots. We got pretty good running around corners with them, and tripping them up.

It would be nice if we got the bots back on solving puzzles. So we can get an idea what are difficult for them.

How did ViennaUTC do?

To get at least some idea, of bot capabilities with switches, I dug up the list of what puzzles Nando’s bot Vinnie has solved.

I searched the list of cleared puzzles by number of states.

Now I don’t know the names of all of Cynwulfs complex switches. But it looks like the Vinnie has not taken many of these designs down. No surprize there. They are super hard. Probably not just for humans.

Here is an overview of what Vinnie has solved of switches up till this moment:

3264 puzzles with 2 states

228 puzzles with 3 states

4 puzzles with 4 states

2 puzzles with 8 states

Which is pretty good.

It seems there is a steep curve when it comes to more states. The more states, the less likely it has a solve.

@Nando, is Vinnie still running? The puzzles I see in its list don’t seem to hold any of the most recent puzzles.

cynwulf28 · January 20, 2018, 11:12pm

I would really like to see how the bots do against simplified versions of the switches that have already been discussed here. Perhaps after Open TB :-D

As for the drop off for the Bots solving puzzles…I believe this to be true, that their success in solving switches drops off with the number of states, however…we must make sure that we don’t forget the relative number of switches of each state for there is also a decrease in the number of puzzles the higher the number of states. I think that in order to confirm a trend we must factor in the population of puzzles of number of states n and then run standard statistical analyses to see if the values obtained are significant. Ultimately to get an accurate view of the situation many more puzzles with n>3 states would need to be made.

Currently there are 5177 player-made switch puzzles, of these 4053 (78%) are 2-State, and 1067 (21%) are 3-State. Thus 99% of all puzzles are 2 or 3-State switches.

Eli_Fisker · January 22, 2018, 9:56am

These are good points.

The solving percentage around follows the amount of puzzles in a state category for now.

There may be another way to go about this than make many more puzzles. This is something I have been thinking about recently.

Eli_Fisker · January 22, 2018, 10:31am

Can switch puzzles be split up into puzzle types?

Switches don’t all pull a switch the same way. Just to show an example I picked two of Cynwulf’s puzzles.

Some puzzle types covers the switching central point up inside the puzzle like this puzzle. I have marked the start and the finish base in the puzzle. That starting stem is static.

Where for the below puzzle lay the switching central point bare in state 1. It switches across two of the necks for one of the other states.

Mandala

I wonder if there is a hidden potential fourth state in this puzzle? And perhaps also a 5 and a 6th?

Different kind of lab switches

From lab we know there are different puzzle types, just depending on the inputs. And many of them can be combined

Switches with aptamers
Switches with RNA inputs (microRNA, biomarker inputs, etc)
Switches with MS2

Just to mention a few.

Different kind of single state puzzles

Also just for single state puzzles there are different kind of puzzles. Here are a few of the types.

Puzzles with special elements (like loop next to a multiloop, zigzags)
Puzzles with repeat elements (2-2 loops)
Puzzles with repeat structure (Snowflakes)
Puzzles with short stems
Puzzles with long stems
Puzzles with equal length stems
Snowflake puzzles (Symmetry over several axis + sequence repeats)
Kyurem puzzles (short stems, similar length, bent and bulges)
Spacebar puzzles

The bots were tested at different types on single state puzzles. As for categories like that.

The bots fared bad at most of these puzzle types (Except the more long stemmed ones) where players in general did better with solving.

For background see this blog post.

Why we need to categorize switch puzzles after their type

The bots did not fare equally well on each single state puzzle type. I expect something similar to be the case for switch puzzles. Just it may be some other things that gives problems. We need to figure exactly what.

Simply sorting puzzles in smaller categories of similar type puzzles will make it easier to see exactly what type puzzles the bots tends to get in trouble with.

Not all switch puzzles are going to be equally hard for bots to solve. Hence we need to categorize the switch puzzles after type, to show what type of puzzles bots tend to get stuck on. Are they the same as humans? From what I have seen so far on switch lab puzzles, the answer is no. Just as it was the case for single state puzzles.

Here are some different kind of switch puzzles. There are overlaps between single state and switch puzzle types.

Different amount of states
Asymmetric switches
Mirror switches (Jmf and more)
Spacebar puzzles (Will switch bots be just as stuck on these as the bots solving static puzzles?)
Zigzag puzzles
2-2 loop puzzles - and other repeat element puzzles (Wawan)
Small switches versus large (also look at actual number of switching bases)

Somehow asymmetric and very multistate puzzles seems way harder to solve than multistate puzzles with strong repeat structure and sequence. At least to me.

Switch Puzzles with symmetries

This is just preliminary listing. There are different kinds of symmetries and repeats related with switch puzzles.

Symmetry

Translational symmetry
Snowflakes (Mirror symmetries) (Ding and more)
Fractals (Cody, Cynwulf)
Symmetry created by repeat sequence (Cynwulf puzzles)
Symmetry created by structure repeats
Mandala (Cynwulf)
Palindrome sequence (Cynwulf)
Different amount of symmetry axis

Repeat causers

Prime numbers as repeat causes (Cynwulf)
Repeat sequence
Repeat structure

These are just some of the puzzle types. What more switch puzzle types are there?

You who have lots of experience with making and solving switches, what switch puzzle categories do you see?

Snowflakes belongs to the switch world

Back in the static days of EteRNA, we got snowflakes stalling the bot algorithms. The bots had much trouble solving static versions of snowflake puzzles.

The bots weren’t as good as human players to vary the solves, to prevent misfolds.

But on switches with repeat structure and repeat sequence, the bots may need to embrace exactly that and reduce sequence variation for an easier solve style. Because repeat sequence and structure are switch causing features.

Which reminds me, I once did run NuPack on some static puzzles just to see how it would solve them. It made heavy overuse of GC’s. Totally christmas tree style. I ran it on a big symmetric puzzle of the snowflake kind, that had strong repetitive structure and short stems. But it wasn’t a surprize NuPack solved like this. It did the same in labs.

The snowflakes puzzles were the key to identify symmetry as trouble maker for static RNA. Whereas natural RNA switches and our switch lab solves have long seemed to crave symmetry.

Easy memory rule: Symmetry belongs to the switches.

So perhaps these pretty snowflake puzzles really belong more in the switch RNA world than they ever belonged in the static RNA world. That’s if they have long enough stems to not make massive overlaps in our puzzlemaker.

I have revived one of our past single snowflake puzzles and made it into a switch puzzle.

Merryskies Snowflake as switch

Let it snow - The snowflake challenge

Basically I would really like to see both human and bot going about solving switching snowflakes.

In other words, I wish for a blizzard of switching snowflakes.

Let the switching begin…

Eli_Fisker · January 30, 2018, 10:49pm

INFO-RNA - Natural Born Switch Maker

Intro

Futile search for a switch solving algorithm yielded interesting results
Same old bot - new perspective
INFO-RNA is perfect for creating switch puzzles
How to get a sequence back from INFO-RNA
How to make new target states for switch puzzles
Split motifs in groups - benefits switching
Question: Will more single state RNA bots be helpful for designing switches?

Futile search for a switch solving algorithm yielded interesting results

“With the current interest in using bio-molecules in nano-technology, the ability to design artificial riboswitches reacting to changes in conditions will become increasingly important. Hence an implementation capable of solving the inverse folding problem for multiple structures is a key development in structure design.”

https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-13-260

I wanted to know how bots solved our switches. I was searching for energy models with capabilities with solving switches. So far with little luck. At least when it comes to getting a web server. EternaBot has gained switch capabilities for lab, but I’m not aware of it having an interface when it comes to that.

As I was searching for potential switch folding algorithms, my eyes fell on an old EteRNA acquaintance: INFO-RNA. INFO-RNA was one of the bots that were put at solving our single state puzzles.

Just for the fun of it I decided that I wanted to look at how INFO-RNA went about solving one of the snowflakes.

Those of you who have read my various posts about the energy models behaviour on single state puzzles, know that I have been scratching my head about how the bots went about solving lab puzzles and puzzles too. Doing lots of stuff that will not be legal in nature. Or nature as I know it: Lab.

Things that would create misfolds and mean that the static RNA would not fold into the intended structure.

However I have just totally changed my mind on one of the energy models: INFO-RNA.

Same old bot - new perspective

INFO-RNA solved the puzzle with no problem at all. No big surprise there.

When I pasted the letter sequence of the snowflake it gave me, into the puzzle again and looked at it, I got super happy.

I saw heavy GC repeats in a supposed to be static RNA design and as something new I loved it. INFO-RNA had designed a perfect switchable sequence.

Misfold is really just another word for switching.

I decided to do exactly what I had been doing the last week or so after Cynwulf got me real curious about switch puzzles. Try make a switch puzzle of it.

The bot solved with heavy GC repeats. Even the GC repeats were placed in a repetitive manner. Things that I have pointed out as problematic if in a static RNA.

INFO-RNA is perfect for creating switch puzzles

However INFO-RNA would be absolutely perfect for creating switching RNA: All I had to do were clean the loops up a little bit and make a couple of GU’s in the stems to make the puzzle go unstable and I had a new target structure (alternative structure - like a second state) for a switch. This were the start of my switching snowflake puzzles. Except the first two, they are all designed by bot.

In all cases I could simply run the bot on the ground structure, the sequence it spewed out was so heavy in repeats, that I could easily spark a symmetric misfold.

So to get a switchable structure, all you have to do is give INFO-RNA the structure of a single state design that has lots of symmetry and repeat structures. It goes heavily repeat sequence on such puzzles, making them the perfect starter points for making switches.

Sometimes one don’t have to do much more than add in a few instabilities to make a new target state for switch puzzle. Not even touch the loop bases. I just threw in the sequence as is and used the Mutation booster to introduce the instabilities where I wanted them. (I’ll get into detail later of how I did this.) My Saccharomyces Cerevisiae puzzles is one such example.

No promises that these switches will also work in lab. That could be worth a test though.

They don’t harbour my favorite switch repeat sequences: GA and CU rich stretches. A bot could be made to spew these.

Basically I would love to see INFO-RNA with a tiny tweak. It should do exactly the same as it is doing on symmetrical repetitive structures, but with the twist that it changes some of the GC’ pairs to AU pairs. And the C and U’s should line up, and so should the G and A’s. And it would be cool if some palindromic tendencies were programmed in too. That would make for max switchability and complementarity between sub structures.

Plus it should cut down a bit on the G loop boosting as that makes the puzzles too stable. Or practice downboosting. Just a tiny notch. Have enough to make the puzzle stable, but balancing it on the edge of being unstable. Which it already does, but now it is what I like most about INFO-RNA.

How to get a sequence back from INFO-RNA

Here is what I did. I opened INFO-RNA.

I gave it the dot bracket structure for the structure I was interested in seeing a solve on.

(.((((((((…))))…((((((((((((((…((((…))))((((…))))((((…))))…)))))))(((((((…((((…))))((((…))))((((…))))…)))))))(((((((…((((…))))((((…))))((((…))))…))))))))))))))…((((…)))))))).)

I had made a downsized version of Merryskies puzzle, with 4 corners instead of 6.

I set the field Maximal numbers of violations to 0.

I only want a sequence that is an exact solve to the structure I put in, else it may not stabilize in EteRNA. It may not either, as INFO-RNA is neither Vienna nor NuPack - the ingame folding engines. But so far all sequences I have gotten back have made a solve to the structure I had in the first of the Vienna folding engines.

Hit the START button - and wait.

Here is an image of the job output. First I can see what structure the job was run on.

http://rna.informatik.uni-freiburg.de/INFORNA/Result.jsp?toolName=INFORNA&jobID=6956337

My search query (Should expire in 30 days)

Next I get a sequence output that I can lift - In the Direct output for copy and paste field.

Output:

GGACCGGCCGGUACGGCACGCCCCCCCCCCCCCAAUCUCAAAGAGAGGGGGAAACCCCGCGGACACCGCACGGGGGGGUCCCCCCAAUCGGAAACCGAGGGGGAAACCCCGCCCGAAGGGCACGGGGGGAGGCCCCCAACCCCAACGGGGGGGGGAAACCCCGCCGAACCGGCACGGGGGCCGGGGGGCAUCCCCUCAGGGGCGGUGC

(.((((((((…))))…((((((((((((((…((((…))))((((…))))((((…))))…)))))))(((((((…((((…))))((((…))))((((…))))…)))))))(((((((…((((…))))((((…))))((((…))))…))))))))))))))…((((…)))))))).)

Both these structures match up with each other so everything is fine. No violations.

I already had the puzzle in the puzzlemaker. I pasted this sequence directly in the puzzle. The puzzle solved.

https://www.eternagame.org/web/puzzle/8568786/

There is some real heavy christmas tree sequence there. Which is bad for something that is supposed to work in single state lab.

You can get INFO-RNA to output alternative sequences solves, but usually it isn’t necessary as the first sequence it outputs generally use so much GC repeats and place them in such a way that the sequence will fit the bill for being a switch.

Sometimes it adds in a few AU’s as well and then it may be an advantage to hand make these into GC’s and make them follow the general sequence repeat pattern of the GC pairs. The more repetitiveness - the merrier - for switches that is.

How to make new target states for switch puzzles

After I saw the switch potential in the INFO-RNA solve, I did exactly what I have been doing to create switches. I tried out making a few GU’s out of GC’s and plus crossed version just to see if they would spark instabilities and new beautiful symmetric structures.

I started to remove some of the dirty loop bases that weren’t really doing anything and could potentially mess up the symmetry for the new target state. Then I added a few U’s to make GU’s here and there. Or removed some hairpin loop boosts. In no time I caught three new potential target states.

Here is my snowflake catching frog puzzle precursor. Notice the instability in the target icon. Half the puzzle has gone red, which here is a great sign, as it suggest the two branches had made a switch with each other.

Frog target state sequence

GGACCGGCCCAAAGGGCACGCCGCCCCCCGCCCAAGCCCAAAGGGCGGGGAAAACCCCGCGGACACCGCACGGGCGGGUCCGCCCAACCGGAAACCGGGGGGGAAACCCCGCCCGAAGGGCACGGGUGGAGGCGCCCAACCCCAAAGGGGGGGGGAAACCCCGCCGAAACGGCACGGGCGCCGGGUGGUAACCGGAAACCGGCGGUGC

Switching to native state. This is new target state I want to use.

Copy the sequence. Paste it into a puzzle of similar length or paste it to a larger one and delete the extra bases. (as Cynwulf explained to me)

Put the puzzle in native mode. Beam this to the puzzlemaker. And voila, new target shape that is stable.

Then I put both structures in the switch maker for two state puzzles along with one of the 2 sequences and made a puzzle. Which of the sequences you want to use, is probably a matter of taste.

I prefer the one where I introduces the mismatches, as I can then see in my new puzzle, exactly where I put them. I also like to put a highlight marker around the mutated bases in the single state where I made the mutations.

My first snowflake Once upon a snowflake 1 - took real short time to stabilize. Froggie caught a snowflake took me a couple of days. I also had to change a couple of the triloops to tetraloops.

All 3 target states were derivatives made from destabilizations I had made to the original INFO-RNA solve of the puzzle structure I fed it. The new target structures were very fast and easy to find.

Split motifs in even groups to benefit switching and counter bot limit

INFO-RNA has a structure length limit of max 300 bases.

If one plan a structure with 4 motifs, like eg this puzzle, it can be a good idea to half the structure. So take two of the motifs, run them in INFO-RNA and just double the structure in the puzzlemaker again plus add in the sequence twice. That way you not only beats the structure limit, but you also makes sure that there are real good matches between motif 1,2 and 3,4. Because the two groups are identical, they will come with natural attractions built in. Which is perfect for making a new target structure. That’s how I made this puzzle.

Will more single state RNA bots be helpful to make switches?

Anyway, since INFO-RNA is being so helpful making highly repetitive solves on highly repetitive structures, it is really an excellent tool to create additional symmetric and repetitive solves for puzzles in no time. Not all these target states will be easy stabilizing, but just that INFO-RNA spews highly repetitive sequence is real helpful on its own.

Give INFO-RNA symmetric puzzles with repeat structures and it it will spew switchable sequences.

I won’t be surprised either if NuPack should turn out to be helpful on the same account, knowing its tendency to go heavy in GC and to be too high in repeats. Practically all I have complaining about NUPACK and INFO-RNA doing wrong on static RNA, is now perfect for making switches. What a wonderful switch world.

Will Vienna and Nupack be helpful on switches too? Help with figuring that out…

Symmetric switches are much easier solving than asymmetric switches. Even should these bots not be helpful making symmetric switches, they can still be helpful. They may be helpful making hard RNA switches.

Also are there other RNA inverse folding algorithms that will be helpful on the same account?

Eli_Fisker · January 30, 2018, 11:17pm

How to make new targets states with the Mutation Booster

Creating instabilities

Introduce instabilities into the puzzle you intend to make a switch and see what alternative shapes are sparked. This can be done in several ways.

Make a GU of an AU or GC pair in a stem
Make two crossed GU’s
Downboost the boostspots in hairpin loops, etc.

Like a GG mismatch in a hairpin loop will make things go more unstable, same will a UU. Even just unboosting G boosts will often help. Basically U’s and C’s are your best new friends for creating instabilities. These are just examples, there will be multiple ways of doing this.

Downboost 1-1 loops

A UU in a 1-1 loop will weaken the area, perhaps to an extend where a switch will happen.

Find two opposite base pair spots (Symmetry) in two stems. Mutate them against each other.

I used the origin puzzle to play around in, here is a link to the actual puzzle.Noticed the black marker ring highlights. These are the mutation spots. Where I on purpose made the puzzle unstable to provoke a different folding.

You can do this with the mutation booster or by hand. I used the booster until I figured how to do it by hand. You can also let it run over a whole puzzle to see what instabilities may spring. If the puzzle is unstable beforehand this can work well. Generally I find it fastest to spark larger changes by mutating two times two base pairs against each other.

You can also mutate more bases. As long as you can solve the puzzle yourself afterwards.

The above puzzle I did by hand by adding a UU at the one site and a AA at the other site. That will cause instabilities. If you like the shape occurring, copy the sequence and make it a new target. When you have found an alternative structure that you like, beam it to the puzzlemaker.

The background sequence in the above puzzle were just as I had received it from INFO-RNA. Here is that original unmutated sequence.

GCGCCCCCCAAGCCCUAGCGUUUGGGCGUCCCCGUAAAUAGGGGACAUCAACCCCGUCUUCAGGGGUGGGGGGCAGUCGCCCCCCAACCCUAAAAUCAAAGGGGCCCCCGUGUAAAGGGGGCACUACCCCCGCGUAAAGGGGGGGGGGGCAA

Almost translationally symmetry mirrored GC repetition. Cerevisia is born to be a switch

This was the new alternative structure rising from the above instability introduced.

Ways of solving instabilities

I have found the following to work.

Try solve, just as if it was a regular switch puzzle. It is, just with the only difference that you are the maker.
Create a 1-1 loop to deal away with mismatching bases and introduce the molecule to stabilize the newly created loop.

On the later: If you have two mismatching bases in a stem, where you need a base pair and you can’t figure how to solve, then the following will sometimes work. (The stem can be too short for this to work.) Add two single bases beside the mismatching base pair. Delete the mismatching base pair. Fill in the mismatching bases, that will now go into a 1-1 loop where they should be perfectly happy. Things are fine, thats if you are not disturbing anything in the other state/s. And should the new 1-1 loop not be stable on its own, and you haven’t used the molecule bonus yet, you know just where to use it. That’s how I got my Phoenix rising puzzle stable.

Why making a Ground state of the puzzle you want to make a switch of is helpful

You can save several steps while making switches, just by making and publishing a ground state of the puzzle you intend to make extra states of.

Also it will allow you to run the mutation booster in the puzzle. This will allow you to harvest fine misfolds, that will be potential new target states for a switch. That you can’t do in the puzzle maker.

Worked example with the puzzle Binary Star

I took the structure from my ground state for the binary Star puzzle which is taken from mod of Malcolm’s binary star.

I dumped it in INFO-RNA as described in the above post.

Inforna input: (.((((.((((.((((.((((…((((.((((.((((.((((…)))).)))).((((.((((…)))).)))).((((.((((…)))).)))).((((.((((…)))).)))).((((.((((…)))).)))).)))).))))…)))).)))).((((.((((…)))).)))).((((.((((…)))).)))).((((.((((…)))).)))).((((.((((…)))).)))).)))).)))).)

Inforna output: CGCCCCGCCCCAGGGGGGCCAGGAAAGGGGGCCCAGGGGGCCCCGAAAGGGGGCCCCAGG
  GGGCCCCGAAAGGGGGCCCCAGGGGGCCCCGAAAGGGGGCCCCAGGGGGCCCCGAAAGGG
  GGCCCCAGGGGGCCCCGAAAGGGGGCCCCAGGGUGCCCUGAGGUGGUGCCCCAGGGGGCC
  CCGAAAGGGGGCCCCAGGGGGCCCCGAAAGGGGGCCCCAGGGGGCCCCGAAAGGGGGCCC
  CAGGGGGCCCCGAAAGGGGGCCCCAGGGGGGGGGGG

I dumped this sequence in the puzzle.

http://rna.informatik.uni-freiburg.de/INFORNA/Result.jsp?toolName=INFORNA&jobID=5357546

I cleaned the puzzle a bit up, and removed the 1-1 G boosts to help the puzzle switch better.

Then I pulled the mutation booster, marked 4 bases to make sure they would be mutated well against each other. It often takes at least two mutation at once to generate an interesting misfold, aka switch. As with crossed GU’s. Given there are a crossed GC or AU pair there beforehand.

Here is the mutation sequence I started out with:

Starter mutation sequence: CGCCCCACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGAGGGGGG

I put the mutation points at far ends of the puzzle to ensure that I would get a long range switch. Here is one of the mutants I decided to use to create my new target structure.

Notice that the 4 mutations created two mismatches. These mismatches broke the structure and made for a swapping over point. The new shape looked exactly the same.

To watch the new unstable structures created by the mutation booster, swap to native state and go through the mutants. Pick any alternative target state you fancy, to make it a part of a switch puzzle.

New native state

Mutated sequence

CGCCCCACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGAACCCCGAAAGGGGAACCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGUACCCCGAAAGGGGAUCCCAGGGGACCCCGAAAGGGGACCCCAGGGGAGGGGGG

I put this in my Snowflake ground state 2 puzzle, switched to native state and beamed it to the puzzle maker. Then I had my new target shape.

Then I pulled the switch maker and put in both dot bracket structures plus my new mutated sequence. I placed the molecules. I then did a few base changes to stabilize the puzzle and published the puzzle as Binary Snowflake 1.

So it seems the more structure and sequence two shapes share, the more likely they are to switch. At least in simulation. But this is similar to lab.

Apparently if you pick two base pairs at mirroring spots at each end of a mirroring puzzle, you get the puzzle opposite.

The shapes look the same, but the numbers tell on that a switch has happened.

Puzzle solve:

CGCCCCACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGUACCCCGAAAGGGGAGCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGGACCCCGAAAGGGGACCCCAGGGUACCCCGAAAGGGGAGCCCAGGGGACCCCGAAAGGGGACCCCAGGGGAGGGGGG

Solve

I can do this again with a new set of mismatches a different place and get a new switching snowflake in the same style. As long as the mutated base pairs are opposite each other at the same spot and the puzzle is solved in a symmetric manner, I think this will spark a similar structure.

New mismatches

New target structure

Eli_Fisker · January 31, 2018, 1:30am

What makes a RNA switch hard?

Practically the opposite of what works well for switch labs. What works well there are repeat sequence and symmetry.

Things that makes for a hard switch

Asymmetry
Well varied sequence (Lack of repeat sequence)
Large shifts in structure between states (lack of shared structures between states)
Larger puzzles
More states (to a certain degree)
Many small and uneven length stems (simulation doesn’t care about them being too long to ever switch in real life)
Many varied sizes of elements. (That be internal loops, bulges, smaller loops in particular and multiloops too)

This is a hard RNA switch

What will make a real hard switch puzzle to solve, both for humans and bots (I suspect the later too for now) is asymmetry and greatly varied sequence.

Basically sequence that stems from a natural RNA should be a perfect candidate for a hard to switch puzzle or lab. Probably same goes for structure.

The perfect nightmare switch can be made out of a perfect static RNA design structure and sequence. Its asymmetric, it has varied elements size, varied stem lengths, varied elements and varied sequence all in all. Else it wouldn’t be a good static design.

All it takes to make a hellish switch of such a good static RNA sequence is just mutation points are randomly added to it and new target states are made into a switch. Especially if said static RNA is large. And the structure changes between the states are large. That simulation puzzle will be hard by default.

When structure is varied there are no equal regions for touch up and pairing. (Similar size of elements aids them pair up with each other.)

Example from a most beautiful puzzle Cynwulf created. Notice how the hairpin loop and the internal loop that are present in each of the repeat structures, are used for making two such shapes pair with each other for turnoff in that shape.

Despite it being symmetric, there is nothing easy about Cynwulfs large symmetrical switches.

Discussion, cryptography and trapdoors

I have been discussing hardness of switches with Omei. Here comes part of our discussion. Back then there were still no solvers of my switching snowflakes.

At first I thought that my snowflakes would also be hard to solve for humans. (The single state snowflake puzzles earlier were hard to bots, but not humans) Basically I was new to making them switch, so I didn’t had a feel yet. While not yet in huge numbers, players have caught up with most of them. Except for one of my 3 state snowflakes. They are not easy, but they are not impossible.

However none have yet solved my asymmetric switch monsters that were based on structure from a single state RNA puzzle. (IRES_VEGF_A: As nature never intended it) I didn’t even try with the original natural sequence. I don’t even know if the puzzle structure is 1:1 in size with the native structure. Just that the sequence from the solve itself which were varied a lot (not much repeat bases) seemed to be enough.

Tuesday 23 january

eli [3:01 PM]

Sending you a teaser puzzle made by my new method. It took me very little time doing so whereas I had struggled to make puzzles of those shapes I showed you and intended for the 4 state switch maker. They looked so easy to make, as I had their shape, but were trouble when I attempted to solve them. [Note: I was trying to make the misfold in the sequence by hand - it was easy sparking a new target shape, but harder to make a solve also when I had to pre-fit the whole sequence on both states.]

http://www.eternagame.org/web/puzzle/8567161/

eli [8:01 PM]

As I said, I have found a shortcut to make real sweet switches

eli [8:03 PM]

No one has solved yet. But me

omei [8:06 PM]

Hm. This may be a good model of a “trapdoor” function, essential to modern cryptography. It’s a function that is easy to compute, but computationally infeasible to invert, i.e. discover the input from the output.

eli [8:07 PM]

Yes, exactly. I was actually surprised how easy it was designing switches and make them stable, when I had first gotten help on cracking using the switch maker.

[8:07 PM] The hard thing is solving them after the fact. [From scratch]

Cynwulf had to greatly simplify a number of his switches for them to even have my interest attempting to solve. Cynwulf still has crazy switch making skills.

Friday january 26

Small intro that is related to the following discussion.

Cynwulf had put up a puzzle that morning that I think I worked around 1⁄2-1 hour on. I could only get one state stable. The puzzle shape was messy - aka not symmetric.

http://www.eternagame.org/web/puzzle/8570732/

It is long time since I have been so inspired by a puzzle I couldn’t solve.

The puzzle is called Tripping switch, for some reason it made me think of a Tripwire instead.

That said, I am getting more and more thankful for the consideration that Cynwulf shows in many of his complex switches, when he locks up a good part of the switch.

I decided I wanted to make a asymmetrical switch and went back and dug up some of our early challenge puzzles, that were inspired by real and mostly static RNA. After playing around with this and getting some puzzles up I talked with Omei.

eli [1:31 AM] Ok, it is getting bedtime here. But just wish to show you what I managed to make today:

eli [1:34 AM]

I borrowed the bird from Quasispecies, but I made it switch.

The original puzzle was called Phoenix rising. And off with me. Wishing you a good day.

omei [2:18 AM]

Whoa! That’s probably the most artistic puzzle I have ever seen!

eli [11:13 AM]

Hehe. I liked the bird, and it had mirrored parts so I created complementarity between the wings with the sequence I put in. (edited)

I have been thinking about what you said about cryptography, trapdoors and snowflake switches. It turned out that people are able to solve them. Cynwulf must have heard my whisper about him being stalled as he took down several after. Malcolm seem to have a specific knack for them. I think it is not the symmetric puzzles that will be the hardest as the more [shared] shapes there are, the more it will lead back to the original sequence. Because of the symmetry puts a lock on how many possible solves there can be.

eli [11:33 AM]

Just like there are only very limited solves to Wwei23 extreme multistate puzzles. Where I think the trapdoor thing can be true is if one take a big asymmetric puzzle, make a mismatch somewhere and stabilize the new target. It will be hard afterwards to see where the change has been made. It will probably be easy to make, but hard to solve.

I haven’t tried that yet. But I suspect that it will take far longer solving. That could stand for a test. Me back to find some big natural asymmetric static RNA, and play with it.

eli [11:50 AM]

I just did this with a monster of a puzzle. Took me about 5 minutes stabilizing after I had decided on which puzzle and where to put a mismatch. Unfortunately - and fortunately for the rest - this puzzle is way over the 400 base limit. But here is my proof:

eli [11:51 AM]

eli [11:52 AM]

I built it over this puzzle: http://www.eternagame.org/game/puzzle/259159/

eli [12:09 PM]

Because I already had the key - the knowledge of the original sequence for state 1 - plus the knowledge of which base pair[s] I changed in state 1 to get the shape of state 2 - it was fairly easy for me to iron out the small differences that needed to be changed to make the two states both agree with each other. (edited)

eli [5:58 PM]

Basically I’m saying that asymmetric switches will be harder to solve, the bigger and the more states there are.

I have a 3 state monster. Its an asymmetric switch and as ugly as it comes.

http://www.eternagame.org/web/puzzle/8571025/

eli [6:04 PM]

I think the asymmetric switches will be harder, exactly because they don’t share any common structure between the states.

Of cause they can be made share parts, as the sequence may form into similar structures. I however tried to avoid that with those I picked for the switch, as I suspect that would be easier to solve.

[8:38 PM]

The more asymmetric the structure, but also the more varied the sequence, the harder the switch.

[8:39 PM]

Basically static rna sequences are perfect candidates for hard switches.

Structure and sequence wise

omei [8:40 PM]

When you say hard switch, are you including both creation and solving?

eli [8:40 PM]

I mean more solving

[8:41 PM]

Creation is a bit harder when it is asymmetric, but not much. The hell to pay will be on the solver side. Your trap door thing.

omei [8:42 PM]

This does make sense.

eli [8:42 PM]

I still can’t say much about creation difference as yet I’m still rather new to them.

RNA switches, encryption and keys

Today I have been watching some Khan videos about RSA encryption (because they mentioned trap door). I think that the mutation points that I introduce in the ground structure (state1) that gives me a new target - are to be compared to prime factorization. Its a key part.

When one is given only the structure then one has no idea where these mutation points were made.

Thats except if it is a symmetric puzzle. Because then there will be repeat structure and repeat sequence. Repeat structure is also a kind of a key. Just a puzzle having 4 similar parts, is a enormous reduction of complexity.

Just having a section of a puzzle fold in a concerted way is already a reduction of complexity. Something I have gone into for lab switches in the post Christmas snakes.

Plus to create symmetric new targets, I typically place the mutation points in a symmetric manner. Just from the new state one will be able to say something about where these mutation points were more likely to be put. You have no chance of that with an asymmetric puzzle.

RNA encryption with Ribozyme Pistol

I am making a puzzle series that I will use to demonstrate this.

I have made 3 puzzles with up to 4 states. They were easy making. Took me around 5 minutes to stabilize each new state.

First I give the key to the ground state - a repeat of 4 sequences + a specified amount of A’s in between.

For each new state I make, I add 4 changed bases. Sometimes I only change 2, but since they both are in a pair, a pair are affected. So for 2 states there are 4 mutation points, 3 states, there are 8 mutation points, for 4 states, there are 12 mutation points. Each point affecting multiple other bases. Especially because the different states are entangled.

If one takes the sequence from the last puzzle with the most states and use together with the new target, one introduces less spots to stabilize.

The dot bracket structure of RNA can be thought off as a kind of the public part of a key. That in itself put some limits on what sequence is possible, because pairs have to be legal.

I will also put up a ground state of the mentioned puzzle series, as to help the realization that the key sequence alone can solve this. At last in the series I will give the encryption key. Where I lock just my mutation points. Then everything needed to solve the puzzle, is there. Else it will be a hard puzzle despite it has symmetry and is made from repeat sequence.

I will later make easier versions of some of my switch puzzle. For now I am testing my wings. Plus I need real feedback on what is hard or not. I can see that in the numbers of solvers.

cynwulf28 · February 3, 2018, 3:01am

In regards to bot testing for switches, I know that ElNAndo888 has created a number of switches which fit the criteria you mentioned Eli, though he may have already tested them. For example, see this puzzle’s description: http://www.eternagame.org/web/puzzle/4036433/

Eli_Fisker · February 5, 2018, 9:17am

I asked Cynwulf to further elaborate his point to make sure I understood. He was thinking about asymmetry as I suspected. I here bring his comment back.

“I noticed that many of his designs lack any obvious symmetry. Yes, I was hinting at that in the post, also, I thought that his comment about testing switches with bots (in the puzzle description) was worth pointing out, if only for historical reasons…I wonder how far he got with that project… it seemed to be outside of the more general Labs…though I know that many of the older labs were Independent projects managed by individual players…so I am unsure how it fits in with everything else that was happening on Eterna at the time.”

Good point, Cynwulf. Nandos switches do have a lot of asymmetry to them. He sure got Vinnie chewing through a lot of switches.

While I was digging around in the eterna archieves, I hit upon this puzzle maker guide by Nando.

How to create FMN switch puzzles

When thinking about asymmetric switches, as far as I recall, there is a lot of asymmetry in Malcolm’s 2 and 3 state puzzles too. They may not be pure asymmetric as I think Nando’s group of switches are.

There is another thing I wonder about. I suspect that asymmetric and symmetric switches call for different solve style. Ever since I realized about magnet segments and sequence repeats from the lab, I have regularly tried to solve in a similar style in switches.

The asymmetric switches seems to resist my attempt. Malcolm’s in particular. Meaning, they seem to want a more varied sequence solve style. Which is more as what I would expect of a static RNA lab design.

Eg. if I try solve with AU as I typically do first, the puzzle often don’t want to tolerate a lot of sameturning AU’s, but will rather have them like every other base an A or an U. This typically seem to happen for puzzles where there are big structural changes. Where as puzzles with slides, do need a repeat solve style.

Whereas the off late symmetric switch puzzles to a further degree allow for and need magnet segments and sequence repeats. In other words, they behave more as I would expect a lab switch to behave.

Although Lroppy hinted at that I had taken that game a bit too far on puzzles, when I made a variation of your Three way Switch.

Lroppy sent me this puzzle hint:

"Cynwulf’s Three-Way Switch play is actually simpler than what you created in your puzzle Two Way Switch. Like many of your new switching puzzles, I begin by placing one CG in the best energy configuration at the end of a stack closing a multiloop. I then place the Gs up the stack on the same side and do the same for the Cs on their side of the stack. If these placements are on static (non-switching portions) of the puzzle, then I am happy. And if these placements are on a switching portion, I am usually (almost always) presented (in the other states) with stacks that have just one side filled in completely with G or C. I then add then other side, adding Gs to complete Cs and vice versa.
Now - for many of your new puzzles, that is enough to solve them.
However, Cynwulf’s Three-Way has a wrinkle. One (and only one) small section does not solve, but instead shows a stack that is wrong because it shows as CC or GG when I need real bonds. I deduced there was an easy way to resolve this stack - alternating AUs. Add some blocks in the bulges and it was solved.

I hope this helps you get to a solve on Three-Way Switch."

Eli_Fisker · February 5, 2018, 12:04pm

What makes a switch harder or easier?

We have worked on switches for 5-6 years now. The forum is loaded with material on what helps dealing with lab switches. As we have shared our solving strategies, our thoughts about what we thought working and discussing why specific things posed problems.

Cynwulf recently pointed out that it is often hard for newcomers to the game to find the relevant material in the forum.

“I’ll get to it…Eterna has too much info…too many projects…too much history for anyone to make sense of who hasn’t been here from the beginning…and I suspect that it would still prove a challenge even to those veterans.”

He got that absolutely right. I have been working on and off for the last year to pull together an overview of some of the switch material of the forum. About what seems to be working for lab switches. Some of this will also work for switch puzzles. But again as with the single state puzzles, the puzzle engines are far less picky about what they allow than lab. (What makes an RNA puzzle hard?) They need to be.

So it will be interesting knowing where the bot engines differs in their approach to switch puzzles compared to lab. Hence it will be helpful testing out which characteristics from lab switches, that the bots seems to be blind to. You can help with investigating that by making different types of switch puzzles, like Snowflakes, Fractals, Symmetric and asymmetric switches etc. For a list of such puzzles see here.

Remember I have pulled together a lot of material, so don’t try read it at once. Spread it out. I have attempted to sum up what I consider some of the most important points in relation to lab switches. Then I link to background material with further explanation. But for all the new stuff on switches, forum is generally the best place to follow and add to the discussion.

This is not and cannot be a complete sum up. Also this materials collection is of cause biased towards what I think works in lab. If you think other things will work for switches - please write it up or pull your own list.

I hope this will serve as inspiration for making new switch puzzles and testing what will stall bots and humans on switch puzzles. Plus of cause help with lab.

A few posts will turn up at several posts, as they cover more than one topic.

Lab puzzle puzzle solving strategies

General switch rules sum up

Switch Lab Intros - Distillation of switch rules
A Pattern Language for Riboswitch Design
Different types of switches - Deduction of switch rules from early switch cloud rules.
Lessons from the past - designing switches with the MS2 hairpin
Also see this short sum up.

Central Switch lab discussions

Overview of our past main switch discussions. Attempted sorted somewhat in order with newest on top.

Area to submit design for discussion?

Area to discuss Ways to analyze Lab results

OpenTB results

Designing switches for the first round of OpenTB

Blueprint of the MS2 and FMN Riboswitch

FMN/MS2 Riboswitch Structure

Kissing loop riboswitches

Logic Gates

RNA in - RNA out Puzzle Analysis

Cooperativity Puzzle Analysis

The Real Logic Challenge using NuPACK

Our first multi-input puzzle

Johan’s microRNA lab

Switch Scores for EteRNA Switch Puzzles

Round 97 Riboswitch Lab Discussion

Round 98 NG Switches Lab Discussion

WHAT MAKES A SWITCH LAB EASIER?

Here are a list of things that can aid solving switch lab puzzles. I will try go short. A title, a short sum up of the pattern, its relation to static lab and plus a mention of what I think the bot algorithms react to it for now. The latter is based on my switch puzzle solving experience. Last I put links to past forum posts explaining the pattern.

SWITCHES AND SEQUENCE

Base repeats, sequence repeats

Switches: Switches loves base repeats. Lower sequence variation aids switching (Periodic sequence repeats). The more and large sequence repeat regions, the prettier and symmetric the switch.

Static RNA: For static RNA repeat bases and repeat sequence on repeat structure was the sure way to not getting a stable structure. Well varied base distribution is less prone to switching.

Simulation: Switch puzzles seems to care less about repeat bases and repeat sequence than lab. Symmetric switches seems to call for more repeat bases than asymmetric switches.

Past strategy resurfaced

Huge RNA

Periodic repeats in RNA switches - How can they be programmed?

CU and GA rich stretches in switch elements and switches

Switches: Repeat base sequence is not just random repeat base sequence. There is a pattern to the madness. Lab switches and switch elements in particular (MS2, aptamers, RNA inputs etc) seems to be particularly fond of specific kinds of base repeats as CU and GA rich sequences. These repeats spreads to the rest of the switch too.

Static RNA: CU and GA rich stretches in static RNA tended to cause slides and misfolds if not packed away in longer stems. Well varied base distribution is less prone to switching/misfolds.

Simulation: Much less particular about getting CU and GA repeats than lab.

Natural occurring riboswitch holding an adenine molecule. Image from post below

Adventure in Riboswitch Wonderland

Palindrome base repeats

Switches: If sequence repeat is not just done like random GA’s or CU’s, but palindromic I think it can have even more switching ability. Especially when in the aptamer or switching elements. Advantage is that it leaves more orientations for switch element turnoff.

Static RNA: Palindrome were what made hairpins slide or misfold. Sequences like GAAG or CUUC in small 4 base bair hairpins were sometimes enough. In particular if there were more of them.

Simulation: Cynwulf has found simulation to agree. Switch puzzles love palindromes.

Palindromic Switch puzzles

Palindrome sequence

Magnet segments

Switches: Small regions of repeat C’s and G’s gave trouble in static RNA if there were too many, but these are most welcome in switches. Especially in islands of C’s and U’s, plus G’s and A’s.

The strong bases, G and C stands for making the connection and hook up a stretch in a switch. The weaker bases A and U stands for making the region unstable enough to allow the puzzle to switch also.

Static RNA: Such regions in static RNA tended to make the RNA misfold aka switch.

Simulation: Cares less about it. Switch puzzles we can often make switch, while solely being solved with AU or GC. Nature I doubt quite so much. However symmetric puzzles seems to crave magnet segments more than asymmetric puzzles.

Symmetric puzzles, asymmetric puzzles and magnet segments

Magnet segments in natural RNA

Reverse engineering magnet segments

Skipping magnet stones on the sequence sea

Part III - Potential switch pattern?

Christmas Snake

Number of RNA inputs and strength of magnet segments

Switching magnet stem

OFF switches wants C magnet landing sites, ON switches wants G magnet landing sites

SWITCHES AND STRUCTURAL CHARACTERISTICS

Symmetry

Switches: Symmetry or identical structure regions has turned up in a good number of natural riboswitches plus in our switch labs too. I took note of the two almost identical single glycine structures in the cooperative glycine riboswitch while we were trying to make our first cooperative switch. They first caused me quite a headache along with the beautiful proteinlike (aka symmetric) structures I saw in natural occurring tandem aptamers. Because of the nature of static RNA I had came to expect asymmetry and associate symmetry with misfolds and bad designs.

Static RNA: Misfolds are really just another word for switch.

Simulation: While symmetry got single state RNA bots on thin ice, one of these bots is now excellent for making symmetric switches. Will switch bots also be on thin ice with symmetry while solving switch puzzles? Help find out by making snowflakes or other of the puzzles listed here.

Image from here.

Protein switches

Huge RNA

Glycine riboswitches

Protein shape versus RNA

Same State blueprint - now with more symmetry

Riboswitches - it’s all about the symmetry…

Symmetric switch elements

Things that sparks symmetry in switches

INFO-RNA: Natural born switch maker

Coaxial stacking

Switches: Omei took note of coaxial stacking in our RNA lab switches being beneficial to help inputs and reporter binding. It has turned out useful in a wealth of different places. Coaxial stacking in itself creates symmetry.

Static RNA: This is one of the features that seems to be beneficial no matter if it is an a static or switch lab design.

Simulation: Doesn’t seem to care about it being there or not. Not needed as in lab.

Omei’s image of stem coaxial stacked with reporter

Is NUPACK’s energy estimation of flush stacking leading us astray in the OpenTB puzzles?

Get free royal flush for lab