Let's get started!: http://www.eternagame.org/web/lab/689...
This is it! :http://www.eternagame.org/web/lab/689...
Initial, preliminary data are available for some puzzles in the first round.
Google Spreadsheet: https://docs.google.com/spreadsheets/...
Excel file: https://drive.google.com/file/d/0B_N0...
Use the Glue Tool to create and maintain the puzzle structure you want in your puzzle, while working on making a stable solve. I think doing this will be particular helpful for the two hardest TB puzzles.
Zama found the Progression tutorial that introduce the Glue Tool. Here is a written intro to the Glue Tool.
Here is a lab puzzle example where I found it useful. It is not stable yet.
Astromon made me aware that the puzzle do not remember the structure, so you can't see it when you open the puzzle. It is only remembered in my browser and visible when in target state.
I made 10 base segments from both ends, except for the reporter binding region. (Black highlight rings)
Notice the purple structure icons in the image. (green box)
I wish it were possible to conserve the structure also when the puzzle gets put up.
Limiting the length of switching stems
The above puzzle is inspired by some of the Brourd/Nando round 2 puzzles. But structurally it is slightly different.
It deals with direct pairing between inputs and complements and no overhangs between states. Earlier small labs (like the microRNA labs) with inputs perferred overhangs, so I'm not sure this will work. However I am attempting to cash in on the coaxial stacking energy bonus. :)
I have tried make the puzzle bind solely with magnet segments. And made a limit to how long the hairpins stems can get. I try pick the input complementary sequence that I put in the loop area so it doesn't bind with itself.
I made all stems and strands 10 bases long. So each input is set to bind with 10 max bases.
Because hairpins stems that gets too long have a harder time switching. Or don't switch at all.
I am attempting is to make solutions that are less sequence dependent - when it comes to binding with itself, while still taking advantage of the magnet segments and the sequence bias present in the inputs for binding and detatching from the inputs.
I have made a drawing of what I am attempting.
The A and B input can be more different in sequence. (In this lab they are not too different in bias) I added some extra colors to the image below to illustrate.
Even the C's part don't need to target the same region in the C input. Doing intersecting style may allow wider variation in the binding sequence picked.
However there are still limits. I strongly suspect that GA and CU rich regions will be preferred for binding, as this is the trend I see for switching elements in need of an effective switch.
Adjusting strength balance
The strength balance of the inputs can be adjusted in three ways.
1) Changing what sequence is targeted for binding to the input
2) Changing the region in the biomarker where the input is cut from
3) Changing the structure of the puzzle
Strength balance or imbalance between the A and B input can be adjusted by a slide of what sequence one cuts from the biomarkers. Or by just sliding what one targets for binding (Since not the full input is bound with). All that needs to change after a change of what part of the input one is binding with for the 10 base input section, is to make sure the complementary sequence in the loop matches whatever is chosen for the input.
Another way to wary binding and the calculation is to adjust the lengths of the C's in relation to the A and B input. All that is needed is to just match the loop that holds the complementary sequence to the same size.
The puzzle mentioned in the above post follows this base distribution pattern:
10 10 10 10 Reporter 10 10 10 10
If the C's (around the reporter) are too strong they can be weakened like this.
11 9 11 9 Reporter 11 9 11 9
Or if it is the A and B input that is bound too easily, the C's can get a longer binding spot.
9 11 9 11 Reporter 11 9 11 9
I did recycle some of these designs which were dug up with Omei's spreadsheet. This resulted in me getting a fine bunch of winners in some of the sub labs, thanks to that.
Omei helped me with making the continuation for the last category of labs that wasn't covered. Here is the full collection.
Digging out future TB winners from failed designs
The two hardest labs are not shown on their own as these you can get, just by sorting after global fold change.
If you recycle, remember to filter so you don't take designs with way too high fold change error rate. Try something like a max of 1.25.
Promising design for ABC2INC
While these spreadsheets were in the making, I noticed that there were a good ABC2INC candidate that I had missed out on. Because I had only sorted for global fold change in the hard labs, not while also looking at the sublabs. Omei and I discussed this design. Since we have a new round of TB now, I wish to bring it up as for us to use this knowledge.
NB, the design in question is a round 1 design with different inputs, but if we can ape the structure, I think it will be really interesting.
1) Copy in the design from round 1 to the open ABC2INC lab
2) Native mod may be able to display the overall structure
3) You can use the glue tool to force hold the structure
4) Change the inputs to fit round 4
5) Change the region that pair with the inputs, to fit the updated inputs
I have made an early attempt. It is not stable.
Note also that Round 1 and 3 often has input reversal compared to round 2. Meaning if B comes before A in round 1 and 3 (can't remember which way now) then A tends to come before B in round 2.
Discussion between Omei and I
Eli: While there were no general surprise of the GF of the non hard labs, there was one single surprise. There did turn out to be one additional design that scored better GF than the one of mine you picked out for ABC2INC. And its a failed RO design.
This one: http://www.eternagame.org/game/solution/6892307/7053820/copyandview/ It got a GF of 2.19, which is better than my 2.03 one. And it has a far lower KDON. Wish I knew what the switch graph would look like. Its a round 1 design so it doesn't have one. Its similar to my RI designs that did well but was below in potential compared to Atanas design style. (edited)
It doesn't even have any landing spots for C inputs. It does the calculation right, with just the A and B input
----- Thursday, May 4th -----
omei [12:35 AM]
Hi Eli! This is indeed an interesting design. I'm not sure why you think the switch graph is missing. The URL is https://s3.amazonaws.com/eterna/labs/histograms_R104/7053820.png (989 kB)
and the data browser displays it.
This is not a typical switch graph for Open TB. Note that that many of the FMAX values have values greater than 1. This implies that there is more going on than NUPACK is picking up on. Nine times out of 10, when this happens with a design that has an adequate cluster count (which this does), I find unpredicted coaxial stacking to be involved.
Here's NUPACK's prediction of the no-ligand folding. Looks quite reasonable, but doesn't account for a FMAX of 1.56.
omei [12:48 AM]
But now consider this possible folding. Only 5 of the 10 reporter bases are bound, but it is being reinforced by the long hairpin. And it is not competing with the other reporter binding site. In fact, with only 2 bases separating the helices, there might be a little bit of additional boost when a reporter oligo binds to both sites at the same time.
I had also prepared some target structures showing how C could be quite reasonable be bound by being reinforced by a contiguous stack. Unfortunately, we had an (uncommon) power outage, and the target structures were lost before I could take screen shots. But my impression is that this is actually a very complicated design to understand, because under many conditions, it has many possible foldings that are probably energetically similar, and thus the experimental data reflects a mixture of foldings.
I can't edit the caption above, but when I said "with only 2 bases separating the helices" I meant only 2 bases separate the two (full/partial) reporter complement segments.
eli [7:36 AM]
Hi Omei! I'm sorry about the power outage. Sucks.
Oh, on the missing switch graph, I meant your slick 3d view. I really like that one. :)
However I find what you highlighted very interesting. There is almost a double reporter binding site at two spots. This may just be another way of making both ON and OFF state perfectly happy. It is just the other route around compared to your winning mod Atanas RI design. He split the inputs in two to leave them two different ways to bind up. Here it is just the reporter landing site that is split in two. This may be the easier route, when the puzzle gets harder.
I don't think I have heard Fmax connected with extensive coaxial stacking before. I find your observation very interesting. Feel free to spill in the forum when you feel ready. I think this is worth looking out for and could help us understand the data better.
By the way, I put in the sequence of the RO design into the ABC2INC design and it turns out that there is a binding site for 1 C input. So now I wonder if this puzzle really do the same calculation. I mean, it is A*B/C and not A*B/C2.
But this C landing spot also kind of explains why the puzzle work at all. This leaves the OFF states (1-3) some room to get distance to the reporter, given that OFF states are generally not fond of having inputs close to the reporter.
Also both ends of the puzzle seems involved in covering up sequence inside the design at times.
RO moonlighting as ABC2INC
omei [9:09 PM]
There's a landing site on the 5' end, too.
eli [9:10 PM]
Ok, I see, but it seems rather short.
omei [9:10 PM]
Line up the four exposed A's with the 4 U's on C, and then extend it. It will break up that loose hairpin.
eli [9:11 PM]
Ah, good point. The double C's can pair directly with G's in the C input
Ok, so doing the right calculation
And I think it may have a higher inbuilt potential than my design as it binds the reporter at so low KD. Me pairing the A and B complementary sites with each other helps hiding the reporter, but it also makes it harder for A and B to reach a concentration big enough to attach in state 4. As these two are low concentration.
omei [9:13 PM]
... and it gets reinforced by the coaxial stack formed when A binds.
eli [9:17 PM]
I am not sure I understand the last bit
Unless perhaps in state 4 when both A and B binds, they are close to coaxial with the reporter.
omei [9:18 PM]
When both A and C bind on the 5' end, the stacks they form have no unpaired bases between them, and this they become essentially one long stack.
eli [9:19 PM]
omei [9:20 PM]
As a first approximation, they have a combined energy which is the same as though there was a continuous backbone connecting the A and C.
eli [9:22 PM]
This is similar to what happens in my highscorer. The first C input is close before the A.
omei [9:23 PM]
eli [9:23 PM]
One base distance
Can be seen in state 4
omei [9:25 PM]
Yes. As a rough estimate, the coaxial stacking bonus where there is one unpaired base is about a quarter of the boost when there is no unpaired bases.
eli [9:25 PM]
Thats a nice rule of thumb
omei [9:26 PM]
To be honest, I made it up just now. But I think it accurately reflects the data I have seen.
eli [9:28 PM]
I suspect the RO design works, because it allows the reporter to be much closer to both inputs as you have wanted. (State 4) But that it still can be made into decent offstates, because either the C inputs tip the balance away from B binding. (State 1) State 2 has the reporter away from one of the inputs. State 3 the C concentration takes care of burrying the B input.
omei [9:31 PM]
I thought you had said that in the lab it failed as an OFF switch.
eli [9:31 PM]
So both ON (Inputs next to reporter) and OFF state (Inputs distanced to the reporter) can be made happy. And don't have to compete and do a compromise as in mine
Yup. Its a crappy RO design
omei [9:32 PM]
That's what I would expect. It only looks good in Eterna because NUPACK gets coaxial stacking all wrong.
eli [9:32 PM]
It has reporter inbetween two inputs which makes for a perfect ON design/ON state. OFF state are not happy about that configuration.
But the placements of the C inputs, helps tip the balance so the A and B inputs can be kicked off or bind less well, helping the advancing the OFF states. Not strong off states, but still
omei [9:34 PM]
I understand now. You're referring to the OFF state when tested with C concentrations.
eli [9:35 PM]
Yes. One of the big challenges for making good hard lab designs is how to deal with making the OFF states differ from the ON states, as they don't like the same.
Atanas design did that brilliantly for the RI lab, but it is a complicated way. This RO design gives me hope of finding a simpler way, that will also work for the hard labs
I mean, here we can tip the A and B input away from the reporter (for OFF states) with concentration of C. Despite both A and B being close to the reporter. And when Both B and A are present, this tip the balance back to them being being next to the reporter for ON.
Ok technically this only happens for the B input.
I mean it overlaps with C. A do not.
But B won't go full on as long as A is not around, so same effect.
omei [9:43 PM]
One thing I have discovered is that overlapping inputs does not necessarily mean they are mutually exclusive.
In the right conditions, they can actually reinforce each other's bindings instead of kicking the other out.
eli [9:44 PM]
I wonder, can the tail from one input pair up with the tail of another - if there are complementarity
omei [9:45 PM]
I can't think of any reason they couldn't.
eli [9:46 PM]
omei [9:46 PM]
That would be a second mechanism, not the one I was thinking of.
eli [9:46 PM]
How much input landing sites overlap also matters for the switching ability. Too long a stretch and they are not switching well
What is the one you are thinking off?
omei [9:48 PM]
I posted an example in the forum some time ago; let me check.
eli [9:49 PM]
omei [9:58 PM]
Consider the above situation where the middle line is is out switch design and the top and bottom are oligos. (edited)
On the surface it looks like they would be competitive
But in fact, the lowest energy would be for both of them to bind at the same time, forming one longer stack 15 bases long.
eli [10:01 PM]
Because it is a real short overlap between them, right?
But wouldn't the two GG sections repeal each other?
So is it always more energetically favorable to have stacks forming comparable to having more loose bases?
omei [10:05 PM]
Only one of the either oligo could bind to the design at a time. But the fact that both oligos are extended well past the section in "competition" means that they both stick around even when the other (temporarily) has control over the disputed segment.
eli [10:06 PM]
Gelatinous slow down of switching...
omei [10:08 PM]
I've constructed this case to be simple. In this case, the choices nature has is for 1) one or the other to bind (but not both) and end up with an 8 or 9 base stack, or 2) both bind and end up with a 15-base stack. The 15 base stack has a much lower energy, so it wins.
The fact that the 3 contested bases will probably be shifting from one camp to the other over time isn't really a factor in the total energy.
eli [10:12 PM]
What you says make sense
omei [10:14 PM]
I believe this is actually the largest single factor in the large number of designs on OpenTB 1 that switched the "wrong" way, i.e. had fold changes < 1.
eli [10:15 PM]
Ah, like socalled shared landing spots were shared parking spots at each side.
And it would good make sense it happens as our biomarkers are rather long
This doesn't happen in the logic gate labs, as the inputs were not overlapping
So even while they were long, they were not in direct competion
inputs - complentary binding sites
omei [10:19 PM]
Yes. I'm looking for a document ...
omei [10:24 PM]
uploaded and commented on this image:
Here's an example of the overlap between B and C in Rounds 1 and 3.
The --- indicate that an appropriate choice of base in the design will bind to either oligo.
eli [10:25 PM]
So the first bit of B that is not overlapping has some rather strong G bases. Not happy to let go.
So this bit will be likely to stick around even if C should have luck attaching
omei [10:27 PM]
uploaded and commented on this image:
... and here's one for A and B.
A and B is even more obvious; it is a more extreme case of my made-up example above.
eli [10:30 PM]
I'm a bit in doubt of the UUCC and CCUU region. I mean they won't both attach to AAGG or GGAA
omei [10:31 PM]
(I didn't realize this was going to be a problem when Michelle proposed the oligos. It was only after looking into why there were so many designs folding the wrong way that I realized this was a major factor that I hadn't given any thought to previously.)
The design sequence GUUGUGGGG can bind to either oligo with no mismatches.
eli [10:33 PM]
Now you mention it. As in both your examples, I suspect the problem will be bigger if there are two strong bases just before or after where the overlaps are made to happen. This would leave less reason for the input to leave
omei [10:34 PM]
So we could end up with a stack of 26 (if I counted right) bases when both oligos bind.
eli [10:35 PM]
Also I still suspect that input order matters for when overlapping is done. I expect that inputs won't zipper equally easy off, just depending on if zippering from 3' or 5' end of the design sequence.
omei [10:36 PM]
I have no feeling for that.
eli [10:36 PM]
I mean beside the flourescent tag effect.
I can't give any proof. But I'm looking out for an eventual effect being there. I expect it could be there.
The A input in your example will have to zipper up from the 5' end of the design sequence (its 3') where the B input will have to zipper on from the 3' side of the sequence (its 5' end)
I don't think they are equally easy - given that input strength had no effect or were equal
omei [10:39 PM]
Anyway, I think that the fact that the original oligos have this pattern of sharing R/Y sequences at opposite ends was bad luck, but had a large effect on the overall results.
When you say zipper in this context, are you referring to one of the oligos displacing the other?
eli [10:41 PM]
I'm imaginine the one zipping on at one end and then just like a zipper working its way to displace the other
And since RNA is chiral
I don't expect each way to be equally easy
omei [10:43 PM]
That certainly seems like the obvious kinetic pathway. But it should happen so quickly that I can't see how it would relevant to the resulting equilibrium.
I.e. how it would show up in the data we get.
eli [10:44 PM]
I don't know how to show it yet as there are many other variables in play such as difference in input strength etc.
Gerry started a lab design analysis thread. Also a special thanks to him for the fine initiative. I suspect this will be extremely helpful for the future.
As a part of that he volontered to pull out design pairs from our TB round 2 based on similarity and how different they were in score. I have been looking at one of his latest spreadsheets, the one on the DEC lab and global fold (GF) change.
Good and bad spots for GU pairings
Here is something I think we can use for making better designs.
Gu's are bad when created between the reporter and its complement.
While I have looked only at a fraction of the designs, a pattern is already emerging. It stands much more out in the DEC spreadsheet with GF than the one for score, while the trend is also there.
Mutations that leads to a GU forming between the reporter and the complement is mostly bad. However there is an exception. If that GU forming between the reporter and its complement, is also helping form a GU or mismatch inside a longer switching stem in another state.
Examples with unmutated reporter binding or with GU
Gu mutation to reporter complement unhelpful (case 1)
Good unmutated reporter complement
Bad mutated reporter complement
Gu mutation to reporter complement helpful as it destabilize long switching stem in another state. (case 8)
Long stems really dislike switching and breaking them up will go a long way to help switching along.
GU mutation to reporter complement partially helpful
No Gu mutation, less helpful as a long stem in another state gets too stable to switch happily.
But to get the helpful effect from the GU in these green cases, takes a toll on the reporter binding.
Use your GU's smarter
There however is a way to get this effect without weaking the bind to the reporter - or to any other input for that matter.
Don't mutate your reporter complement. Make GU in the long switching stems without touching the reporter binding site.
Get the best of both worlds - mutate your GU's here
Avoid putting them in other input complements as well.
Instead of making the weakening bind between the reporter and its complement, make that weakening bind at the other side. If that complement binds up to something else and this is in a long stem. Make an A in that reporter/input complements complement, a G.
And voila you have a free GU will all its benefit and without the cost on the reporter binding.
Just as the reporter complement dislikes mismatches or GU's forming against it, I think the same will be the case to some degree for input complements. However as they grow in length they do need an occasional mismatch or GU forming against them.
In selecting the winning scores for Round 2, we used the global fold change, as defined by Johan, as the measure of the overall "success" of a design. But for the purpose of looking for promising designs to improve for Round 4, I think a different criteria might be more useful.
Explaining the global fold change is best demonstrated using the 3D section of the switch graph. Here's the one for Andrew's winning design.
Looking at the bottom "Target", there is an almost-horizontal black line in the middle of the chart. This actually represents a two-dimensional plain in the "3D" space, but the viewing point lies on the plane itself, so we can't see the top or the bottom of the plane.
The numbered circles represent KD values for each of the 19 conditions that Johan created to test our designs. In the ideal solution of the A*B/C^2 DEC puzzle, all the points above the central plain should have lower KDs (i.e. be more yellow) than all the conditions below the line (i.e. be more blue.)
However, the 19 conditions were chosen so that together, they fairly evaluated all of the puzzles, from simple sensors to full A*B/C^2 puzzles, and they are not all equally relevant to the full A*B/C^2. puzzles. In particular, only conditions 6-12 were selected specifically to target the evaluation of the full A*B/C^2 puzzles. For these seven conditions, oligos A, B and C were all present, in ratios that represented plausible levels in human blood. I have marked these conditions with a red ellipse, and will refer to them as the central conditions.
All the other conditions had one or more of the oligos completely missing, i.e. were out of the range of physiological conditions. There was discussion about whether or not these conditions should be included in the evaluation of the full puzzles, but I think I won't go into those details here. The final conclusion was to not include conditions 17-19 (hence they are grey in the bottom chart) but include 1-7 and 13-16. These became the definition of the global fold change. That is, two KD values would be chosen -- the highest (least yellow) of the yellow dots and the lowest (least blue) of the blues dots, and the ratio of those is the global gold change. The situation is different, but completely analogous for the INC version.
But I have also now calculated the "central fold change", i.e. the same calculation except for being based only on the measurements in the red ellipse. They are available as the fusion table Eterna R105 (Open TB Round 2) results, with Central Fold Change. If you prefer a spreadsheet format, just download the fusion table as a CSV file and load it into your favorite spreadsheet. if you like the fusion table format, I suggest you immediately make your own copy and work with it. Otherwise, Goole doesn't save any of your settings, like filter conditions, new tab views, etc.
I have more to say about what I see in these results, but that will have to be in a subsequent post.
Andrew’s Key: Reporter turnoff proximity matters
The closeness of the reporter to its turnoff sequence matters for strong switchability.
Far apart - less effective. Closer - boom time.
Also it seems to matter how long this switching hairpin is. If it gets too long it seems to lower the fold change. This is really the whole old story all over again. It is harder to make a long stem switch than a shorter one.
Knowing that a short range turnoff sequence if hidden nearby the reporter can can lead to a strong turnoff - and turnon - could be used to improve our lab scores.
AndrewKae’s puzzle demonstration
I have been watching AndrewKae’s OpenTB presentation.
I took note of the smaller design he demonstrated, with the switching hairpin.
Reporter and input with highlighted complementary parts. Separated by only 4 weaker bases - that will become loop in the other state. (Images shot from his presentation).
Input and reporter bound
Actually this design has two such turnoffs. As the small hairpin in the beginning of the sequence is a tail magnet targeting a bit in the input - also a pairing close in sequence and space.
Input and reporter turned off - by each other
A nice portion of the designs with the all time best fold change over our previous 3 OpenTB rounds in the RIRI sensor labs follows a similar pattern.
Andrew is using the exact same technique for reporter turnoff in his round 2 ABC2DEC puzzles.
The switch pattern
The reporter turnoff is hidden as a nearby complementary sequence in the nextdoor input complement. When the reporter and inputs needs to be turned off, part of the reporter and a short stretch of the input creates a short hairpin stem between them.
Illustration of the pattern
What problem does this reporter turnoff pattern solve?
Turning off the reporter in a hairpin stem like way is the perfect way to create a compromise between what an OFF state and an OFF state wants as in certain puzzles they want something different.
- ON state prefer to have the input and the reporter coaxial stacked.
- OFF state that have the reporter and the same input next to it and needs to have both of them off, has a problem as it has what the ON state prefer.
Having the reporter turnoff buried in the nearby input - allows for a swift and strong turnoff. Having the reporter close to or (coaxial) next to the reporter allows for a strong and swift turn on.
This will be of particular use the reporter and input both needs to be ON in one state and OFF another.
Where can this reporter turnoff pattern be of use?
This switching hairpin for reporter turnoff tends to happen more in OFF switches. Its a way to use a nearby input that isn't needed around - for turnoff - when the reporter needs to gets turned off.
However it isn’t solely an ON and OFF switch question. As the pattern is strong in the RIRI sensors. ON puzzles. They are of the kind reporter in, input in.
The pattern happens particularly in puzzles where an input and the reporter both needs to be on in one state and then both off in another state. Like the RIRI sensors, plus if there are more OFF states than ON states. Like the hard dec puzzle.
If the reporter complement and its input complement are too far apart, they will be less effective.
This may also explain why real strong magnet segments tends to turn up in long range turnoffs. Like tail magnets. The further apart, the stronger bases are needed to do the pull.
Different switch puzzle types depends on different reporter turnoff patterns. The more entangled pattern types depends on long range turnoff of the reporter. Where the open ended design type like AndrewKae’s puzzles depend on short range turnoff.
However the reporter could get modified to be better suited for a long range turnoff. Or rather as we have already seen with the MS2 - it has strong magnet segments in itself - that allows for longer range turn offs.
Tail magnets: Long range turnoff
I have been thinking about the TB labs and it occurred to me that if we were to classify designs (for any given sub-Lab) based on the overall schematic layout of the elements (i.e., reporter, oligo-A, oligo-B, etc.) of that lab, that we would find that there are only a certain number of possible arrangements which could ever be employed (similar to the number of possible plots for a story https://en.wikipedia.org/wiki/The_Thirty-Six_Dramatic_Situations ). <br/>
My thought here is that though finite, there are still a great many possible arrangements for any given sub-lab which may be used... and that there are arrangements which have likely never been tested. <br/>
Not all of the possible arrangements, which would work in principle, would be expected to work in lab, but I still wonder if we aren't potentially missing something vital in likely not having tested many of these options. Doing some very rough estimating, I got an upper bound of ~343 possible arrangements of elements for the each of the [A]/[C], [B]/[C], AND A*B labs, and ~4096 possible arrangements for each of the [A]*[B]/[C]^2 labs.
This post isn't directly related to TB. However it is related to switch puzzles in general, plus Logic gate labs and OpenTB. These being both multi input and multi state puzzles.
This is about switch puzzles and about how they potentially relate to switch labs.
Recently Cynwulf asked me a question. Brewed down it adds up to this:
"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." (I bring his full question below)
The more switch states - the simpler the (puzzle) solve
I think that goes for more states as well. Not just inputs. The more states, the stronger the magnet segments and base repeats.
I have observed this for labs, but had yet to find a good puzzle example. Also this is related to the question Cynwulf asked.
Wwei23's multistate puzzles
Wwei23 has made a multistate series called Maximum Ride
I attempted solving the two puzzles with the fewest states a while back, with no luck. Then I tried the one with 21 states to day - suspecting it to be easier - and I recognized a pattern to it. After that I had no trouble at all solving the puzzles with the fewer states.
These puzzles seems to not be solvable in a lot of ways. I started solving the puzzle with 21 states, by filling in U's. I put in one U, moved through the states and filled in more U's. I ended up with half the puzzle filled with U's at only one side. The other side A's. Then I started swapping in GC pairs for AU's, and added an occasional GU when needed.
What stood out to me in the puzzle with 21 states, was a pattern of mainly strong bases. Solely solved in two magnet segments. One half of the puzzle in one style of sequence pattern. Pyrimidine and the other in another Guanine.
I took a guess that this the puzzle with most states, wanted a more similar base solving style than the two puzzles with 13 and 19 states. These too took repetitive base sequence, but in slightly weaker versions.
Which highlights my point. The more states of a similar sized puzzle, the more locked up and shared the sequence becomes among the states.
Wwei noted to me today that Jnicol never has made any 4 state puzzles. This doesn't prevent his 2 and 3 state puzzles from being hellish hard. The hardest puzzles I have solved to this day, has been 3 and 4 state puzzles. Although admitted 5+ states also do give me trouble sometimes.
Wwei's puzzles have the pleasure of being hard, but still in reach of solving and while these puzzles and not lab puzzles, they may hint at the nature of lab switches.
Also take note of Cynwulfs switch puzzles. In a good deal of his kindest ones, he leaves a starting trail of sequence out as a helping hand. And this sequence will to a certain degree repeat itself - it being mirrored onto other sections of the switch with similar structure.
21 states of wonder
I wonder if it will be possible fitting more states into this 21 state Maximum Ride puzzle? What make me wonder is that there are still one weak base present in my solve (at base pairing position). Will the puzzle be solvable with even stronger bases?
Here I bring the conversation between Cynwulf and I.
cynwulf28 → Eli Fisker Fri Dec 15 2017
Hello, I found myself asking a question in chat (included below) which I feel has been investigated in the past, but for which I have never seen a paper or other reference addressing it specifically. I was Wondering if you knew of if there was a paper published for this or perhaps if you happen to know the answer yourself.
cynwulf28: There are about 5270 switch puzzles [8:28 PM]
Astromon: cooL [8:28 PM]
cynwulf28: Of which, 2762 are Malcolm's Swiitches xD [8:29 PM]
cynwulf28: or Mods of his switches [8:29 PM]
Astromon: wow [8:29 PM]
Astromon: Master malcolm [8:30 PM]
wwei23: 3 states is the theoretical maximum for a 6 base puzzle. [8:30 PM]
cynwulf28: At 3 puzzles a day, that's about 920 days of publishing [8:30 PM]
wwei23: 7 states is the theoretical maximum for a 7 state. [8:30 PM]
cynwulf28: cool, good to know wwei23 [8:30 PM]
cynwulf28: for 7 base? [8:31 PM]
wwei23: Yes. [8:31 PM]
cynwulf28: I thought so :-) [8:31 PM]
wwei23: You might have seen my small 7 state switch. [8:31 PM]
wwei23: That's what it looks like. [8:31 PM]
cynwulf28: so is this relationship linear or exponential [8:31 PM]
wwei23: 8 bases is 13. [8:31 PM]
wwei23: I don't know. [8:31 PM]
cynwulf28: would we see the number explode for larger sequences [8:31 PM]
wwei23: 9 bases, I think I got 27. [8:31 PM]
wwei23: I think it would explode. [8:32 PM]
cynwulf28: makes sense [8:32 PM]
wwei23: It's unlikely that you can stabilize ALL the states. [8:32 PM]
cynwulf28: 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 [8:33 PM]
cynwulf28: But HOW MANY could you have AT ONCE? I am not sure how to answer that [8:33 PM]
Eli Fisker → cynwulf28 Fri Dec 15 2017
I like your question. I haven't seen a paper on the topic. But I have the feeling you will be just the right person looking in the question. Don't wait around for it to be written. Investigate yourself!
From my feeling of things structure don't get exponentially harder for the more state there gets. I think the more state, the more limits there are to what you can do. Like lab puzzle going more towards symmetry and simplicity.
I have written a forum post about magnet segments getting reduced in numbers and stronger as the number of states grew. As I see the magnet segments gets stronger and more simplified (fewer of them) - in labs with more states.
Calculation wise, the relationship between sequence and multistate is exponential. However what I strongly suspect is that the sequence will get simpler and more repetitive. This is what I see for just two state puzzles. The sequence becomes more repetitive.
It is my feeling that the more states there get, the more the states will look somehow alike. Also structurally.
You have made some pretty awesome puzzles. While the simulations aren't accurate, I think one way to investigate is to make puzzles.
I have written another post and I have been thinking about you:
I would like you to focus at the bottom of it. I mention one of your puzzles and the similarity of the pattern in it. I would love if you made variations of it, but with different connection patterns between the ground pattern. If anyone can figure, it will be you.
Puzzles are your strength, use them to investigate your ideas.
Good luck from here.
message Eli Fisker → cynwulf28 Fri Dec 15 2017
Also check these forum post, I think it is related to what you are asking about. It is kind of the why things need to get simpler for more states.
So there really are three different levels of repeats in switches. 1) First the simpler level base repeat. Repeat bases like AA, UU etc, in switches. 2) Then there are magnet segment repeats. Which repeat sequence of CU and GA. While their sequence is varied, they are doing the same thing. Making things switch and glide. 3) Then there are structural repeat. This is actually rather beautiful. I understand why you focus on symmetry with your puzzles.
Cynwulf replied to the challenge with the most beautiful puzzle: The Switchiest Switch
I have yet to raise to the challenge of being able to solve it.
A certain someone has made switch puzzles so alluring that they have managed to drag me away from lab.
Cynwulf has taken the use repeat sequence and repeat structure in switch puzzles to a whole new level.
He allowed me to share what he sent me recently. I hereby put our conversation up.
I strongly suspect this shall help us both for switch lab plus up the knowledge about making switch puzzles.
Leviathan - A special sequence
cynwulf28 → Eli Fisker Thu Jan 04 2018
The switches I have made, which share a certain symmetry in how they switch, were all inspired by the same general sequence.
I encountered this sequence while looking for ADAR-mediated A-to-I editing sites within mRNAs:
This sequence inspired me so much that I hacked the site to publish it as a switch, my "Leviathan" http://www.eternagame.org/game/puzzle/7817914/ . A quick note on the puzzle I made, it was supposed to employ the standard ligand boost of -4.86 kcal, but sadly published instead with an older standard of -2.51 kcal....so I don't know if it is solvable. However, if you are curious, you can paste the sequence in and then Beam to puzzle-maker and replace the boost in State 2 with the proper boost from the puzzle-maker tools and the puzzle WILL stabilize.
The sequence naturally occurs in the human gene FBN1 (Fibrillin 1) https://www.ncbi.nlm.nih.gov/gene/2200 . It is essentially the same sequence mapped on top of itself starting at position 60 or so if I recall correctly. Either way, I wished to share this with you. The sequence above was modified slightly to avoid overlap when publishing, but is otherwise the same as that found within the gene and its corresponding RNAs.
Eli Fisker → cynwulf28 Thu Jan 04 2018Hi Cynwulf!
Thx for sending this to me. I had been admiring the puzzle from a distance.
What a great catch. You have found yourself a sequence that itself sparks symmetry. Because of its repetitive nature. It's like it was made to switch.
I beamed the puzzle to the puzzle maker but didn't get to stabilize it fully. I put the molecule boost at base 445 as in second state of the puzzle. I may have done something wrong. Or the puzzlemaker has something changed.
Instead I drew on your image.
I have some thoughts back. Overall there seems to be an equal number of two different sequences, that sparks two different structures. They are stuck in between each other like a harmonica. However some of the structures are slightly variations. Are there sequence variances at those spots too? Or are the mRNA made up of true repeats?
One more thing I wonder about. Could the puzzle be solved if it were not a mix of every second structure in between each other, but lets say, there were two of the structures with the green highlight for every two of the blue highlights?
I suspect you can take the same basic repeat sequence and break it up in different ways and create new switches with different structures.
I have tried count and it seems like the repeat sequence consists of a 25 (green stretch) and 28 bases (blue stretch). So 53 bases all in all for the two stretches. I wonder if you could create a similar puzzle, by changing some of the bases in the sequence, but still let it repeat the same way. So the stretch being the same length and repeat in the same way, but with a few bases changed?
Eli Fisker → cynwulf28 Thu Jan 04 2018
Now I also wonder how you got to the structure (dot bracket) in the first place.
cynwulf28 → Eli Fisker Thu Jan 04 2018
I played around with the original sequence in puzzle maker....I started by simply pasting the original sequence into a large enough design to allow for all of the bases to paste, then I switched from target to natural mode, and made a single modification to turn that natural mode into the target design.
Here is the ACTUAL original sequence from the gene FBN1:
To follow up on the harmonica metaphor, the sequence seems to have been stamped over itself nine times. I ran a BLAST of this sequence against itself and got the result foud here https://blast.ncbi.nlm.nih.gov/Blast.cgi (page has expiration after a short time, but the BLAST can easily be repeated if necessary)
I also ran this sequence through the RNAfold server:
And here is a Dot Plot found on that page:
Eli Fisker → cynwulf28 Thu Jan 04 2018
Thx for your additional explaining. This is super cool. There are even repeats in the entropy plot. :)
So you used the natural fold in the puzzle maker to make the structure. I did a try myself to get the structure and what I tried was run the reduced main part of the sequence through Vienna RNAfold in multiple repeats to get a structure but didn't get very far.
I really like what you have done. I would love if you would one day write down your thoughts on your puzzle making as you explain them here to me and post them in the forum. I suspect that we will learn quite a lot. Especially because switch puzzles seems to be tied more up with lab, than are static puzzles are. I suspect there will be a spill over from learning from puzzle switches that shall prove helpful for lab designing.
@eli Thanks so much for posting this! It seems like this could/should be the start of a topic of its own.
For solving the ABC2INC puzzle for first round OpenTB, I focused on concentrations alone. Using them to tip the balancing point between states. Lately I have been thinking about that we could also use the binding length of the inputs, to also tip balance between states.
Winner sequences with large touch zone
What characterises a good deal of the best ABC2DEC and ABC2INC designs? Their sequences have a large touch up zone with the inputs.
This made me think about if there were a way we could use input binding length to cover up for the low concentrations of A and B in state 4. If we could make the binding with A and B full length, but also make sure they went well away, when concentration of both were not present.
Making the most likely RNA fold
While I have been talking a lot of entangled hairpins this round, lately I have been thinking a lot about unentangled hairpins and that being worth a shot also. From what I have seen in RNA the statistically most likely fold that happens most often, is the nearest neighbour strand pairing. It is therefore hairpin loops and stems are so frequent. Multiloops and internal loops form frequently, but a bit rarer. Yet rarer are long range crossovers. This is what I have seen for static RNA. It may not work this way for switch RNA.
How to gain most possible touch between sequence and inputs?
An approach to doing so is to either make the input complement make a hairpin with itself, or to make the input complement make a hairpin together with the reporter. Most of the sequence of the input complements sequence will be intact and ready for an almost full bind with the RNA design. When no longer packed away.
Atanas C locks
I took note of Atanas round 2 designs for ACINC and BCINC.
They were rather different. They put the reporter and the A or B input shared state with next to each other. No surprize there. That is generally a good strategy for an input one wants turned on.
This design were among the better for the ACINC sublab.
It was rather the turnoff that was surprising. The C input needed to be alone in the first state. This was done by it pairing in both sides of the A input and reporter, thus hiding them away. The reporter was made fold up with the A input. A few bases were changed to make sure the input and reporter could make a hairpin together. But mostly their whole sequence were preserved so they could do a full bind up when they needed to go into action.
Competition of input lengths for making a massive turnon
With this drawing I try to illustrate how inputs may be packed up with them selves and away for some states, but packed out for full pairing, in another state. This is based on an ABC2INC design I made this round. (See second image below)
Showing there is a big difference in
amount of binding bases per state. State 1-3 should be like a harmonica,
with input A, B and R each folded up with itselves. And state 4 should
be the massive readout where every input should be bound up, the C’s
I have made each input complement fold up with itself and being away in some states. Similar I made the reporter fold up with itself. And I made the C input bind on both sides of all of that in state 1-3.
Packaway sequence with maximum touch
I decided I would try this approach in the two hard labs. By fusing two such puzzles.
It isn’t stable. So it may not work. I’m however interested enough to find out what lab thinks about it.
Also I’m aware that I may not get one C binding across the whole puzzle but rather two at each their end, as in the last state.
Still I think this is worth a shot. I have tried a similar approach in the ABC2DEC lab.
Reporter transplant - Reusing successful structure from earlier labs
This is a lab discussion between Omei and I. I mentioned a new found realization to him about reusing structural parts from past switches to solve new switch puzzles. The discussion expanded into other topics and since I think this will be useful to us in general, I share it. I have added a few extra images and links afterwards.
eli [8:53 PM]
By the way, I finally had success with something I have struggled with for lab.I have had trouble making stable designs of the type I really wanted to make.
It was something very specific that ended landing me the success.
omei [8:53 PM]
I'm all ears for that!
eli [8:54 PM]
eli [8:54 PM]
I could get state 1-3 stable but not get the reporter off
Or many other combinations of states - 3 stable, always one unstable
What changed my whole perspective and success, was when I thought about AndrewKae's design.
I wanted the reporter next to the C input. Just as he had in his lab.
So I decided to do a reporter transplant
along with a part of the C input complement.
The point was taking a reporter complement and its turnoff complement that I knew to be working
Both for being stable and for solving in lab.
I couldn't do the job fully with AndrewKae's version, so I nicked a part of Whbob's design too.
eli [8:57 PM]
eli [8:57 PM]
So basically it is an old idea recycled. But more radical.
I have before borrowed MS2 turnoffs from one lab and made them work in another lab. But I have not taken bigger sections, as this is.
I basically think this can help for switch lab solving. Both solving + make designs work in lab also.
That was my story :)
omei [8:59 PM]
eli [9:00 PM]
Plus the design I made working is of a new type for the hard labs.
omei [9:01 PM]
Can you distill this down to a simple C sensor?
eli [9:01 PM]
I have taken what Atanas did in a smaller lab, and followed the logic continuation.
I can for the slightly bigger lab.
This design uses some of the same principle
Here the C input reaches on both side of B and R
In the hard lab, I put R outside.
I basically made A and B each fold with themselves so they are away most of the time. Unless concentration of both of them are strong.
Here is one of the hard dec designs. Flip around between the states and I think you will see what I mean.
And illustrated with Sensor C
eli [9:11 PM]
[Sequence: AAAAAAAAAAAAAAAAAAAAAAAAAAAAACCACCUGUGUCAGAACUUAGUCUCUCUAUGUACAAAAAAAAAAAAAAAAAAAAAAA , lab: http://www.eternagame.org/game/browse/8489860/ ]
eli [9:12 PM]
The basic principle behind this kind of puzzle is that it relies not only on concentration. But also of the length of the inputs. Because in this kind of design, most of the input length gets used.
So while concentration of A and B is weak, I give them strength by having them appear both at once and in rather long stretches.
But have them packed away as both are not present.
By locking them in by one sole C input.
omei [9:14 PM]
Yes, I can see the pattern (i.e. "Let the oligo complement fold itself into a hairpin when it isn't bound") as the unifying principle in both the simple case and your full puzzle solution.
eli [9:14 PM]
I'm really happy I got it stable.
I might not have realized the reusability part, had I not struggled. (edited)
I mean had I had no trouble solving, I wouldn't have thought about reusing parts.
omei [9:17 PM]
I've seen hairpins like this in Brourd/Nando designs, but I'm not sure they got them in this specific way. It seems like this has the potential for being a very basic tool.
eli [9:18 PM]
Yes the ground structure of mine resembles theirs very much. However there is overlap between stems in the states.
I mean, strands from one stem overlap half and half between states. So the stems struggle
They are not structures on their own.
What I used is the nearest neighbour strand principle. That two strands next to each other that have matching sequences, would very much like to pair
Instead of long distance folds that are more rare.
I made the structures share joints.
So long distance folds do happen. I'm counting on that for the C to lock down the structure holding A and B folded.
omei [9:23 PM]
A heuristic I have been trying in recent rounds, but not yet gotten good data on, is to not "fight" any helix formation showing up in the dot plot. But stated this way, it serves more as a check of a tentative design. Your's is more of a method of construction, which is more useful.
eli [9:23 PM]
The inputs do not fully match for a pair up with themselves, and neither should they (they would be bad inputs then - more happy to bind with themselves than interact)
But what I did is to tack on two GC pairs at bottom of the input complement hairpin stem
omei [9:24 PM]
It sounds like there are multiple ways to view these designs; we seem to be coming from somewhat different angles.
eli [9:25 PM]
Which is why it is inspiring discussing.
And this was the design of mine I intended showing, I somehow ended up showing its partner. This one is the more symmetric.
omei [9:29 PM]
BTW, do you evidence for the statement "The inputs do not fully match for a pair up with themselves, and neither should they (they would be bad inputs then - more happy to bind with themselves than interact)"?
eli [9:29 PM]
eli [9:29 PM]
I only have "evidence" in form of my observation. I noticed that natural microRNA's, the ones I checked seemed to have a particular sequence bias.
So that they would not pair with themselves strongly.
The ones I ran through vienna came out with high entropy
Something not to be expected for something that can form a hairpin.
I have used this observation when I cut the TB biomarkers
So I can't prove I'm right. Although I strongly suspect that I am. :)
You are far better in the proof department. :)
omei [9:36 PM]
I know that we "all" agreed that our oligos shouldn't form strong hairpins. Intuitively that makes sense. But it seems like the kind of assumption that blind one to new possibilities. That's why I asked, not that I had evidence to the contrary.
eli [9:37 PM]
Excellent point. Actually my new design type would be the first kind of design that could benefit if that was the case. ;)
I mean if the input could make a weak hairpin with itself, but open up to its complement make a somewhat stronger bind - so I didn't need to tag extra bases onto the bottom of the hairpin forming of the complement.
omei [9:38 PM]
I think micro RNAs typically have very low affinity, which would make them poor switches when evaluated by fold change. I think for their purpose, specificity is more critical than fold change. (edited)
eli [9:39 PM]
My aim with this design type was to have as many of the bases in the sequence actually pair up with the inputs. In other words maximum touch.
That is a really good point.
Although I did find a paper stating that two miRNA's could compete for the same landing spot.
I was wondering about it.
omei [9:41 PM]
This is wandering from your initial point, but I do think specificity is going to be a big issue when we try to test actual blood.
eli [9:41 PM]
Happily follow. That was also part of what I was trying to aim towards.
To have long stretches of the inputs pair up.
But unfortunately mismatches and weaker bases are needed to make a solve to the labs
Except Nando/Brourds design type
Those generally couldn't (edited)
omei [9:42 PM]
I think there may be another reason they are important.
eli [9:43 PM]
tolerate mismatches (edited)
omei [9:44 PM]
... and that is to break up unwanted cooperative binding between two oligos (which are intended to be competing for a shared sequence) due to the coaxial stacking bonus when both bind.
eli [9:45 PM]
But there are no shared sequence in neither Brourd/Nando's or my new design type.
omei [9:47 PM]
And that's where I am thinking that these designs may have their advantage. Not necessarily larger fold changes, but better specificity.
... which wouldn't be appreciated by our normal scoring.
eli [9:49 PM]
I wonder if there would be any way to pick these designs out. Would your Central Fold change help show this better?
omei [9:54 PM]
I don't think so. The way I usually pick them out is by comparing the simple conditions. For example, take a A*B/C^2 INC design. Now look at the KD ON values for no ligand, 100nM_A, 100nM_C and 100nm_A_C.
We would expect the 100nM_A KD to be lower than KD_noligand, (i.e. increase the reporter binding), KC 100nM_C KD to be higher, and KD 100nm_A_C somewhere between just A and just C.
But what often happens is that A and C together result in lower KDs that either A by itself or C by itself.\
In all the cases I have looked at, this can be explained by the A and C actually both binding, instead of one of them kicking the other out, because that's the lowest energy configuration once the coaxial stacking effect is considered.
So it is looking at these simplified test concentrations that I would try to use to pull out designs that might have this problem.
eli [10:03 PM]
So this is specifically a problem of lane sharing in the hard labs.
Another thing. Brourd/Nando's designs seemed to have their A and B inputs behave more similar in relation to concentration. Probably also due to what you mention above.
omei [10:05 PM]
Yes, if I understand your terminology correctly. But it can also be a source of strength. For example, an A and B complement might overlap with a result that was good.
But getting back to the specificity, I'm concerned that other oligos in the blood will take advantage of this phenomenon even if they have a relatively short matching bases -- say 6.
eli [10:08 PM]
That is a very good point.
Thx for a good discussion. This has been most helpful.
Bad bot breaking constraints
Someone ought to tell our bot that this is a bad idea... :)
I know that nature allows longer stretches of G’s and C’s, but that lab has a problem with them.
Only 3 get a fold change error below 1.25. None of the designs score above 60.
Similar only 3 designs gets a fold change error below 1.25. None of the designs score above 60.
EternaBot also allows too long stretches of A and U. Although it takes slightly more of these to trigger lab and score problems.
I stumbled on the problem eterna bot designs, as I was taking a look at the error rates in the TB labs. I I was checking up on if longer stretches of G and U also triggered score and fold change error problems, just as it did in the latest Riboswitch and kissing loop labs.