# Logic Gates

• Article
• Updated 3 years ago
This is a conversation for the logic puzzle results from Round 102: Logic Gates

johana, Researcher

• 96 Posts

Posted 3 years ago

johana, Researcher

• 96 Posts
• 2222 Posts

Oligo order and trends

I earlier shared a drawing of my working hypothesis for last round - the image below.

I have been checking how it went. Here are the crude overall trends for oligo position in this round's winners.

Overall the oligo colors are trending in the same direction as I expected - plus a bit back and forth. However there is something else standing out now. Which is actually rather pretty.

I have been watching a few videos on domino’s and logic gates the latest days. In one of them I heard that that the opposite of an AND gate is an NAND gate and the opposite of an OR gate is a NOR gate. Here are one of my favorites on domino computing so far. :) And this one gives the best visual explanation I found.

When I look at the trends for the labs above, it becomes clear that I can pair them two and two and not only will they be their own opposites in function - but the orders of the oligos will literally be reversed.

So to get to an NAND gate from an AND gate, one just reverses the oligos. Sometimes MS2 position will change a little too in the process.

So here I line the designs up just in pairs as sorted in pairs and oligo and switch element order.

Only the last pair A AND NOT B and the A OR NOT B, don’t have this reversal pattern. Not sure what goes on there.

I really like the logic table overview of our 8 basic logic gates, that Johan has put up in his results distillation for this round's results, so I’m reposting it here with a few arrows added. This is basically what I have done above.

MS2 position and trends

MS2 position also matters a lot. I was aware when fiddling with making the NOR lab. That one I wanted an end positioned MS2 not between the oligos, just as its OR partner lab.

Another trend stands out clear now, but has been present earlier also is that when MS2 is in between the oligo complements, it has a favorite oligo complement neighbor. This is not in all labs but in a higher amount of labs than not).

More often the MS2 wants to be close to the input later in the RNA sequence, over being close to the oligo complement earlier in the sequence. This goes for the XOR, NAND, A AND NOT B, A OR NOT B - out of the all in all 6 labs, that have the MS2 in between the oligo complements. The other two labs in that series have their MS2 at a somewhat middle position between the oligo complements.

• 2222 Posts
Crossed GU’s are now legit :)

One thing I see pop up more and more are crossed GU’s. In particularly in switching arms - where more than one stem in a row need to be switching.

GU’s getting more and more present compared to earlier single input labs. Also as same turning GU base pairs.

Earlier the only place crossed GU’s made any kind of sense in a static lab, was if the design had real long stems.

Crossed GU’s worst characteristics is that they split stems open in static lab, which however can be their finest quality in switch labs, where stems needs to get moving.

One of the horrors of static lab has now come useful. :)

• 2222 Posts
Number of RNA inputs and strength of magnet segments

Magnet segments seem to be more dominant and longer now in the two RNA input labs compared to the 1 input microRNA lab and even more compared to the molecule input MS2/FMN riboswitches on a chip. I think this pattern shall grow stronger the more inputs we get.

Some of the magnet segments now also more often have the C in their GC switch for an U, so a GU now pops up in the magnet segment. Probably to help things not get too bound.

This is also a way to balance strength of the magnet strands. One magnet strand in the switching magnet stem, can be full strength where the other can be weaker. Thus the strong magnet segment can go on to become a partner with another strong magnet strand. So it is a way of controlling strength of the magnet strands and when they should go full power.
• 2222 Posts
Uneven energy distribution in two input switches

Mat mentioned my even energy distribution thoughts when I mention the closeness in energy between the state 2 and state 3 with either oligo bound. As they were asking for similarities in energy. We were analyzing the first round data.

This got me inspired. I have earlier watched for signs of uneven energy distribution turning up in switches as I was expecting them to behave differently to static designs.

However I haven’t seen much of it so far. That is until the logic gate labs. I was starting to get a whiff of it in first round. I think I start see more of it with all the nice winners we have gotten. Not every design has it. I’m mainly interested in energy unbalance in the design - when it pairs with itself. As the inputs are locked.

I’m aware that both microRNA’s contain strong sections with C’s that results in G magnet sections in the sections. So part of the magnet elements present are caused by the inputs.

I think the more RNA inputs there are, the more we are going to see uneven energy distribution in the switching area. Just as the strength and length of the magnet segments seems to have gotten longer, the more inputs there are.

In the designs below I have highlighted energy rich areas (with green) - which will be contrasted by other more energy poor regions.

Intro and fold change error

We seem to have higher fold change error rate this round, so I have set my cut off range far higher than I normally would. My cut off point is 1.4 and in labs when having lots of winners, I will set it lower.

Most of the designs I draw overview - there are multiple winners of the same type, so the fold change error shouldn’t have as much effect as there will be similar designs but with a better error rate. I have picked the design with highest fold change and if there were minority types too that was rather different.

Lab overview drawings

XNOR

http://www.eternagame.org/game/browse/6434648/?filter1=Id&filter1_arg1=6501007&filter1_arg2=6501007

XOR

Score 98%

http://www.eternagame.org/game/browse/6434627/?filter1=Id&filter1_arg1=6471802&filter1_arg2=6471802

NAND

Score 100%, minority

http://www.eternagame.org/game/browse/6434644/?filter1_arg1=6612031&filter1_arg2=6612031&filter1=Id

Score 98%, majority

http://www.eternagame.org/game/browse/6434644/?filter1_arg1=6623784&filter1_arg2=6623784&filter1=Id

AND

Score 100%, majority

http://www.eternagame.org/game/browse/6434647/?filter1_arg2=6471708&filter1=Id&filter1_arg1=6471708

Score 97%, minority

http://www.eternagame.org/game/browse/6434647/?filter1_arg2=6494152&filter1=Id&filter1_arg1=6494152

Score 95%, minority

http://www.eternagame.org/game/browse/6434647/?filter1_arg2=6590217&filter1=Id&filter1_arg1=6590217

With extreme amount of GU’s - even a crossed set.

NOR

Score 98%

http://www.eternagame.org/game/browse/6434625/?filter1_arg2=6496405&filter1=Id&filter1_arg1=6496405

The pattern that I recently mentioned for reducing amount of possible pairings, with concerted move of several magnet segments at once, runs through many of the logic gate winners.
OR.

The NOR design overview above, shows it strongly.

Score 100%, minority

http://www.eternagame.org/game/browse/6434654/?filter1=Id&filter1_arg1=6605332&filter1_arg2=...

Score 100%, majority

http://www.eternagame.org/game/browse/6434654/?filter1=Id&filter1_arg1=6507103&filter1_arg2=6507103

Notice the crossed GU’s

A OR NOT B

Score 100%, majority

http://www.eternagame.org/game/browse/6434649/?filter1_arg1=6484949&filter1_arg2=6484949&filter1=Id

Interestingly enough here are a lot of GU’s mixed in around the magnet segments. I think we are going to see this a lot more. Especially for 2 input labs. Whereas for uneven energy distribution I think it will first get full into play with 3 inputs.

I also generally see a lot of crossed GU’s in the switching stems. Here is one case from the above design.

A AND NOT B

Score 100%

http://www.eternagame.org/game/browse/6434626/?filter1_arg1=6508587&filter1_arg2=6508587&filter1=Id

(Edited)
• 2222 Posts

I missed a few working and winning mutants in the first run. So here they come :)

Also I did a redrawing of my early expectations (reposted below) from before we had the lab data

Redrawing after lab data

Two labs are way more tolerant of reversals of input landing site than the others. AND and A OR NOT B.

It is not always related to how easy the lab seems - judged by the amount of winners. As A AND not B has a ton of winners, but only show up as one main type in relation to the inputs.

However for AND it do make sense that both input ways are possible. As Omei said:

“Consider the AND puzzle. If you increase the amount of either input, in any combination, the output keeps changing in the same direction. But that isn't the case for XOR and XNOR.”

• 2222 Posts

Uracil in switches versus static designs

I was watching a lesson on RNA versus DNA in Khan academy. Sal said that the RNA base Uracil was less stable than the corresponding DNA base Thymine. This caught my attention.

Molecular structure of RNA

Beware of non Eterna base colors ;)

I have for a while been wondering about the difference in base content between switch and static labs. And as I mentioned in an earlier post:

U repeats also seems to be beneficial in a higher degree than usual for static labs. Something that has also been visible in our recent MS2 and mirRNA lab results.

Early in the Riboswitch on a chip labs, long stretches of U’s seemed a problem, but after Johan got barcodes on the designs, we seem to have more U content than earlier.

Uracil content in different switch labs

I don’t think a switch will need the same high amount of U bases no matter what. I have long wondered why eg the full moving designs seemed to have more U’s, than both the open ended switches and in particular the partial moving switches. What Sal said, I think goes to explain that well. Uracil making things more unstable.Which is more needed in full moving switches compared to switches that do not move much.

Similarly I suspect something else may also have an effect on U percentage - the amount of inputs. The more inputs and switching regions, the more it is needed it is to get the switching gliding. And the more U’s I will presume.

Salish earlier made a graph of the U content in relation with score, for our first round of Riboswitch on a chip labs.

Salish’s graphs

From our latest Riboswitch on a chip lab, round 101

These Riboswitch on a chip lab don’t have an especially high a U content. However I’m interested in seeing the U content of some of the more full moving switches. Exclusion 5 and 6, from an earlier round. Unfortunately there weren’t really enough designs and high scorers in these two labs, to get a clear picture - although I do think they will tend to harbor more U’s.

However something else stood out. The microRNA single input labs, which have more bases moving than the riboswitch labs, have a high U percentage compared to the majority of the Riboswitch on a chip labs.

Uracil content in winners in the Logic gate labs, round 102

I wanted to see how our A/B labs with one and two inputs and no MS2, did in comparison. And seemingly most of the labs that have two inputs, R2, R3 and the two predefined labs, are in the heavy end when it comes to Uracil percentage. R3 don’t pan out as heavy, something which I suspect is due to its few top scoring designs and them exclusively being of the lane sharing type. Since lane sharing sharply reduce how much of the RNA sequence the design complex uses, a part of the design can be tied up in a regular static stem, so it doesn’t need as many U’s.

Similar mostly the single input designs have a little less U’s, Sensor A MS2 OFF excepted, compared to the designs with two inputs.

MS2 neighbor bases - continued

Now my observation of the UU bases on each side of the MS2 in logic gate lab starts to make even more sense, although I already suspected U’s to have a gliding/destabilizing effect.

Drawing over first round of logic gate high scorers taken from this post.

I have made a drawing based over the winning designs from round 2 of the logic gates. Many of these designs are mutation of the same design and as such do not point to what will be allowed if mutation was done in this region. I will expect most of the trends will hold, but that a few of them may change.

The two labs that have most their MS2’s turned on (3 of 4) have the potential stabilizing U and A around their MS2. (NAND and OR)

When we got the data back on the latest Riboswitch on a chip lab, I also noticed that the strange PWKR design with the extreme high fold change and potential for holding two FMN molecules, almost exclusively favors U’s around its MS2. Most of the designs where other bases on the side scored less well or got hurt on their fold change.

UU around the MS2, notice the many winners

With C in front of MS2

With C after MS2

Here there still two pyrimidine around the MS2, so still gliding and not hurt. Except it isn’t getting the prettiest fold change, compared to its siblings with UU around the MS2.

With G before MS2

With G after MS2

With A before MS2

With A after MS2

Fold change of the designs that have the UU mismatch around their MS2

Sum up and perspective on use of Uracil in switches

Switches in contrast to static designs, seems to benefit more from a growing amount of Uracil's due, which would likely be due to its destabilizing nature according to what Sal said science have already figured out.

Not that I think every switch lab will benefit equally much. Partial moving switches with stabilizing static stems, seems to need less Uracil's compared to fuller moving switches. Also I expect switches to benefit more, the more inputs they have.

With 3 input switches just around the corner, I will be expecting ridiculous amounts of uracil. :)

(Edited)
• 2222 Posts

Position and changed kcal

It was the XNOR design results that got my adventure from the other day started. I had made a design for the logic gate lab XNOR that I really liked and I was kind of expecting it to do well. (XNOR 16) But it didn’t. That made me compare it with the winning design series.

The only difference between those two are really the placement of the MS2 hairpin. Afterthought: Ok, it also has a static stem too. That may affect things - oops. Bad example. Still made my mind click though. :)

So I will play this out and I shall come up with some better examples afterwards and demonstrate what I mean.

In my design the MS2 was placed somewhere between 2/4 and the 3/4 part spot, and in the winner it was placed earlier at the 2/4 part spot. Then I decided to check these series energies. And the winning design series, had more negative energy in state 1, than my XNOR 16 design series.

Showing state 4 for overviews sake. Same energy pattern there though.

Loosing series, XNOR 16, score 35%

Highest score 62%

The mutants (series 6499042) based on the design improved, but suffered a similar fate. Less negative kcal and no high scores. A similar pattern played for the XNOR 15, XNOR 17 and other mutant series too. Less negative kcal than the actual winning series.

Winning series, score 100%, static stem in 4/4 region

http://www.eternagame.org/game/browse/6434648/?filter1=Id&filter1_arg1=6501007&filter1_arg2=6501007

Notice the far more negative kcal

Now just because one has high kcal doesn’t mean one will get a winning design. All the ones with 92 last in their title belong to the winning series. But as can be seen there are other designs beside that series, with a negative kcal.

As a sure way to high kcal is to go Christmas tree and put in lots of GC pairs. Note: Switches hate Christmas tree style, just as static lab.

Here is one design that is related to the winning series, but goes christmas tree on the static stem. Christmas trees are something D9 helped warn us about - they are not as nice in the RNA world as in our big size world.

Score 32%

http://www.eternagame.org/game/browse/6434648/?filter1_arg1=6619276&filter1_arg2=6619276&filter1=Id

This design is very helpful for showing that even just one stem solved in total Christmas tree style, despite the rest of the design being alright, seemingly is enough to throw the score overboard.

Now the other designs with high GC base pair count, didn’t all go directly Christmas. But they used more GC pairs - which is another way to make kcal more negative.

When I pull a sorting after GC content, I get more designs from the winning series at a lower GC count (for 1 state)

http://www.eternagame.org/game/puzzle/6434648/

And when I pull a sort of the higher GC content, I get the designs with more negative kcal, but not winning score. Also notice that there is a relation between GC pairs and negative kcal. The more GC pairs, the more likely kcal is more negative.

Hopefully this goes to illustrate how you can get large negative kcal by using more GC pairs - but also why it should be avoided as a strategy for achieving a high kcal. Too many GC pairs will halt the switch from switching.

What will be too little or too much GC pairs, will vary with lab and lab type. Best trick is to watch out for normal GC content for winners in similar past labs when such are available.

NB. Note that the kcal shown in the interface for state 1, is Vienna energy engine, but the kcal for the puzzle is shown with NUPACK, so they vary. But I think they are trending similar.

• 2222 Posts

AND logic gate - and a slide

I have been thinking some more about compacted designs that do not fill out the full space of the RNA sequence.

There is one more of the logic gate labs that had some of its designs not using the full space of the RNA sequence, just as the XNOR logic gate winners.

There was one design series that achieved a winning score. However I think this series would have given serious back wheels to the rest of the winners so far, if it was just slided to the left. This design is of the type that do not fill out the whole design, which is exactly the kind of design that I think will benefit from a slide. (Background article: What has Gibbs energy got to do with it?)

I have highlighted the unused areas of the RNA sequence.

Score 94%

http://www.eternagame.org/game/browse/6434647/?filter1=Id&filter1_arg1=6467496&filter1_arg2=6467496

Here is how I slided the design. Notice how kcal change.

1. I highlight the area I wish to slide with Shift + mouse dragging

2) I hold shift down and use the back arrow to move the design towards the 5’ end of the design. (Base 1)

Now I open PIP mode again and watch the kcal. It is more negative compared to what I started with, which is a good sign.

Original puzzle, energy for middle placement

Left slided, kcal goes more negative for all states, but state 3. State 3 has same kcal for each puzzle version.

Why not slide the design to the other side then? I can imagine some cases where this will be of benefit.

But when I slided the design right in this case, I get less negative kcal in first state and second state, although state 4 remains the same. The puzzle goes unstable in the energy model too. Something that is often, although not always, a bad sign.

I conclude that left slided is overall best, since kcal goes more negative, compared to what I started with.

I still have a somewhat dangling end at the last end of the slided design, that will most likely benefit from being made into a static stem, just as in the XNOR winners. By making a static stem, kcal will go more negative. It is important not to overdo it and throw in tons of GC pairs, as I illustrated here the other day.

I threw in a line of G’s and of C’s to make things pair up. Notice the huge jump in kcal.

Now I fix the stem by throwing in a more fair amount of AU’s into the mix. Now I’m almost done. And kcal is still way more negative than what I started with - in all states. Without doing any monster GC cheating.

And since the stem is 8 base pairs long, it will start benefit from a GU somewhere in the middle also.

Check and I’m done

• 2222 Posts

Which end of the design should I place which oligo complement at?

I was wondering if I could use my newfound understanding of kcal to also help tell which end of the design the ologo’s should be placed at. And for now it really seems so.

Most labs with RNA inputs show a clear preference for which end to have which oligo complement. (The AND gate lab accepts having oligo complements at each far end and also having them swapped around, but still there is a majority of one type.

The kcal pattern stands clearest out in designs that do not use the full stretch of RNA. So I picked my XNOR mutant for the experiment. Then I hooked up the oligos in reverse order and left the rest of the design undisturbed. The newly made design still solved but looked more ugly - that bend in state 1 is nasty. Plus it had less negative kcal. So I bet it will be no real competition to the original.

And the real sweet thing is that NUPACK already knows. :)

Ugly reversed oligo solve - with less negative kcal

CGAAUGAGGGUACUGCUUUCCCACAUGAGGAUCACCCAUGUUCCGUCCUUAUUCUUUAUUGUUAGCACUGACUAUUAGUCAGUGC

Original solve, score 100%, more negative kcal in all states

http://www.eternagame.org/game/browse/6434648/?filter1_arg1=6501007&filter1_arg2=6501007&filter1=Id

While we can make designs work in lab that NUPACK says will fail and while we can also make up for some of the things that NUPACK think will work, but that we know won’t, I think it has a pretty good idea on energy - even as simulation. As long as we don’t totally GC hack it.
• 2222 Posts
Use of GU in two input labs

With the two input labs, we have seen a far higher amount of GU’s in the switching area compared to earlier switches. But even in earlier switches GU’s often plays a role.

Mostly I couldn’t delete GU’s already embedded in the switching area of winning and high scoring Riboswitch on a chip designs, without a score and fold change drop. I think the GU’s are really important for switch-ability.

I find it interesting that the crossed GU’s turns up in a design with an extreme high fold change.

Double same turning GU’s are also routine now. I have earlier said that that designs when having 3-4 GU’s rather close in the same stem tended to get grumpy and that still happens sometimes. But I have now seen it several times in winning designs too. So still be careful putting in too many. Just be alert that it seems allowed now to a bigger degree than before.

I decided to shoot some of the designs with GU. I typically pick the highest scoring and with highest fold change of each type representative.

AND

In my design I have a double set of crossed GU’s. Thinking about it, these crossed GU’s particularly seems to pop up specifically when the oligo complements needs to be turned off.

What is real fascinating is that each half of the crossed GU sets in the complement turnoff area, actually folds with each other in 3’d state to fold an additional set of crossed GU’s, outside of oligo complement area

Score 98%, fc (fold change) 58, fc error (fold change error) 1.26

http://www.eternagame.org/game/browse/6434647/?filter1=Id&filter1_arg1=6466266&filter1_arg2=6466266

As in the above example, each oligo complement that is turned off (state 1) by its neighbour sequence, also gets a set of crossed GU’s.

Design by NasimeBehesht

97%, fc 52, fc error 1.20

http://www.eternagame.org/game/browse/6434647/?filter1=Id&filter1_arg1=6494152&filter1_arg2=6494152

Design by Malcolm

Example with 3 GU pairs in same stem - state 2.

Score 95%, fc 44, fc error 1.13

http://www.eternagame.org/game/browse/6434647/?filter1=Id&filter1_arg1=6590217&filter1_arg2=6590217

NAND

Design by Worseize

Also notice the 2 nt bulge with crossed GU closings (state 1 and 3). I also seen 1 nt ones of that type. I’m still making my mind up on if they turn up mainly in designs with high fold change error rate also.

Score 100%,  fc 82, fce 1.31

http://www.eternagame.org/game/browse/6434644/?filter1_arg1=6612031&filter1_arg2=6612031&filter1=Id

Mutation based on Brourd design

Score 95%, fc 43, fce 1.18

http://www.eternagame.org/game/browse/6434644/?filter1_arg1=6623792&filter1=Id&filter1_arg2=6623792

A OR NOT B

Mutation based on JR design

This design is the one with the absolute highest fold change in the lab.

Crossed GU, Score 100%, fold change 282, fold change error 1.28

http://www.eternagame.org/game/browse/6434649/?filter1_arg1=6484949&filter1_arg2=6484949&filter1=Id

Mutation based on same design as before

Same turning GU, score 100%, fc 96, fc error 1.25

http://www.eternagame.org/game/browse/6434649/?filter1_arg1=6485450&filter1_arg2=6485450&filter1=Id

Mutation based on Eternacac design

This one has its oligos reversed compared to the other designs in this lab

Score 98%, fc 64, fce 1.25

http://www.eternagame.org/game/browse/6434649/?filter1_arg1=6508752&filter1_arg2=6508752&filter1=Id

Ok, the state 2 crossed GU’s shouldn’t form as the A inputs needs to fold up in that region and that is what it is doing in lab, although not in simulation.

A AND NOT B

The designs with highest fold change don’t have double GU’s. Not all labs seems to need them equally much. This lab in particular had many winners suggesting it was rather easy.

Mutation on Malcolm design

Score 100%, fc 98, fce 1.20

http://www.eternagame.org/game/browse/6434626/?filter1_arg2=6508587&filter1=Id&filter1_arg1=6508587

NOR

This lab has 4 winners. All of them carrying crossed GU’s. With the absolute winner carrying most of them.

Mutation of Astromon design

Score 98%, fc 59, fce 1.09

http://www.eternagame.org/game/browse/6434625/?filter1_arg1=6496405&filter1_arg2=6496405&filter1=Id

Just like the AND winner, this one has crossed GU’s in each its folded complement inputs in state 1. Plus an extra made from both the sets, in state 3.

OR

Designs with static stems in the switching area, has fewer parts involved in the switching and as such has a smaller need for having crossed or lots of GU’s in the switching area

Here is only one GU per switching stem. (MS2 excluded) Static stem highlighted with blue.

Score 100%, fc 116, fce 1.34

http://www.eternagame.org/game/browse/6434654/?filter1_arg2=6605332&filter1=Id&filter1_arg1=6605332

Mutation of Brourd design

Score 100%, fc 97, fce 1.40

http://www.eternagame.org/game/browse/6434654/?filter1_arg2=6507103&filter1=Id&filter1_arg1=6507103

XOR

There are no directly crossed GU’s or some same turning blocks of them in the winning XOR designs. Unless one count crossed GU’s that are in the same stem, but next door neighbors. I have long advised crossing GC pairs in static designs. I never would have thought I would recommend crossing the GU pairs. :)

But that too is a pattern that turn up in a lot of the higher scoring designs - in the same stem. Often distanced by a GC pair. Here is one example from the third highest scoring design in this lab.

Nando mod by Omei

Score 96%, fc 47, fce 1.20

http://www.eternagame.org/game/browse/6434627/?filter1_arg2=6651806&filter1=Id&filter1_arg1=6651806

XNOR

No closely crossed GU’s in this lab either. All the winners were of the design complex abbreviated type. They were having a static stem at the end. Thus reducing the amount of switching basepairs. Still there was a good deal of GU in use, just more spaced out.

GU’s highlighted in the winner.

Score 100%, fc 87, fce 1.32

http://www.eternagame.org/game/browse/6434648/?filter1_arg1=6501007&filter1_arg2=6501007&filter1=Id

AB labs with two inputs

Now the logic gates are not the only labs with two inputs. I see a similar pattern ocour in the R2 winners that are not abbreviated by lane sharing or static stems.

Here JR’s winner from R2

It contains one of the crossed GC 1 nt bulges too.

Score 97%

http://www.eternagame.org/game/browse/6204761/?filter1_arg2=6326622&filter1=Id&filter1_arg1=6326622

Sum up on GU’s in two input labs

While logic gate switches are generally more GU sponges compared to earlier switch labs, not all labs needs equally high amount of GU’s. It also depend on design type. Designs with static stems (OR, XNOR) and designs complexes that don’t fill the whole of the RNA sequence, don’t seem to need as much GU. (XNOR, R3) Similar there are some labs that don’t have high amount either, which I can say why.

Not all the labs need their GU’s the exact same way. But there are a strong pattern towards using more GU, crossed GU sets and same turning GU sets for particular labs.

(Edited)
• 2222 Posts
Mismatches between oligo and complement

Last round I mentioned 1-1 loops seemingly turning up as a pattern between oligo and oligo complements. They seemed to turn up in the middle or close to magnet segments.

I mentioned that some of the designs may even benefit from more than 1 set of 1-1 loops and that I suspected that not each oligo would appreciate equally.

While 2 1-1 loops against the same oligo is rare, there did turn up a pattern. The weaker input A appreciates 1-1 loops to a far smaller degree than the stronger B input.

In many of the labs and winning designs, the weaker A input actually prefers having no 1-1 mismatches, where the stronger B input regularly has one.

I think having a mismatch or not between an input and its complement is a balancing act.

What is to be won by adding a mismatch, is that the oligo doesn’t bind too strongly to the design - thereby slowing the switch down or not having it happening.

On the the other hand each time a mismatch between oligo and complement is made a prize is paid. As the kcal can’t get as negative.

So it makes sense that not all labs needs this kind of mismatches equally much.

Labs that have few mismatches between oligos and complements are the XOR, NAND.

AND and XNOR has few mismatches against the weaker A input.

What accounts for both inputs, is that if a mismatch occurs between input and design, it regularly pops up next to some stronger magnet regions - likely because the design needs a little help getting loose from the oligo.

Here are a few examples of mismatch patterns

What I find worth noticing is that this mismatch pops up next to the magnet segments as was found beneficial in other labs. Similar this 1-1 mismatch pops up in in the middle which has also been suspected to be beneficial.

XNOR

Score 100%

http://www.eternagame.org/game/browse/6434648/?filter1=Id&filter1_arg1=6501007&filter1_arg2=6501007

Another thing worth noticing is that the weaker A input doesn’t have a mismatch. No matter what side it is on. This is revealing that this weaker input has a need for a far closer grip. The trend continues for many of the other labs.

The lab designs in the NOR lab breaks this trend. There the weaker A input also have breaks in them. There are only 3 of them so I can’t say if it will continue. This lab has its MS2 late in the sequence and not between the oligo complements.

AND

100%

http://www.eternagame.org/game/browse/6434647/?filter1_arg2=6471708&filter1=Id&filter1_arg1=6471708

XOR

Score 98%

http://www.eternagame.org/game/browse/6434627/?filter1=Id&filter1_arg1=6471802&filter1_arg2=6471802

• 2222 Posts
Kcal difference between state 2 and 3 in logic gates

Last round I noticed there seemed to be a relation between kcal in state 2 and 3, for higher scoring designs. If kcal difference gets too big it gets more and more hurtful for score. Basically this is like my even energy distribution idea - just between states with similar inputs, as Mat pointed out, when I presented him with the idea then.

I think the reason for this kcal relation, is that both state 2 and state 3, which each bind either the A or the B input - get a somewhat similar kcal score - due to both inputs being of similar length and them not holding equally strong bases.

Of cause other base pairs also regularly form in the switching area and as such also add to the picture. If there are many base pairs difference between the two states - this will also result in a bigger kcal difference.

However as I have long been saying, the more switching pairs, the harder it is to get things switch correct.

Last round I set 5 kcal difference as cut off, but also suspected that some labs would need a slightly larger difference. Indeed that is the case for the NOR lab. Its winners have a difference range going up to 6.1 kcal difference.

Here is a winner from the NOR lab with a difference at 6.1 kcal.

However the main pattern still holds. The bigger difference, the more likely it is that the design is not doing well. So I think we can use this pattern to rule out a good deal of the bad designs, without touching too many of the better designs.

• Equal energy between state 2 and 3 seem to be more prevalent more low scoring designs - while it can be present also in winners

• Small energy difference like 0-1 kcal also seems to be more prevalent in low scoring designs - again winners also do carry the pattern.

• A large energy difference happens when one oligo is judged by the energy model to not bind. This is present in high scoring designs too, but also more prevalent in lower scoring designs

I put up a strategy for this.
(Edited)
• 2222 Posts
Switching magnet stem

Last round I began to expect switching stems of magnet segments to begin play a stronger role in our logic gate designs.

It did not turn up as close to the MS2 as I had expected. But it is still there and based on a stretch that is not part of the input complements.

Really when thinking about it, the magnet segments are the periodic repeats of the MS2 switches - created by the MS2, just like the locked aptamer was creating this repeat pattern.

Later I realized that designs that had static stems in them, blocked the repeat pattern from propagating to the rest of the design. And those designs were easier solving than those filled with periodic repeats.

And this is really the same I’m saying too in the post Christmas snake. The fewer the repeat magnet segments, the more likely it is that the right ones find each other. And one way to do this is to place in static stems.

A OR NOT B

Mutation based on JR design

Score 100%

Now state 3 probably fold different, as it wouldn’t solve if it didn’t.

A AND NOT B

Think the original design behind the mutations is one of Malcolms. Switching stem in front of MS2 in state 2.

Score 100%, fc 120, fc error 1.16

http://www.eternagame.org/game/browse/6434626/?filter1_arg1=6609865&filter1=Id&filter1_arg2=6609865

Here the MS2 gets involved in the switching magnet stem also. Really when thinking about it, the MS2 pyrimidine stretch has moved a little away from the MS2.

XOR

Malcolm’s original XOR solve, XOR Gate #45 rerun

This one have the structure around MS2 that I expected.

Score 100%, fc 79, fc error 1.11

Notice that they have the pyrimidine stretch before the MS2 and the purine stretch after the MS2. Same pattern as for the aptamer gate in the best scoring same state NG 2 designs in the riboswitch on a chip labs. (Link)

Jieux, Mat mod of Malcolm design

Here the B input complement is involved too in state 2. Else the switching magnet stem is mostly MS2 turned off by a pyrimidine stretch before it. Just like Exclusion NG 2 in the riboswitch on a chip labs.

Score 100%, fc 132, fc error 1.18

http://www.eternagame.org/game/browse/6434626/?filter1_arg1=6653286&filter1=Id&filter1_arg2=6653286

XNOR

Score 100%, fc 87, fce 1.32

http://www.eternagame.org/game/browse/6434648/?filter1_arg2=6501007&filter1=Id&filter1_arg1=6501007

OR

This mutant doesn’t have as much of the magnet segment repeats. But it also has a static stem in the switching area

Score 100%, fc 115, fce 1.34

http://www.eternagame.org/game/browse/6434654/?filter1=Id&filter1_arg1=6605332&filter1_arg2=6605332

Mutation of Brourd design

Score 100%, fc 97, 1.40

http://www.eternagame.org/game/browse/6434654/?filter1=Id&filter1_arg1=6507103&filter1_arg2=6507103

NOR

Mutation of Astromon

Score 98, fc 59, fce 1.09

http://www.eternagame.org/game/browse/6434625/?filter1_arg1=6496405&filter1_arg2=6496405&filter1=Id

NAND

Worseize design

Score 100%,  fc 82, fce 1.31

http://www.eternagame.org/game/browse/6434644/?filter1_arg1=6612031&filter1_arg2=6612031&filter1=Id

Mutation based on Brourd design

Here the input B complement gets taken in use too in state 1 and 2.

Score 97%, fc 53, fc error 1.24

http://www.eternagame.org/game/browse/6434644/?filter1_arg1=6623784&filter1_arg2=6623784&filter1=Id

AND

99%, fc 67, fce 1.36

http://www.eternagame.org/game/browse/6434647/?filter1_arg1=6471708&filter1_arg2=6471708&filter1=Id

The AND and XOR lab original gave raise to the special structure around the MS2 already in first round. A bubble between the MS2 and a stem afterwards.