Puzzles with opposing outputs, for use in diagnostic molecules

  • 2
  • Idea
  • Updated 1 year ago
  • (Edited)
Eli and I were exploring new ways to combine good OpenTB A/C and B/C switches into  good A*B/C^2 designs when we stumbled on an idea that could be useful when designing diagnostic molecules, not for this round, but possibly in future ones.

[Background: An ideal OpenTB switch is one that has only two (energetically available) foldings, with one folding occurring  when the signature formula is at or below a threshold value and the other when it is above.  The overall folding, in itself, is neither ON nor OFF.  It is only when we introduce a fluorescent "reporter" that binds to a design section that is available in one folding but not the other that the two states can be labelled ON or OFF.  And the designation of INC versus DEC puzzles is simply determined by whether the reporter binds to the folding where the A*B/C^2 ratio is high or low.]

Anyway, we were doing a (somewhat) systematic search of the ways to combine "entangled" solutions to the simple ratio puzzles into a "monster entangled" full solution when he suggested that when combining the designs, we try keep both of their original reporters instead of having them share one.  We worked through how that would work in a specific case, and found that the result would be a molecule that always shone, with one of the reporters getting brighter when the other dimmed. That wouldn't be a useful behavior for the experiments as designed to date.  But then we realized that if the reports could be distinguished, say by fluorescing at different wavelengths, it could be very useful.  Essentially, it would function as both an INC and a DEC solution, but requiring only a modest increase (or possibly not even that) in the design length.

Having both INC and DEC indications in a diagnostics is highly desirable because together they act as a check that the device isn't simply broken (or degraded).  For example a diagnostic that simply lit up in the presence of active tuberculosis wouldn't be very practical because the absence of light could mean "no tuberculosis" or it could mean "this device has a manufacturing flaw" or "this device has exceeded its shelf life".  Having the same molecule function as both INC and DEC at the same time could simplify (and hopefully reduce the cost of) the device.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes

Posted 1 year ago

  • 2
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
That's a rather neat application of the architecture I had used in the previous rounds. I hadn't really considered its use as a two signal fluorescing design, given I've always thought that one end of the device that they aim to design will be tethered to something, making the design rather difficult.

However, the only possible negative comment I've had about this architecture is that there tend to be these heavily bound helical regions within the RNA design, that may not be kinetically accessible on the timescale of a point of care device.

The other *other* issue is that you can mitigate this due to the flexibility of the architecture. The individual lengths of each oligonucleotide binding can be increased or decreased, and even the helices use in these so called 'entagled' solutions can be designed smartly, with the addition of artificial loops, decreasing the number of G-C pairs, and so on and so forth. It's *this* issue which always made me slightly hesitant about trying to explore it, given one person searching through hundreds of thousands of iterations is a task I placed near the top of my *don't have time to explore* list. Perhaps the use of the theoretical binding probabilities that Michelle has generated will give you some awesome insight on designs that do and don't work. ^_^
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
Thank you Brourd.

First of all, I want to explicitly acknowledge that your work, and in particular your presentation at Eternacon, has really opened my eyes to the opportunities available through what Eli and I have started referring to as "entanglement".  This is something I had not previously seen as a fundamental attraction pattern.  I shouldn't speak for Eli, but I believe he feels the same way about the significance of your work.

What is your notation for the template that wuami's bot-generated designs used?  At this point, I'm not really clear on the exact relationship between your templates and the "patterns" that Eli and I are working with.  I have a general sense that your templates specify stronger constraints than our patterns, which would have both advantages and disadvantages.  But I think we've collected enough experience with each that it would be productive to start comparing them in a more systematic way if you are interested.   
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
Because the entanglement strategy that Eli has mentioned in previous posts is an adaptation of one of the strategies found for solving the AB/C2 DEC and INC puzzles, and I think he mentioned that it was an adaptation of one of the sequences I submitted in one of his previous posts. Or maybe I'm not correctly recalling what he wrote.
Strategy2Diagramjpg

This being the second strategy I found for solving these puzzles (showing the example for AB/C2 DEC in this instance, but switching the A and B binding sites with C1 and C2 allows for design of INC solutions). It's rather interesting that you guys happened upon this architecture as well from an independent perspective ^_^

It was one of the more promising strategies imo, but it had issues of requiring a lot of long helices. I had also originally envisioned this version could have an internal loop by having non-bonding regions between A' and B' and B'' and A'', but again, it has such a *large* potential space for valid solutions, that automating solutions for it is far more difficult than strategy 3, which is what Wuami and Nando designs are based on.

Granted, there is some difficulty in finding novel ways to solve these puzzles. To put it in perspective, a combination of [A,B,C1,C2,R,A',B',C1',C2',R'] is an array of size of 10!, and right now I'm trying to think of novel logical rules that could be used to filter out 'incorrect' (based on Eterna game constraints) combinations. However, there is a sneaking suspicion that the three strategies I've found classify the vast majority of possible solution architectures (not based on competitive binding), that fulfill Eterna requirements. But I won't know until I've used logical rules to begin filtering out all the bad strategies, and that may not be done until the summer.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
Here's an example of a diagram we drew in a recent discussion
The similarities are more obvious than the differences. :-)  But we have only two sets of "constraints" -- the helices to form in the ON state and the ones to form in the OFF state.  If I went back and reviewed your talk, I could probably figure this out for myself, but what do the the three sets of colors distinguish in yours, and what is the difference between a three-story and a one-story pairing? 
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
They are a crude representation of the four states that the Eterna puzzle constraints are based on. It's mostly just to show the ideal way that these domains should base-pair from constrain/state 1 to constraint/state 4. I made it like 3 years ago when I needed to rapidly draw these strategies up so they could be used by Nando to develop a short script for auto design, so nothing is well-labeled :-D

Something I'm not entirely sure of in your example is the self-dissociation of the reporter oligonucleotide. One thing I tried to avoid in my strategies is the assumption that the reporter will self-dissociate without having a base-pairing domain complementary to it. Given we can't model the binding of these oligonucleotides to 'internal' loops, the Eterna model is more than willing to just say a design is 'good' if the region these oligonucleotides bind to is no longer accessible. Then again, I think having more than half the reporter bases inaccessible is enough to be close to fully dissociated at our concentrations, so it's also difficult to say whether steric effects of these bases all being close together in a hairpin loop will halt binding.
(Edited)
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
OK!  Things are coming into focus for me.  Our pattern implicitly (but purposely) says there are only two energetically available foldings, so any design that was predicted to not have the same folding for states 1-3 would be rejected.  Your diagram makes that explicit.

Re the issue of the disassociation of R, instead of trying to specify how to make sure the reporter doesn't bind in both states, our pattern leaves it to NUPACK to predict that.  For my submissions this round, I'm placing more weight on the wuami charts than the state-based evaluation, but that may change when we get lab results.
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
I understood what your chart was saying. I believe at the most basic level, you could describe the system as being the association and dissociation of (AB) and (CC)  with R as the signal. You can kind of then describe it as a two-input logic gate (in this case, either a weak AND gate or a weak OR gate, depending on the DEC or INC nature). Or even as a TRUE/FALSE logic gate. My chart was designed to provide domain interactions for each output/condition, simply given that future puzzles may have more complex logical states, so I'm just getting used to it.

And having NUPACK decide everything is a pretty decent strategy. The thing I wonder is if Wuami's charts take into account the binding of the reporter sequence, given I don't see a third axis or the binding probabilities for R associated with either the AB or C2 states.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
Michelle produces the charts from just one NUPACK run, with one set of concentrations.  She does this by using more details available from the evaluation of the partition function, not just the MFE folding.
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
I don't know enough about what NUPACK includes in its partition function, but I'm fairly certain that certain conditions like temperature, volume, concentrations, etc. are fixed. Perhaps NUPACK runs more of a grand canonical ensemble that evaluates the change in fraction bound with respect to a change in particles in the system as well?

I'm also a tad confused by Pbound in the original post. Eli defined it as

"The P in Pbound stands for proportion of the inputs that are bound"

Is Pbound actually the fraction of designs that the reporter oligonucleotide is bound to? Because that would make far more sense from what is reported on the graphs.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
A NUPACK run allows you to specify the temperature and, if there are two or more stands, their concentration.  The Web server version is http://www.nupack.org/partition/new.  I'm not sure what you have in mind by volume.

As to how the wuami chart is created from the NUPACK outputs and what it "means", only wuami knows the details. I don't think she is trying to keep it a secret, but when I asked, she said it was complicated, it involved some judgement on her part, and unfortunately she hadn't written up anything about it yet.

I'm not sure where Eli posted the quote you referenced, but he was probably taking it from something I wrote, and yes, it should refer to the reporter, not the inputs.
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
Awesome! That makes a lot more sense ^_^

As for the charts, I'm thinking it must mean there is an option to set concentration gradients somewhere. Otherwise, (I would think) the partition function is based on the microstates of a steady state system, which means all concentrations are constant.

As for the meaning, it's quite simple really. The graphs are heatmaps that describe the fraction of the microstates to which the reporter oligo is bound as a function of the concentrations of A, B, and C. At least, that's what they appear to be, unless there is some clarification.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
The intent, as you say, is to predict the reporter binding in certain planes of the three dimensional space.  But they are, indeed, extrapolations made from calculations that NUPACK makes at just one set of concentrations.

If you would like more explanation from Michelle, I suggest you ask her in the topic about the charts.  I can't promise she will respond, but I will draw her attention to the fact that you asked.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
I would summarize our current notation as being geared toward a set of problems distinct from the logic gate problems. That is, they are intended to generate designs where the goal is to compute a linear inequality (linear in log concentrations, not raw concentrations).  Those designs might be adequate (but not necessarily optimal) for simpler logic gates, and completely inappropriate for convex functions like XOR.

This would identify them as a subset of what you can potentially specify.  On the flip side, the simpler constraints make for more possible pattern variations, which should be easily enumerable.  I think Eli has done this, coming up with 12 unique patterns for the full OpenTB puzzles, and constructed at least one sequence acceptable to NUPACK for each one. (I may have the details wrong.)

As I understand it, the Khatri lab has identified several more mRNA signatures for serious global-wide diseases, and all of them fit the linear inequality model. So there should be relevance for this type of solution, even after TB has been vanquished. :-)
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
While it is true that we are designing a device that is capable of essentially recognizing a change in the concentration/activity and equilibrium of several genetic markers within a system, to a very specific reaction quotient, I would argue that given the way we approach the design of solutions to this problem has binary features to it. I would argue that it's mostly due to the fact that we have only two conditions that we (in the game gui) can see the reporter RNA adopt. That is, either the reporter is bound to the RNA substrate, or is dissociated.

From this, the way we design the solutions will typically be binary in nature as well. The decrease in [C]^2 is tied to either the association or dissociation of the reporter, and the easiest way to do this is through the association of [R] binding with either [A]*[B] or [C]^2. This binary nature is present in a number of designs. Now, there are some variations to this, which typically occur as designs where only the change in [C] is driving the change in the substrate structure, but when players design these solutions, do they realize that they aren't designing to compare against the activity of [C]^2, which in a physical sense means we're wanting to measure the change in activity for two of a chemical species?

Granted, that's where I see the power of the fraction binding charts that Michelle was kind enough to make. It provides information that a binary ON/OFF condition could never tell a player. 

The above reasoning was why Nando and myself agreed that strategy 3 (the same used for Michelle's designs) was one of the better strategies, given the independent binding of A and B both individually affected the binding of a single C and R, so you get a certain degree of binding selection that you can theoretically tune based on what looks like it could work.
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
Have you recorded somewhere what strategy 3 is?
Photo of Brourd

Brourd

  • 452 Posts
  • 82 Reply Likes
It's in the presentation and other places, but here is another image
Strategy3Diagramjpg
Photo of Omei Turnbull

Omei Turnbull, Player Developer

  • 980 Posts
  • 308 Reply Likes
Thanks.