A New Trick For Solving Puzzles: Catalyst Points

  • 13
  • Article
  • Updated 6 years ago
lroppy coined the term "boost points" a while ago (a red or green nucleotide put in a loop that lowers the energy of a loop), but since then, thanks to Brourd's insightful puzzles, we have become aware of another way to use nucleotides in the loops.

A "catalyst point" is a U or C that doesn’t seem to lower the energy of a loop in the way a boost point would, yet when placed in a loop, helps solve the puzzle.

Here’s how it works. Sometimes you have a loop that's too big because a bond is not bonding that should be. Here is an attempt at a solution for the puzzle “Simple Single Bond”:


But, this does not solve the puzzle. Here it is in natural mode:


Notice that the energy of the big loop (lower picture) is -0.5, while the energy of the two loops that you want (upper picture) is -1.9 + 3.83 = 1.93. This is why bond 7-39 falls apart, because the energy is much lower when it forms the big loop.

Now, the first thing many would try is to use traditional boost points, perhaps at 16 and 38. This will not work here, since the energy of the bigger loop will still be much lower than the energy of the two loops. In order to solve this puzzle, you must raise the energy of the big loop—the loop that you do not want. That way, it will not be so eager to form.

So, how do you raise the energy of the loop? It turns out, a uricil placed at 16 will do the trick:


(Note that it is necessary to put a uricil at 30 as well or else 16 will bond with 30). Now, when the shape is in natural mode you can see that the energy of the loop has been raised to 0.2. Here is the shape in target mode at this point:


Now the energy of the sum of the loops is -1.9 + 3.13 = 1.23. So there is a much smaller energy difference between the shape that forms and the shape that you want. We are almost there. Now we can use a traditional boost point at 38 to lower the energy of the loop on the left:


Now the energy of the two loops together is -1.9 + 2.03 = 0.13. This is less than 0.2, so the tendency is no longer to form the bigger loop, and the bond 7-39 stays together. Solved!
Photo of starryjess

starryjess

  • 35 Posts
  • 2 Reply Likes

Posted 7 years ago

  • 13
Photo of Adrien Treuille

Adrien Treuille, Alum

  • 243 Posts
  • 33 Reply Likes
This is really beautiful.
Photo of Brourd

Brourd

  • 425 Posts
  • 77 Reply Likes
You did an amazing job explaining this Starryjess.
Photo of Creatine

Creatine

  • 1 Post
  • 0 Reply Likes
This is great but I'm wondering why placing a C at 16 to block doesn't work?
Photo of hoglahoo

hoglahoo

  • 141 Posts
  • 39 Reply Likes
It doesn't work because this particular puzzle needs a different kind of catalyst point: one that both discourages the misfold *and* encourages the target shape at the same time. C only discourages the misfold, it does not further encourage the target shape (because of this, the catalyst point lroppy describes that does not boost target shape is not enough to solve this puzzle)

"So, how do you raise the energy of the loop? It turns out, a uricil placed at 16 will do the trick" Yes, a Uracil at 16 does raise the energy of the loop, but not enough by itself. A C would also raise the energy, but also not enough by itself.

"(Note that it is necessary to put a uricil at 30 as well or else 16 will bond with 30)" Yes, that is one way to look at it, but the Uracil at 30 is also needed anyway to raise the energy of the misfolded loop even further. A C would also raise the energy further.

The reason Uracils are used instead of Cs is because the Uracils are working double duty: they raise the misfolded loop energy yes (slightly more effectively as Cs would), but they also lower the energy of the target loop This kind of double-duty efficiency is very powerful. Every puzzle is solved by encouraging the target shape and discouraging all misfolds. So any mutations that can perform both these functions directly at the same time are worth noting :)

So to sum up what starryjess said a little differently, C does work to block, but it does not boost the target loop, so can't overcome the natural tendency to misfold. In fact, neither C-U, U-C, nor C-C mismatches at 16-30 will lower the energy of the target shape. But a U-U mismatch does lower the target loop energy, encouraging the target shape just enough to overcome the discouraged natural shape misfold

PS I realize this thread is 9 months old, but it seemed like the best place to post this. And I'm sure starryjess knows this stuff twice as well as I do so I hope nobody takes it as me trying to correct it, but rather expanding on it so anyone who goes back to read has a more complete picture why this particular tactic works
Photo of jandersonlee

jandersonlee

  • 522 Posts
  • 106 Reply Likes
Thanks for the clarification/update hoglahoo, and good to bring it back to the top of the list with so many new players around.
Photo of janelle

janelle

  • 29 Posts
  • 5 Reply Likes
I think this was a really good way of explaining in two ways to this type of puzzle.
Photo of starryjess

starryjess

  • 35 Posts
  • 2 Reply Likes
Thanks for your comments. :) Creatine, if you put a C at 16, the energy of the left loop is raised to 2.73 which is still too high to make the bond form. (For this puzzle, anyway. Sometimes C's do work).
Photo of paramodic

paramodic

  • 77 Posts
  • 7 Reply Likes
This is fantastic work, thank you.
Photo of bentrem

bentrem

  • 41 Posts
  • 3 Reply Likes
When you started talking the area 16 / 30 I thought you'd jumped the track.
Increase to stabilize? Whoo, yes! :-)
Photo of kcabral28

kcabral28

  • 1 Post
  • 0 Reply Likes
Wow, I wish I had found this thread earlier. Great explanation of catalyst points Starry. It made perfect sense!