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jeff101's picture
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On recent Design Puzzles, I have been making barrels from 
loops and parallel sheets. I have tried barrels with 
triangular cross-sections and square cross-sections. 
Below is about Puzzle 1546 where I tried square barrels.

Sequence and Secondary Structure:

In Puzzle 1546, I used 2 different starting sequences 
& secondary structure settings, each with 107 residues:

     000000000111111111122222222223333333333444444444455555555556 
     123456789012345678901234567890123456789012345678901234567890 
     eeHeeHeeHeeHeeHeeHeeHeeHeeeeHeeeeHeeeeHeeeeHeeeeHeeeeHeeeeHe 
Je1a=vtLvtLvtLvtLvtLvtLvtLvtLtvtvLtvtvLtvtvLtvtvLtvtvLtvtvLtvtvLt 
Je1b=tvLtvLtvLtvLtvLtvLtvLtvLvtvtLvtvtLvtvtLvtvtLvtvtLvtvtLvtvtLv 

     00000000000000000000000000000000000000011111111
     66666666677777777778888888888999999999900000000
     12345678901234567890123456789012345678901234567
     eeeHeeeeHeeeeHeeeeHeeeeHeeHeeHeeHeeHeeHeeHeeHee
Je1a=vtvLtvtvLtvtvLtvtvLtvtvLvtLvtLvtLvtLvtLvtLvtLvt
Je1b=tvtLvtvtLvtvtLvtvtLvtvtLtvLtvLtvLtvLtvLtvLtvLtv

Each contains many sheets (e) of length 2 or 4 made 
of valine (v) and threonine (t) residues separated by 
helices (H) of length 1 made of leucine (L) residues.
I chose these residues because I had read that the 
best sheet residues are tyrosine (y), phenylalanine (f), 
tryptophan (w), threonine (t), valine (v), or 
isoleucine (i) while the best helix residues are 
methionine (m), alanine (a), leucine (l), glutamate (e), 
or lysine (k). 

My goal was to have the hydrophilic threonines on the 
outside of the barrel and the hydrophobic valines on the 
inside of the barrel. I also wanted the leucines to end 
on the outside of the barrel, despite being hydrophobic. 
Surprisingly, in previous puzzles, leucines seemed to work 
better at these positions than other (generally hydrophilic)
residues that I tried.

I chose single-residue helices instead of multiple-residue 
loops between the sheets because alpha-helices turn about 
100 degrees per residue. For triangle-shaped barrels, I 
wanted 120 degree turns between sheets. For square-shaped 
barrels, I wanted 90 degree turns between sheets.
Having 100 degree turns seemed like a good compromise.
Using less residues might also help the barrels fold 
properly in the lab, letting residues meant to 
hydrogen-bond with each other be closer in the sequence 
to each other.

Once I set the desired sequence and secondary structure,
I went into the selection interface, selected all 107
residues, and then did 5 2 5 2 to idealize the structure.
This made the sheets flat and put bends at the helices.
Next I unfroze everything. Then I used the recipe 
FreezeSelectSome1 (https://fold.it/portal/recipe/102617)
to freeze only the backbones for the sheet residues. 
This left the helices free to move and left all sidechains 
free to move. Then I saved the structures as Je1a or Je1b.
jeff101's picture
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Banding Strategy:
Next, I needed to plan out a banding strategy. Since 
I wanted all valines to end inside the barrel, I needed 
many bands between pairs of valine beta-carbons (atom #5). 
My plan was to use the recipe Band Copy-Paste 1.5 
(https://fold.it/portal/recipe/100369) to make all these 
bands, so I list below the inputs needed for this recipe 
in the following format: 
residue1-residue2-atom1-atom2-goallength-bandstrength-1

38 valine-valine bands for Je1a:
   1-4-5-5-0-1-1     4-7-5-5-0-1-1    7-10-5-5-0-1-1 
 10-13-5-5-0-1-1   13-16-5-5-0-1-1   16-19-5-5-0-1-1 19-22-5-5-0-1-1 
 22-26-5-5-0-1-1
 26-31-5-5-0-1-1   31-36-5-5-0-1-1   36-41-5-5-0-1-1 41-46-5-5-0-1-1 
 46-51-5-5-0-1-1   51-56-5-5-0-1-1   56-61-5-5-0-1-1 61-66-5-5-0-1-1 
 66-71-5-5-0-1-1   71-76-5-5-0-1-1   76-81-5-5-0-1-1
 28-33-5-5-0-1-1   33-38-5-5-0-1-1   38-43-5-5-0-1-1 43-48-5-5-0-1-1
 48-53-5-5-0-1-1   53-58-5-5-0-1-1   58-63-5-5-0-1-1 63-68-5-5-0-1-1
 68-73-5-5-0-1-1   73-78-5-5-0-1-1   78-83-5-5-0-1-1 
 81-85-5-5-0-1-1 
 85-88-5-5-0-1-1   88-91-5-5-0-1-1   91-94-5-5-0-1-1 94-97-5-5-0-1-1 
97-100-5-5-0-1-1 100-103-5-5-0-1-1 103-106-5-5-0-1-1

38 valine-valine bands for Je1b:
   2-5-5-5-0-1-1     5-8-5-5-0-1-1    8-11-5-5-0-1-1
 11-14-5-5-0-1-1   14-17-5-5-0-1-1   17-20-5-5-0-1-1 20-23-5-5-0-1-1
 23-27-5-5-0-1-1
 27-32-5-5-0-1-1   32-37-5-5-0-1-1   37-42-5-5-0-1-1 42-47-5-5-0-1-1
 47-52-5-5-0-1-1   52-57-5-5-0-1-1   57-62-5-5-0-1-1 62-67-5-5-0-1-1
 67-72-5-5-0-1-1   72-77-5-5-0-1-1   77-82-5-5-0-1-1
 25-30-5-5-0-1-1   30-35-5-5-0-1-1   35-40-5-5-0-1-1 40-45-5-5-0-1-1
 45-50-5-5-0-1-1   50-55-5-5-0-1-1   55-60-5-5-0-1-1 60-65-5-5-0-1-1
 65-70-5-5-0-1-1   70-75-5-5-0-1-1   75-80-5-5-0-1-1
 82-86-5-5-0-1-1
 86-89-5-5-0-1-1   89-92-5-5-0-1-1   92-95-5-5-0-1-1 95-98-5-5-0-1-1
98-101-5-5-0-1-1 101-104-5-5-0-1-1 104-107-5-5-0-1-1

I also wanted to try clockwise (CW) and counterclockwise (CCW) 
versions of both Je1a and Je1b. Each required different 
hydrogen-bonds between the sheets. I list below the inputs 
used for these, again in the format:
residue1-residue2-atom1-atom2-goallength-bandstrength-1

Here atom1-atom2 is always 4-1 for oxygen (O) to nitrogen (N) 
atoms on the backbone, goallength is always 2.6 for 
2.6 angstroms (a little shorter than most O-N distances in 
hydrogen-bonds, but it seems to work), and bandstrength is 3 
(larger than 1, which I used for the valine-valine bands above).

Also below are charts giving the residue #'s for all the 
sheet residues. Between certain pairs of residue #'s are 
\ or / to indicate the hydrogen-bonds I want to form using 
bands. These are the hydrogen-bonds that will hold the 
barrel together.

48 bands for Je1a CW or Je1b CCW: 
   If residue #'s rise from left to right, 
   the atom # order is 4=O to 1=N (both on backbone).
   All Je1a CW bands go downward from v to t.
   All Je1b CCW bands go downward from t to v.

    1 2          4 5          7 8         10 11
     \            \            \            \
   13 14        16 17        19 20        22 23
  /  \         /  \         /  \         /  \
25 26 27 28  30 31 32 33  35 36 37 38  40 41 42 43
  /  \  /      /  \  /      /  \  /      /  \  /
45 46 47 48  50 51 52 53  55 56 57 58  60 61 62 63
  /  \  /      /  \  /      /  \  /      /  \  /
65 66 67 68  70 71 72 73  75 76 77 78  80 81 82 83
     \  /         \  /         \  /         \  /
   85 86        88 89        91 92        94 95
     \            \            \            \
   97 98       100 101      103 104      106 107

48 bands for Je1a CW or Je1b CCW: 
 1-14-4-1-2.6-3-1   4-17-4-1-2.6-3-1   7-20-4-1-2.6-3-1  10-23-4-1-2.6-3-1
25-13-4-1-2.6-3-1  13-27-4-1-2.6-3-1  30-16-4-1-2.6-3-1  16-32-4-1-2.6-3-1 
35-19-4-1-2.6-3-1  19-37-4-1-2.6-3-1  40-22-4-1-2.6-3-1  22-42-4-1-2.6-3-1
45-26-4-1-2.6-3-1  26-47-4-1-2.6-3-1  47-28-4-1-2.6-3-1 
50-31-4-1-2.6-3-1  31-52-4-1-2.6-3-1  52-33-4-1-2.6-3-1 
55-36-4-1-2.6-3-1  36-57-4-1-2.6-3-1  57-38-4-1-2.6-3-1 
60-41-4-1-2.6-3-1  41-62-4-1-2.6-3-1  62-43-4-1-2.6-3-1
65-46-4-1-2.6-3-1  46-67-4-1-2.6-3-1  67-48-4-1-2.6-3-1 
70-51-4-1-2.6-3-1  51-72-4-1-2.6-3-1  72-53-4-1-2.6-3-1 
75-56-4-1-2.6-3-1  56-77-4-1-2.6-3-1  77-58-4-1-2.6-3-1 
80-61-4-1-2.6-3-1  61-82-4-1-2.6-3-1  82-63-4-1-2.6-3-1
66-86-4-1-2.6-3-1  86-68-4-1-2.6-3-1  71-89-4-1-2.6-3-1  89-73-4-1-2.6-3-1 
76-92-4-1-2.6-3-1  92-78-4-1-2.6-3-1  81-95-4-1-2.6-3-1  95-83-4-1-2.6-3-1
85-98-4-1-2.6-3-1 88-101-4-1-2.6-3-1 91-104-4-1-2.6-3-1 94-107-4-1-2.6-3-1

48 bands for Je1a CCW or Je1b CW:
   If residue #'s rise from left to right, 
   the atom # order is 4=O to 1=N (both on backbone).
   All Je1a CCW bands go downward from t to v.
   All Je1b CW bands go downward from v to t.

    1 2          4 5          7 8         10 11
     /            /            /            /
   13 14        16 17        19 20        22 23
     /  \         /  \         /  \         /  \
25 26 27 28  30 31 32 33  35 36 37 38  40 41 42 43
  \  /  \      \  /  \      \  /  \      \  /  \  
45 46 47 48  50 51 52 53  55 56 57 58  60 61 62 63
  \  /  \      \  /  \      \  /  \      \  /  \  
65 66 67 68  70 71 72 73  75 76 77 78  80 81 82 83
  \  /         \  /         \  /         \  /
   85 86        88 89        91 92        94 95
     /            /            /            /
   97 98       100 101      103 104      106 107

48 bands for Je1a CCW or Je1b CW:
 13-2-4-1-2.6-3-1   16-5-4-1-2.6-3-1   19-8-4-1-2.6-3-1  22-11-4-1-2.6-3-1
26-14-4-1-2.6-3-1  14-28-4-1-2.6-3-1  31-17-4-1-2.6-3-1  17-33-4-1-2.6-3-1 
36-20-4-1-2.6-3-1  20-38-4-1-2.6-3-1  41-23-4-1-2.6-3-1  23-43-4-1-2.6-3-1
25-46-4-1-2.6-3-1  46-27-4-1-2.6-3-1  27-48-4-1-2.6-3-1 
30-51-4-1-2.6-3-1  51-32-4-1-2.6-3-1  32-53-4-1-2.6-3-1 
35-56-4-1-2.6-3-1  56-37-4-1-2.6-3-1  37-58-4-1-2.6-3-1 
40-61-4-1-2.6-3-1  61-42-4-1-2.6-3-1  42-63-4-1-2.6-3-1
45-66-4-1-2.6-3-1  66-47-4-1-2.6-3-1  47-68-4-1-2.6-3-1 
50-71-4-1-2.6-3-1  71-52-4-1-2.6-3-1  52-73-4-1-2.6-3-1 
55-76-4-1-2.6-3-1  76-57-4-1-2.6-3-1  57-78-4-1-2.6-3-1 
60-81-4-1-2.6-3-1  81-62-4-1-2.6-3-1  62-83-4-1-2.6-3-1
65-85-4-1-2.6-3-1  85-67-4-1-2.6-3-1  70-88-4-1-2.6-3-1  88-72-4-1-2.6-3-1 
75-91-4-1-2.6-3-1  91-77-4-1-2.6-3-1  80-94-4-1-2.6-3-1  94-82-4-1-2.6-3-1
97-86-4-1-2.6-3-1 100-89-4-1-2.6-3-1 103-92-4-1-2.6-3-1 106-95-4-1-2.6-3-1

The above give 38+48=86 bands in all for each of 
Je1a CW, Je1a CCW, Je1b CW, and Je1b CCW. 

When I used Band Copy-Paste 1.5 
(https://fold.it/portal/recipe/100369) to create 
all these bands, I checked the sidechain bands box, 
copy/pasted all of the text for the 86 bands above 
into the import box as one big block of text, 
clicked import, waited, then clicked quit. At the 
end, I had to enable all the bands. Then I would 
save the banded structures as Je1a CW, Je1a CCW, 
Je1b CW, or Je1b CCW.
jeff101's picture
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Hand-Folding:
Once I had the structure banded and partially frozen,
I would do many manual steps. I'd cycle among shake, 
wiggle sidechains, wiggle backbones, & wiggle all in 
no particular order, all at low wiggle power, usually 
with clashing importance (ci) set to 1, but sometimes 
with ci set lower (like 0.1).

I also found it helpful to add some extra "anchor" 
bands by hand during an early wiggle sidechains step.
I would attach one band to each end of the barrel and
stretch them out as far as I could to make an axis for
the barrel. This helped keep the barrel from tangling
with itself. Once I had this axis, I would attach bands 
from each helix residue far out into space to enforce
the CW or CCW shape I wanted. I would try to make these
bands perpendicular to the axis of the barrel. 

To assess the CW or CCW shape, I'd color the barrel as
rainbow and view the barrel from its blue or red end, 
tabbing on residue 1 (blue) or 107 (red) and then using 
the arrows to scan towards the opposite end. I wanted 
these scans to go CW from each end for the CW barrels 
and to go CCW from each end for the CCW barrels. That is,
when viewing from the blue end, scanning from residue 
1 to 107 should go CW for the CW barrels and CCW for the
CCW barrels. Similarly, when viewing from the red end,
scanning from residue 107 to 1 should go CW for the CW
barrels and CCW for the CCW barrels.

The charts below helped me position the anchor bands 
from the helix residues to space to enforce CW or CCW 
barrels. N E S W are just compass directions. They
could just as well be up right down left on the screen.

For CW barrels:
 N   E   S   W viewed from blue (residue 1) end
 N   W   S   E viewed from red (residue 107) end
 3   6   9  12 
15  18  21  24 
29  34  39  44 
49  54  59  64
69  74  79  84
87  90  93  96
99 102 105 

For CCW barrels:
 N   W   S   E viewed from blue (residue 1) end
 N   E   S   W viewed from red (residue 107) end
 3   6   9  12 
15  18  21  24 
29  34  39  44 
49  54  59  64
69  74  79  84
87  90  93  96
99 102 105 

During the process of wiggling, shaking, & varying
ci, I'd often adjust the positions of anchor bands
to improve the barrel's appearance.

Below are screen-shots near the end of this stage 
of folding showing Je1b CW & its anchor bands. All
images are colored with rainbow & shown as cartoon. 
The secondary structure & sequence are set as in my 
original design (2 or 4-residue sheets w/sequences 
TV or VTVT & 1-residue leucine helices). The sheet 
backbones are still frozen. I label residues 9 and 
105, which should have bands pointing S (down). In 
the top image, residue 1 is labeled "Je1b CW":

foldit_1533265949.png

foldit_1533266736.png

foldit_1533266411.png

foldit_1533266194.png
Once things looked alright, I'd save the structure
and then do a stage with ci=1 and low wiggle power.
I usually began with wiggle sidechains and would 
remove all but the 2 axis anchor bands while it ran.
Then I'd do wiggle backbone, shake, and wiggle all,
in that order. Then I'd save the structure.

Next I'd do another stage with ci=1 and low wiggle power.
In this stage I'd start with wiggle sidechains and 
remove the rest of the anchor bands while it ran.
Then I'd do wiggle backbone, shake, and wiggle all,
in that order. Then I'd save the structure.

At this point the structures all still had frozen
sheet backbones and 86 internal bands (38 between
valines & 48 to form hydrogen bonds).
jeff101's picture
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Recipe-Folding:
Next I'd unfreeze the structures but leave their 
86 bands intact. Then I would run Loop rebuild 9.0a
(https://fold.it/portal/recipe/102557) with ci=1 and 
low wiggle power on them. I would use this recipe's 
default settings but would set the rebuild length to 6, 
the rebuild criterion to 4, check the 'use remix' box, 
and set MSflag to 0 (shake but don't mutate). I would 
let this run until a full cycle (102 rb attempts) with 
no gains would occur. Then I'd quit this recipe and 
save its results.

Next I'd run Loop rebuild 9.0a again with almost
the same settings, but this time I'd set the rebuild
length to 4. I would run this until a full cycle
(this time 104 rb attempts) with no gains would
occur. Then I'd quit this recipe and save its results.

At this point, the structures still had 86 bands,
no frozen residues, and their original sequences 
and secondary structure settings.

Next I'd run Loop rebuild 9.0a again with almost
the same settings, but this time I'd set the rebuild
length to 6 and MSflag to 1 (mutate then shake).
Again I'd let this run until a full cycle (102 rb 
attempts) with no gains occurred. Then I'd quit
this recipe and save its results.

Next I'd run Loop rebuild 9.0a again with almost
the same settings, but this time I'd set the rebuild
length to 4 and MSflag to 1 (mutate then shake).
Again I'd let this run until a full cycle (104 rb 
attempts) with no gains occurred. Then I'd quit
this recipe and save its results.

After that I'd run a variety of recipes on the 
barrels with ci=1 and low wiggle power. Sometimes the 
valines would mutate to other amino acids & this would 
remove some valine-valine bands. 

Next I'd run some recipes with ci=1 and medium 
wiggle power. At some point, one of these recipes
would remove all remaining bands.
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Results:
Below (and at http://foldit.wikia.com/wiki/Puzzle_1546)
are screen-shots of my best-scoring structure 
(solo rank 49) soon after Puzzle 1546 ended. I ran
auto secondary structure, colored as abego, and
viewed as cartoon before taking these screen-shots.
Note that all residues have become sheet or loop:

foldit_1531887217.png


foldit_1531886289.png
Below is a distance map for the same structure
made using DistMap1.1 with its default settings 
(https://fold.it/portal/recipe/101868), also
after clicking on auto secondary structure:
Je1bCCWx.png
See http://foldit.wikia.com/wiki/Distance_Maps and 
http://memorize.com/protein-distance-maps/jeff101
for more details about distance maps.
Joined: 09/22/2017
Groups: Beta Folders
Interesting to note

that GFP adopts a similar structure albeit much more round than square

https://www.rcsb.org/structure/1GFL

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Very cool!

This is impressive work, jeff101! I especially appreciate your documentation, and the thoroughness with which you describe your methods. Maybe others will try to reproduce your results!

My main concerns with these types of folds are usually (1) backbone strain and (2) core packing. On the one hand, we want an unstrained backbone that makes good hydrogen bonds, with all residues in the densely-populated regions of the Ramachandran map; on the other hand, we want a well-packed core with no voids and no unbonded polar atoms. I think there is usually something of a trade-off between these two traits, as a perfectly-ideal backbone will need to contort in order to accommodate good packing, and it can be difficult to find an arrangement that satisfies both of these traits. Looking at some of the solutions you shared, jeff101, I think you've done a pretty good job on both counts! There are a few more strained residues than I typically like to see (look for residues with negative "backbone" sub-score), and a couple buried polar atoms that are a little worrisome, but still we'll put it through Rosetta@home analysis and see how Rosetta likes it!

If anybody wants to read up on natural proteins with a similar fold (there are just a handful that we know of), you will want to search for the term "beta-solenoid." This fold is generally considered distinct from "beta-barrels" (like GFP), where the β-strands are more parallel with the axis of the barrel.

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