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Recipe: bandsome
Created by jeff101 35 127
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Name: bandsome
ID: 43861
Created on: Sun, 08/12/2012 - 00:19
Updated on: Sun, 08/12/2012 - 02:00
Description:

interactively place bands between specific atoms in protein



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jeff101's picture
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Banding to form disulfide bonds:

To form a disulfide bond between residues 10 and 20, make the following 3 bands:

One with length 2 between atom 6 on residue 10 and atom 6 on residue 20.
One with length 3 between atom 5 on residue 10 and atom 6 on residue 20.
One with length 3 between atom 6 on residue 10 and atom 5 on residue 20.

I often use strength 5 for all 3 bands.

jeff101's picture
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More on disulfides:

I used to use a 4th band of length 3.8 between atom 5 on residue 10 and atom 5 on residue 20,
but I think this commits the structure too soon to one of two possible isomers
(right-handed or left-handed), both of which are observed in natural proteins.

For more details, see page 1 of http://users.soe.ucsc.edu/~gerloff/classes/bme128/Spring12/BME128.Week10_2.June7.disulfides_core_and_pfs48_45_case_study.pdf

jeff101's picture
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Disulfides can even form between adjacent cysteine residues:

http://dx.doi.org/10.1093/protein/gzg088 is an article about vicinal disulfide bonds.
These are disulfide bonds that form between adjacent cysteine residues (like if both residues 19 and 20 are cysteines).

jeff101's picture
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How many disulfide combinations are there for N cysteines?
For      N cysteines (N cys) where N is a non-negative integer (N=0,1,2,3,4,5,etc.):
For  any N, there are T1=(N^2-N)/2 ways 
            to form 1            disulfide (1 s-s) bond.
For even N, there are TM=(N-1)x(N-3)x(N-5)x...x1 ways 
            to form M=floor(N/2) disulfide (M s-s) bonds.
For  odd N, there are TM=(N cys that could be non-bonded)x(N-2)x(N-4)x...x1 ways 
            to form M=floor(N/2) disulfide (M s-s) bonds.

 0 cys: T1=  (0-0)/2 =  0/2= 0 with 1 s-s, TM=              1=     1 with 0 s-s.
 1 cys: T1=  (1-1)/2 =  0/2= 0 with 1 s-s, TM=              1=     1 with 0 s-s.
 2 cys: T1=  (4-2)/2 =  2/2= 1 with 1 s-s, TM=              1=     1 with 1 s-s.
 3 cys: T1=  (9-3)/2 =  6/2= 3 with 1 s-s, TM=            3x1=     3 with 1 s-s.
 4 cys: T1= (16-4)/2 = 12/2= 6 with 1 s-s, TM=            3x1=     3 with 2 s-s.
 5 cys: T1= (25-5)/2 = 20/2=10 with 1 s-s, TM=          5x3x1=    15 with 2 s-s.
 6 cys: T1= (36-6)/2 = 30/2=15 with 1 s-s, TM=          5x3x1=    15 with 3 s-s.
 7 cys: T1= (49-7)/2 = 42/2=21 with 1 s-s, TM=        7x5x3x1=   105 with 3 s-s.
 8 cys: T1= (64-8)/2 = 56/2=28 with 1 s-s, TM=        7x5x3x1=   105 with 4 s-s.
 9 cys: T1= (81-9)/2 = 72/2=36 with 1 s-s, TM=      9x7x5x3x1=   945 with 4 s-s.
10 cys: T1=(100-10)/2= 90/2=45 with 1 s-s, TM=      9x7x5x3x1=   945 with 5 s-s.
11 cys: T1=(121-11)/2=110/2=55 with 1 s-s, TM=   11x9x7x5x3x1= 10395 with 5 s-s.
12 cys: T1=(144-12)/2=132/2=66 with 1 s-s, TM=   11x9x7x5x3x1= 10395 with 6 s-s.
13 cys: T1=(169-13)/2=156/2=78 with 1 s-s, TM=13x11x9x7x5x3x1=135135 with 6 s-s.

0 cys: T1=(0-0)/2=0/2=0 with 1 s-s,    TM=1 with 0 s-s:
0 ways

1 cys: T1=(1-1)/2=0/2=0 with 1 s-s,    TM=1 with 0 s-s:
0 ways

2 cys: T1=(4-2)/2=2/2=1 with 1 s-s,    TM=1 with 1 s-s:
1-2

3 cys: T1=(9-3)/2=6/2=3 with 1 s-s,    TM=3x1=3 with 1 s-s:
1-2 no 3
1-3 no 2
2-3 no 1

4 cys: T1=(16-4)/2=12/2=6 with 1 s-s,  TM=3x1=3 with 2 s-s:
1-2
1-3
1-4
2-3
2-4
3-4
1-2 3-4
1-3 2-4
1-4 2-3

5 cys: T1=(25-5)/2=20/2=10 with 1 s-s, TM=5x3x1=15 with 2 s-s:
1-2
1-3
1-4
1-5
2-3
2-4
2-5
3-4
3-5
4-5
2-3 4-5 no 1
2-4 3-5 no 1
2-5 3-4 no 1
1-3 4-5 no 2
1-4 3-5 no 2
1-5 3-4 no 2
1-2 4-5 no 3
1-4 2-5 no 3
1-5 2-4 no 3 
1-2 3-5 no 4
1-3 2-5 no 4
1-5 2-3 no 4
1-2 3-4 no 5
1-3 2-4 no 5
1-4 2-3 no 5

6 cys: T1=(36-6)/2=30/2=15 with 1 s-s, TM=5x3x1=15 with 3 s-s:
1-2
1-3
1-4
1-5
1-6
2-3
2-4
2-5
2-6
3-4
3-5
3-6
4-5
4-6
5-6
1-2 3-4 5-6
1-2 3-5 4-6
1-2 3-6 4-5
1-3 2-4 5-6
1-3 2-5 4-6
1-3 2-6 4-5
1-4 2-3 5-6
1-4 2-5 3-6
1-4 2-6 3-5
1-5 2-3 4-6
1-5 2-4 3-6
1-5 2-6 3-4
1-6 2-3 4-5
1-6 2-4 3-5
1-6 2-5 3-4
jeff101's picture
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More formulas:
jeff101's picture
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New reference:

More formulas for the number of possible disulfide bonds can be found at:
https://en.wikipedia.org/wiki/Disulfide#Predicting_disulfide_abundance

jeff101's picture
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Different disulfide combinations can exist in the same protein:

https://en.wikipedia.org/wiki/Disulfide_bond#Occurrence_in_proteins says:

A disulfide ensemble is a grouping of all disulfide species with the same number of disulfide bonds, and is usually denoted as the 1S ensemble, the 2S ensemble, etc. for disulfide species having one, two, etc. disulfide bonds.

Under typical conditions, disulfide reshuffling is much faster than the formation of new disulfide bonds or their reduction; hence, the disulfide species within an ensemble equilibrate more quickly than between ensembles.

The native form of a protein is usually a single disulfide species, although some proteins may cycle between a few disulfide states as part of their function, e.g., thioredoxin. In proteins with more than two cysteines, non-native disulfide species may be formed, which are almost always misfolded. As the number of cysteines increases, the number of nonnative species increases factorially.

Isomerases have been identified that catalyze the interconversion of disulfide species, accelerating the formation of the native disulfide species.

Disulfide species that lack one native disulfide bond are frequently folded, in particular, if the missing disulfide bond is exposed to solvent in the folded, native protein.

jeff101's picture
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CMD: A Database of Disulfide Bonding Motifs

For help choosing from the many possible disulfide bonding patterns, see the following article:

"CMD: A Database to Store the Bonding States of Cysteine Motifs with Secondary Structures"
http://www.hindawi.com/journals/abi/2012/849830/
http://dx.doi.org/10.1155/2012/849830

It discusses the database below and lists other useful sounding articles:
http://birg4.fbb.utm.my/cmd/

jeff101's picture
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Oxidizing environments make disulfide bonds more likely:

At http://fold.it/portal/node/2000967#comment-30844 bkoep said the following:

The blood and spinal fluid are oxidizing environments, so we don't need to worry about the disulfide bonds being reduced. Any reduced cysteine pairs would quickly oxidize.

Meanwhile, https://en.wikipedia.org/wiki/Disulfide_bond#Occurrence_in_proteins says:

Disulfide bonds play an important role in the folding and stability of some proteins, usually proteins secreted to the extracellular medium. Since most cellular compartments are reducing environments, in general, disulfide bonds are unstable in the cytosol, with some exceptions as noted below, unless a sulfhydryl oxidase is present.

In eukaryotic cells, in general, stable disulfide bonds are formed in the lumen of the RER (rough endoplasmic reticulum) and the mitochondrial intermembrane space but not in the cytosol. This is due to the more oxidizing environment of the aforementioned compartments and more reducing environment of the cytosol (see glutathione). Thus disulfide bonds are mostly found in secretory proteins, lysosomal proteins, and the exoplasmic domains of membrane proteins.

Over 90% of the dry weight of hair comprises proteins called keratins, which have a high disulfide content, from the amino acid cysteine. The robustness conferred in part by disulfide linkages is illustrated by the recovery of virtually intact hair from ancient Egyptian tombs. Feathers have similar keratins and are extremely resistant to protein digestive enzymes. Different parts of the hair and feather have different cysteine levels, leading to harder or softer material.

jeff101's picture
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bandsomeSS specializes in banding disulfide bonds:

bandsomeSS (http://fold.it/portal/recipe/101275) is similar to bandsome,
but bandsomeSS only makes bands to help disulfide bonds form.
Like bandsome, bandsomeSS is menu-driven,
but bandsomeSS adds multiple bands per set of inputs
while bandsome adds just one.

jeff101's picture
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Banding to form B-sheets:

To make a B-sheet between residues 25-27 and 60-62,
use bands of length 2.8 and strength 5 between
atoms 1 (N=nitrogen=blue in CPK) and 4 (O=oxygen=red in CPK).
View as Stick and Color by CPK help.

There are many different ways to connect the B-sheet.
In general, one would expect more hydrogen bonds to give a more stable structure.

Below are some examples:

(A) Anti-parallel B-sheet with 4 hydrogen bonds:

25 26 27
||    ||
62 61 60

Here use 4 bands:

One between atom 1 on residue 25 and atom 4 on residue 62.
One between atom 4 on residue 25 and atom 1 on residue 62.
One between atom 1 on residue 27 and atom 4 on residue 60.
One between atom 4 on residue 27 and atom 1 on residue 60.

(B) Anti-parallel B-sheet with 2 hydrogen bonds:

25 26 27
   ||
62 61 60

Here use 2 bands:

One between atom 1 on residue 26 and atom 4 on residue 61.
One between atom 4 on residue 26 and atom 1 on residue 61.

(C) Parallel B-sheet with 3 hydrogen bonds:

25 26 27        25O-60N
  \  /  \       27N-60O
   60 61 62     27O-62N

Here use 3 bands:

One between atom 4 (oxygen) on residue 25 and atom 1 (nitrogen) on residue 60.
One between atom 1 (nitrogen) on residue 27 and atom 4 (oxygen) on residue 60.
One between atom 4 (oxygen) on residue 27 and atom 1 (nitrogen) on residue 62.

(D) Parallel B-sheet with 3 hydrogen bonds:

   25 26 27     25N-60O
  /  \  /       25O-62N
60 61 62        27N-62O

Here use 3 bands:

One between atom 1 (nitrogen) on residue 25 and atom 4 (oxygen) on residue 60.
One between atom 4 (oxygen) on residue 25 and atom 1 (nitrogen) on residue 62.
One between atom 1 (nitrogen) on residue 27 and atom 4 (oxygen) on residue 62.

(E) Other parallel B-sheet patterns with 2 hydrogen bonds:

25 26 27        26N-60O
  /  \          26O-62N
60 61 62

One between atom 1 (nitrogen) on residue 26 and atom 4 (oxygen) on residue 60.
One between atom 4 (oxygen) on residue 26 and atom 1 (nitrogen) on residue 62.

25 26 27        25O-61N
  \  /          27N-61O
60 61 62

One between atom 4 (oxygen) on residue 25 and atom 1 (nitrogen) on residue 61.
One between atom 1 (nitrogen) on residue 27 and atom 4 (oxygen) on residue 61.

(F) Other anti-parallel B-sheet patterns with 2 hydrogen bonds:

25 26 27
      ||         
      62 61 60

25 26 27
      ||         
   62 61 60

25 26 27
   ||            
   62 61 60

   25 26 27
   ||            
62 61 60

   25 26 27
      ||         
62 61 60

      25 26 27
      ||         
62 61 60
jeff101's picture
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More on B-sheets:
Joined: 09/24/2012
Groups: Go Science
Thanks for the explanations !

Very interesting, even if difficult to understand. A good chalenge for us to learn a little bit more on Foldit Science. The chalenge now is making it into practice, implementing this in common scripts. Oops, this is quite a chalenge !

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Developed by: UW Center for Game Science, UW Institute for Protein Design, Northeastern University, Vanderbilt University Meiler Lab, UC Davis
Supported by: DARPA, NSF, NIH, HHMI, Amazon, Microsoft, Adobe, RosettaCommons