Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface
Abstract
:1. Introduction
2. Algebraic Geometrical Models of Secondary Structures
2.1. The Gieseking Manifold
2.2. The Hypercartographic Group
2.3. Fundamental Groups of 3-Manifolds
3. Secondary Structure with Helices: Drosophila Melanogaster Histone H3 (PDB 6PWE_1)
3.1. The Primary (Linear) Structure
- IVFSNVK–T-TLVKPKSEMARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEASEAYLVGLFEDTNLCAIHAKRVTIMPKDIQLARRIRGERA-ADTALTCR-SASVLYNRSFS
3.2. The Secondary Structure
- CCCCCCCCCCCCCCCCCHHHHCHHHHCCCCCCCCCCCCCCCCCCCCHHHHHHHCCCCC
- CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCHHHHHHHHHHHHCC
- CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCHHHHHHHHHHHHCCC
- CCCCCCCCCCCCCCCCCCCCHHHHHCCCCCCCCCCCCCCCCCCHHHHHHHHHHHHHCC
- HHHHHCCCCHHHHHHHHHHHCCCCCCCCHHHHHHHHHHHHHHHHHHHHHHHHCHHHH
- CCHHHCCCHHHHHHHHHHHHCCCCCCCCHHHHHHHHHHHHHHHHHHHHHHHHHHHHC
- HHHHHHHHHHHHHHHHHHHHHCCCCCCCHHHHHHHHHHHHHHHHHHHHHHHHHHHHC
- HHHHHHHHHHHHHHHHHHCCCCCCCCCCHHHHHHHHHHHHHHHHHHHHHHHHHHHHC
- CCCCCCHHHHHHHHHHCCCCC
- CCCCCCHHHHHHHHHHCCCCC
- CCCCCCHHHHHHHHHHCCCCC
- CCCCCCHHHHHHHHHHHCCCC
4. Secondary Structures with Helices and Sheets: Myelin P2, Carbonic Anhydrase and the Lsm 1-7 Complex
4.1. Myelin P2 for Homo Sapiens (PDB 2WUT)
- GMSNKFLGTWKLVSSENFDDYMKALGVGLATRKLGNLAKPTVIISKKGDIITIRTESTFKN
- CCCHHCCEEEEEEEECCHHHHHHHCCCCHHHHHHHHHCCCEEEEEEECCEEEEEEECCCC
- CCCHHCCEEEEEECCCCHHHHHHHCCCCHHHHHHHHHCCCEEEEEEECCEEEEEEECCCC
- CCCCCCEEEEEEEEECCHHHHHHHHCCCHHHHHHHHCCCCEEEEEEECCEEEEEEECCCC
- CCCCCCEEEEEEEEECCHHHHHHHCCCCHHHHHHHHCCCCEEEEEEECCEEEEEEECCCC
- TEISFKLGQEFEETTADNRKTKSIVTLQRGSLNQVQRWDGKETTIKRKLVNGKMVAECKM
- CCCHHCCEEEEEEEECCHHHHHHHCCCCHHHHHHHHHCCCEEEEEEECCEEEEEEECCCC
- EEEEEEEECCEEEEECCCCCEEEEEEEEECCEEEEEEECCCCEEEEEEEEECCEEEEEEEE
- EEEEEEECCCEEEEECCCCCEEEEEEEEECCEEEEEEECCCCCEEEEEEEECCEEEEEEEE
- EEEEEEECCCEEEEECCCCCEEEEEEEEECCEEEEEEECCCCCEEEEEEEECCEEEEEEEE
- KGVVCTRIYEKV
- CCEEEEEEEEEC
- CCEEEEEEEEEC
- CCEEEEEEEEEC
- CCEEEEEEEEEC
4.2. The 3-Fold Symmetric Complex for Gamma-Carbonic Anhydrase (PDB 1QRE)
4.3. The Hfq Protein Complex of Escherichia coli (PDB 1HK9)
- GAMAKGQSLQDPFLNALRRERVPVSIYLVNGIKLQGQIESFDQFVILLKNTVSQMVYKHAISTVVPSRPVSHHSCCCCCCCCCHHHHHHHHHHCCCCEEEEEECCCEEEEEEEECCCEEEEEECCCEEEEEEEEEEEEEECCCCCCCCCCCCCCCCHHHHHHHHHHHCCCCEEEEEECCEEEEEEEEEECEEEEEEECCCEEEEEEEEEEEEECCCCCCCCCCCCCCCCCCHHHHHHHHHHCCCEEEEEEECCEEEEEEEEEECCEEEEEECCCCEEEEEEEEEEEEECCEEEECCCCCCCCCCCCHHHHHHHHHCCCCEEEEECCCCEEEEEEEEECCCEEEEEECCCEEEEEEEEEEEEECCCCCCCC
4.4. Other n-Fold Symmetric Complexes
4.4.1. The 5-Fold Symmetric H2A-H2B Complex in Nucleoplasmin (PDB 2XQL)
4.4.2. The 5-Fold Symmetric Acetylcholine Receptor (PDB 2BG9)
4.4.3. The 7-Fold Symmetric Lsm 1-7 Complex in the Spliceosome (PDB 4M75)
4.4.4. Encoding a Protein with the Characters of the Finite Group
5. The 8-Fold Symmetric Histone Complex of the Nucleosome: 3WKJ in the Protein Data Bank
6. Discussion
Author Contributions
Funding
Conflicts of Interest
References
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Index | 1 | 2 | 3 | 4 | 5 |
3-man | m000 | K4a1, ooct02_00001 | ntet03_00000 | m206, otet04_00002 | m407, ntet05_00007 |
m204, ntet04_00000 | m405, ncube01_00001 | ||||
P | (1,1) | (2,1) | (3,1) | (4,1) | (5,1) |
(12,3) | (20,3) | ||||
Index | 6 | 7 | 8 | 9 | 10 |
3-man | s961, otet06_00003 | y886, ntet07_00000 | t12839, otet06_00007 | ||
x252, ntet06_00004 | t12840, otet08_00002 | ||||
ntet06_00005 | ntet08_00002 | ||||
P | (6,2) | (7,1) | (8,1) | (9,1) | (10,2) |
(12,3) | (24,3) | ||||
(24,13) | (24,13) | ||||
(96,70), (192,201) | (9,1), (648,705) | (10,2), (20,3), | |||
lacking P | (72,39) | (320,1635) | |||
extra P | , | (216,53), , | , |
Protein | Model | |
---|---|---|
H3 (6PWE_1) | PSIPRED | [1,1,1,1,2, 2,1,3,5,5 .,.,.,.,.] |
H3 | PHYRE2 | [1,1,1,1,3, 4,1,5,10,10 .,.,.,.,.] |
H3 | PORTER | [1,1,1,2,2, 3,1,12,6,5 .,.,.,.,.] |
H3 | RAPTORX | [1,1,1,1,2, 1,1,2,3,3 .,.,.,.,.] |
m000 | Gieseking | [1,1,1,2,2, 3,1,4,3,5, 4,14,1,5,10] |
trefoil | [1,1,2,3,2, 8,7,10,18,28, 27,88,134,171,354] | |
figure-of-eight | [1,1,1,2,4, 11,9,10,11,38, 26,62,39,89,228] | |
(0,1) | [1,1,1,2,2, 5,1,2,2,4, 3,17,1,1,2] | |
singular fiber II* | [1,1,2,2,1, 5,3,2,4,1, 1,12,3,3,4] |
Protein | aa | Model | |
---|---|---|---|
myelin P2 (2WUT) | 133 | PSIPRED | [1, 3, 13, 84, 336, 4216] |
2WUT | PHYRE2 | [1, 3, 7, 26, 164, 10,669] | |
2WUT | PORTER | [1, 3, 7, 26, 135, 871] | |
2WUT | RAPTORX | [1, 3, 10, 59, 348, 2899] | |
. | (336,118) | [1, 3, 7, 30, 122, 991] | |
. | (384,5589) | [1, 3, 7, 34, 130, 999] | |
carbonic anhydrase (1QRE_1) | 247 | PSIPRED | [1, 3, 10, 43, 135, 1071] |
1QRE_1 | PHYRE2 | [1, 3, 7, 26, 149, 1085] | |
1QRE_1 | PORTER | [1, 3, 7, 26, 415, 4382] | |
1QRE_1 | RAPTORX | [1, 3, 10, 35, 106, 804] | |
. | (336,118) | [1, 3, 7, 30, 150, 883] | |
. | (384,5589) | [1, 3, 10, 47, 148, 1015] | |
protein Hfq (1HK9_1) | 74 | PSIPRED | [1, 7, 17, 114, 1145, 14,275] |
1HK9_1 | PHYRE2 | [1, 7, 14, 149, 1458, 21,756] | |
1HK9_1 | PORTER | [1, 3, 7, 26, 97, 624, 4163, 34,470] | |
1HK9_1 | RAPTORX | [1, 3, 10, 51, 162, 1434] | |
. | (336,118) | [1, 3, 7, 26, 134, 912] | |
. | (384,5589) | [1, 3, 7, 34, 146, 894] | |
H2A-H2B (2XQL_1) | 91 | PHYRE2 | [1, 3, 7, 26, 103, 688] |
2XQL_1 | RAPTORX | [1, 3, 7, 26, 165, 2272] | |
. | (336,118) | [1, 3, 7, 26, 130, 943] | |
. | (384,5589) | [1, 3, 7, 26, 136, 967] | |
acetylcholin receptor (2BG9_1) | 370 | PSIPRED | [1, 3, 10, 35, 151, 1023] |
2BG9_1 | PHYRE2 | [1, 7, 11, 92,288, 2087] | |
2BG9_1 | PORTER | [1, 7, 11, 92, 239, 2058] | |
2BG9_1 | RAPTORX | [1, 3, 7, 34, 169, 1432] | |
. | [1, 3, 10, 47, 124, 1026] | ||
. | [1, 3, 7, 30, 140, 931] | ||
Lsm 1-7 complex (4M75_1) | 144 | PSIPRED | [1, 3, 16, 81, 184, 1800] |
4M75_1 | PHYRE2 | [1, 7, 14, 201, 705, 8850] | |
4M75_1 | PORTER | [1, 3, 7, 26, 139, 1118] | |
4M75_1 | RAPTORX | [1, 3, 7, 26, 125, 747] | |
. | [1, 3, 7, 34, 145, 948] | ||
. | [1, 3, 10, 35, 135, 975] | ||
na | oriented hypermaps | [1, 3, 7, 26, 97, 624, 4163, 34,470] | |
ooct02_00017 | 3-manifold | [1, 3, 7, 26, 40, 231] | |
ooct02_00006 | 3-manifold | [1, 3, 10, 43, 112, 802] | |
noct02_00024 | 3-manifold | [1, 3, 10, 43, 117, 804] | |
ooct02_00009 | 3-manifold | [1,3,7,30,105, 649] | |
ooct04_00001 | 3-manifold | [1, 3, 7, 34, 43, 240, 254] | |
L7a1 | 3-manifold link | [1, 3, 7, 34, 75, 377, 807] | |
ooct03_00019 | 3-manifold | [1, 7, 11, 85, 95, 240, 492] |
(336,118) | dimension | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
d-dit, d = 29 | 29 | 785 | |||||||||
amino acid | . | M | W | C | F | Y | . | . | H | Q | |
order | 1 | 2 | 3 | 4 | 4 | 6 | 7 | 7 | 7 | 8 | |
char | Cte | Cte | Cte | ||||||||
polar req. | . | 5.3 | 5.2 | 4.8 | 5.0 | 5.4 | . | . | 8.4 | 8.6 | |
(336,118) | dimension | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 |
d-dit, d = 29 | |||||||||||
amino acid | N | K | E | D | I | Stop | . | . | . | . | |
order | 14 | 14 | 14 | 21 | 21 | 21 | 21 | 21 | 21 | 21 | |
char | Cte | Cte | Cte | ||||||||
polar req. | 10.0 | 10.1 | 12.5 | 13.0 | 10 | 15 | . | . | . | . | |
(336,118) | dimension | 4 | 4 | 4 | f 4 | 4 | 4 | 6 | 6 | 6 | |
d-dit, d = 29 | |||||||||||
amino acid | V | P | T | A | G | . | L | S | R | ||
order | 28 | 28 | 28 | 42 | 42 | 42 | 42 | 42 | 42 | ||
char | |||||||||||
polar req. | 5.6 | 6.6 | 6.6 | 7.0 | 7.9 | . | 4.9 | 7.5 | 9.1 |
(384,5589) | dimension | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
d-dit, d = 37 | 37 | 1333 | 1333 | 1333 | 1361 | 1367 | . | ||||
amino acid | . | . | M | W | . | . | . | . | . | . | |
char | Cte | Cte | Cte | Cte | Cte | Cte | Cte | ||||
(384,5589) | dimension | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 |
d-dit, d = 37 | 1367 | ||||||||||
amino acid | C | F | Y | H | Q | N | K | E | D | . | |
char | Cte | ||||||||||
(384,5589) | dimension | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
d-dit, d = 37 | 1367 | 1367 | 1367 | 1367 | |||||||
amino acid I | Stop | . | . | . | . | . | . | . | V | ||
char | Cte | Cte | Cte | Cte | Cte | Cte | |||||
(384,5589) | dimension | 4 | 4 | 4 | 4 | 6 | 6 | 6 | |||
d-dit, d = 37 | 701 | 1365 | 1365 | ||||||||
amino acid | P | T | A | G | L | S | R | ||||
char | Cte |
A | B | C | D |
B | A | D | C |
C | D | A | B |
D | C | B | A |
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Planat, M.; Aschheim, R.; Amaral, M.M.; Fang, F.; Irwin, K. Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface. Symmetry 2021, 13, 1146. https://doi.org/10.3390/sym13071146
Planat M, Aschheim R, Amaral MM, Fang F, Irwin K. Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface. Symmetry. 2021; 13(7):1146. https://doi.org/10.3390/sym13071146
Chicago/Turabian StylePlanat, Michel, Raymond Aschheim, Marcelo M. Amaral, Fang Fang, and Klee Irwin. 2021. "Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface" Symmetry 13, no. 7: 1146. https://doi.org/10.3390/sym13071146
APA StylePlanat, M., Aschheim, R., Amaral, M. M., Fang, F., & Irwin, K. (2021). Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface. Symmetry, 13(7), 1146. https://doi.org/10.3390/sym13071146