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Parikh vectors
7TGM_1 2QQY_1 1SDD_1 Letter Amino acid
49 7 8 R Arginine
13 9 11 N Asparagine
38 6 18 G Glycine
26 2 13 F Phenylalanine
46 20 18 E Glutamic acid
12 7 10 M Methionine
33 7 29 S Serine
23 7 16 Y Tyrosine
32 8 22 T Threonine
44 8 15 V Valine
15 5 13 Q Glutamine
16 9 20 I Isoleucine
75 16 20 L Leucine
30 3 15 P Proline
11 10 22 K Lycine
10 0 5 W Tryptophan
70 13 19 A Alanine
40 8 12 D Aspartic acid
5 0 4 C Cysteine
24 4 16 H Histidine 

7TGM_1|Chains A, B, C, D, E|Desferrioxamine synthetase DesD|Streptomyces griseoflavus (35619)
>2QQY_1|Chain A|Sigma B operon|Bacillus anthracis str. (198094)
>1SDD_1|Chain A|Coagulation factor V|Bos taurus (9913)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
7TGM , Knot 236 612 0.82 40 256 558 
MGSSHHHHHHSSGLVPRGSHMSLTDAVAHLSPERWEEANRLLVRKALAEFAHERLFTPEPADGQDGRYVVRSDDGLTSYRFTAVRRALDHWQVDAGSITRTRDGAELPLAALDFFIELRHTLGLSDEILPVYLEEISSTLSGTCYKLTKPQVTAAGLLEGGFQALESGMTEGHPCFVANNGRLGFGVDEYLAYAPETAHPVRLVWLAAHRSRAAFTAGAGIDYASFVRQELGEETVERFDGVLRGRGLDPADYLLIPVHPWQWWNKLSVTFAAEVARQNLVCLGESDDEYLAQQSIRTFFNATHPEKHYVKTALSVLNMGFMRGLSAAYMEATPAINDWLDRLIDNDPVLKSTGLSIIRERAAVGYRHLEYEAATDRYSPYRKMLAALWRESPVPALRDGESLTTMAALVHVDHEGRSVAGELIARSGLAPTAWLRHYLRAYYTPLLHSFYAYDLAFMPHGENTILVLKDGVVQRAVYKDIAEEIVVMDPDAVLPPEVRRVRAEVPEDMKLLSIFTDVFDCFFRFLAAGLATEEVLAEDDFWRTVAEVTREYQEAHPELDDRFRQYDLFAPEFALSCLNRLQLRDNRQMVDLADPSAALQLVGTLRNPLAGL
2QQY , Knot 74 149 0.82 36 116 147 
SNAMSHDVKELIEGLNEDLAGEYSAIIMYNHNAATVSGIYRQVLKPFFESEISDEQGHALYLAEKIKTLGGTPTTIPLRVKQAEDVREMLEYARQSEYETIKRYEKRKEQAANLNMTELVVKLEDMIADETNHMEELDRLLNDKAMVLN
1SDD , Knot 137 306 0.85 40 199 297 
AKLRQFYVAAQSIRWNYRPESTHLSSKPFETSFKKIVYREYEAYFQKEKPQSRTSGLLGPTLYAEVGDIMKVHFKNKAHKPLSIHAQGIKYSKFSEGASYSDHTLPMEKMDDAVAPGQEYTYEWIISEHSGPTHDDPPCLTHIYYSYVNLVEDFNSGLIGPLLICKKGTLTEDGTQKMFEKQHVLMFAVFDESKSWNQTSSLMYTVNGYVNGTMPDITVCAHDHISWHLIGMSSGPELFSIHFNGQVLEQNHHKISAITLVSATSTTANMTVSPEGRWTIASLIPRHFQAGMQAYIDIKNCAKKTR

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(7TGM_1)}(2) \setminus P_{f(2QQY_1)}(2)|=167\), \(|P_{f(2QQY_1)}(2) \setminus P_{f(7TGM_1)}(2)|=27\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:110000000000111101001010011101010010010011100111011000110101101001001100001100001011001100101011010000011011111101110100011100011110100100010100001001010111110111011001100101011100101111100011011001011011111100001110111110010110001100010010111010110110011111011011001010111011000110110000001100010011010010000100110110111101101101010111001100110001110001101100011110001000110000010001111110001111100100100111110100010011101110011110111000101000111001010011111010001111001110011000110011110101111101001010110010110110011001101111111000111000110011010000001010100010000111101110010010100000110110101110111010011111
Pair \(Z_2\) Length of longest common subsequence
7TGM_1,2QQY_1 194 4
7TGM_1,1SDD_1 181 4
2QQY_1,1SDD_1 169 3

Newick tree

 
[
	7TGM_1:96.70,
	[
		1SDD_1:84.5,2QQY_1:84.5
	]:12.20
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{761 }{\log_{20} 761}-\frac{149}{\log_{20}149})=172.\)
Status Protein1 Protein2 d d1/2
Query variables 7TGM_1 2QQY_1 215 132.5
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]