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Parikh vectors
3BAS_1 6HTS_1 9FRG_1 Letter Amino acid
4 0 30 D Aspartic acid
0 69 3 C Cysteine
2 0 26 I Isoleucine
14 0 46 L Leucine
4 0 43 S Serine
3 47 19 A Alanine
4 0 35 R Arginine
3 60 18 G Glycine
2 52 34 T Threonine
0 0 12 W Tryptophan
2 0 11 H Histidine
13 0 21 K Lycine
5 0 22 M Methionine
1 0 20 Y Tyrosine
4 0 35 V Valine
4 0 15 N Asparagine
6 0 15 Q Glutamine
16 0 22 E Glutamic acid
1 0 27 F Phenylalanine
1 0 25 P Proline 

3BAS_1|Chains A, B|Myosin heavy chain, striated muscle/General control protein GCN4 chimera|Argopecten irradians (31199)
>6HTS_11|Chain S[auth Y]|DNA (150-MER)|synthetic construct (32630)
>9FRG_1|Chains A, B, C, D, E|Gamma-aminobutyric acid receptor subunit rho-1|Homo sapiens (9606)
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 \(w=f(c)\)
3BAS , Knot 46 89 0.77 36 61 85 
GSHMPLLSIARQEEEMKEQLKQMDKMKEDLAKTERIKKELEEQNVTLLEQKNDLFGSMKQLEDKVEELLSKNYHLENEVARLKKLVGER
6HTS , Knot 59 228 0.46 8 16 62 
GAATCTGCATTAATGCATCCGCGGCCGCCCTGGACAATCCCGGTGCCGAGGCCGCTCAATTGGTCGTAGACAGCTCTAGCACCGCTTAAACGCACGTACGCGCTGTCCCCCGCGTTTTAACCGCCAAGGGGATTACTCCCTAGTCTCCAGGCACGTGTCAGATATATACATCCTGTGCATGTACTCGGGGTGGCGATAAGTCGTGTCTTACCGGGTTGGACTCAAGAC
9FRG , Knot 197 479 0.84 40 237 452 
MLAVPNMRFGIFLLWWGWVLATESRMHWPGREVHEMSKKGRPQRQRREVHEDAHKQVSPILRRSPDITKSPLTKSEQLLRIDDHDFSMRPGFGGPAIPVGVDVQVESLDSISEVDMDFTMTLYLRHYWKDERLSFPSTNNLSMTFDGRLVKKIWVPDMFFVHSKRSFIHDTTTDNVMLRVQPDGKVLYSLRVTVTAMCNMDFSRFPLDTQTCSLEIESYAYTEDDLMLYWKKGNDSLKTDERISLSQFLIQEFHTTTKLAFYSSTGWYNRLYINFTLRRHIFFFLLQTYFPATLMVMLSWVSFWIDRRAVPARVPLGITTVLTMSTIITGVNASMPRVSYIKAVDIYLWVSFVFVFLSVLEYAAVNYLTTVQERKEQKLREKLPCTSGLPPPRTAMLDGNYSDGEVNDLDNYMPENGEKPDRMMVQLTLASERSSPQRKSQRSSYVSMRIDTHAIDKYSRIIFPAAYILFNLIYWSIFS

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 \(c\).

\(|P_{f(3BAS_1)}(2) \setminus P_{f(6HTS_1)}(2)|=61\), \(|P_{f(6HTS_1)}(2) \setminus P_{f(3BAS_1)}(2)|=16\). 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 1:10011110110000010001001001000110000100010000101100000111010010001001100000100011010011100
Pair \(Z_2\) Length of longest common subsequence
3BAS_1,6HTS_1 77 1
3BAS_1,9FRG_1 208 3
6HTS_1,9FRG_1 237 3

Newick tree

 
[
	9FRG_1:12.79,
	[
		3BAS_1:38.5,6HTS_1:38.5
	]:88.29
]

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 \((0.85)(0.8)(\frac{317 }{\log_{20} 317}-\frac{89}{\log_{20}89})=71.7\)
Status Protein1 Protein2 d d1/2
Query variables 3BAS_1 6HTS_1 57 50
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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