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Parikh vectors
2EAM_1 7TSS_1 4HKM_1 Letter Amino acid
5 12 8 N Asparagine
4 14 20 E Glutamic acid
2 8 10 H Histidine
10 7 19 S Serine
2 14 9 F Phenylalanine
5 11 13 P Proline
1 13 15 T Threonine
1 2 1 W Tryptophan
3 17 19 D Aspartic acid
11 21 34 G Glycine
5 9 19 I Isoleucine
9 14 28 L Leucine
1 11 4 Y Tyrosine
4 13 36 V Valine
8 4 15 Q Glutamine
3 7 15 M Methionine
2 15 49 A Alanine
3 10 23 R Arginine
1 3 2 C Cysteine
0 21 7 K Lycine 

2EAM_1|Chain A|Putative 47 kDa protein|Homo sapiens (9606)
>7TSS_1|Chain A|Trans-state rsEospa|Lobophyllia hemprichii (46758)
>4HKM_1|Chains A, B|Anthranilate phosphoribosyltransferase|Xanthomonas campestris pv. campestris (190485)
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 \(w=f(c)\)
2EAM , Knot 44 80 0.80 38 62 74 
GSSGSSGPRCPVQTVGQWLESIGLPQYENHLMANGFDNVQFMGSNVMEDQDLLEIGILNSGHRQRILQAIQLLPSGPSSG
7TSS , Knot 105 226 0.84 40 158 215 
MSAIKPDMKIKLRMEGNVNGHHFVIDGDGTGKPFEGKQSMDLEVKEGGPLPFAFDILTTAFAYGNRVFAKYPDNIQDYFKQSFPKGYSWERSLTFEDGGICNARNDITMEGDTFYNKVRFYGTNFPANGPVMQKKTLKWEPATEKMYVRDGVLTGDVETALLLEGNAHYRCDFRTTYKAKEKGVKLPGAHFVDHCIEILSHDKDYNKVKLYEHAVAHSGLPDNARR
4HKM , Knot 143 346 0.80 40 189 321 
SMPITPQQALQRTIEHREIFHDEMVDLMRQIMRGEVSDAMVSAILTGLRVKKETIGEIAGAATVMREFSRRVEVTDRRHMVDIVGTGGDGSHTFNISTCAMFVAAAGGAKVAKHGNRSVSSKSGSADALEALGAVIELQPEQVAASLAQTGIGFMYAPVHHPAMKVVAPVRREMGVRTIFNILGPLTNPAGSPNILMGVFHPDLVGIQARVLQELGAERALVVWGRDGMDELSLGAGTLVGELRDGQVHEYEVHPEDFGIAMSASRNLKVADAAESRAMLLQVLDNVPGPALDIVALNAGAALYVAGVADSIADGIVRARQVLADGSARACLDAYVAFTQQATAQG

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 \(c\).

\(|P_{f(2EAM_1)}(2) \setminus P_{f(7TSS_1)}(2)|=37\), \(|P_{f(7TSS_1)}(2) \setminus P_{f(2EAM_1)}(2)|=133\). 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 1:10010011001100110110011110000011101100101110011000011011110010000110110111011001
Pair \(Z_2\) Length of longest common subsequence
2EAM_1,7TSS_1 170 3
2EAM_1,4HKM_1 177 3
7TSS_1,4HKM_1 177 3

Newick tree

 
[
	4HKM_1:89.63,
	[
		2EAM_1:85,7TSS_1:85
	]:4.63
]

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 \((0.85)(0.8)(\frac{306 }{\log_{20} 306}-\frac{80}{\log_{20}80})=71.7\)
Status Protein1 Protein2 d d1/2
Query variables 2EAM_1 7TSS_1 92 62
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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