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Parikh vectors
6XVG_1 6HZK_1 1IKD_1 Letter Amino acid
15 16 0 K Lycine
37 34 0 L Leucine
18 25 0 D Aspartic acid
8 12 0 Q Glutamine
11 21 0 I Isoleucine
25 17 0 P Proline
5 2 0 W Tryptophan
28 22 0 R Arginine
22 27 0 E Glutamic acid
27 26 7 G Glycine
16 14 0 S Serine
20 18 0 T Threonine
21 22 0 V Valine
7 10 0 N Asparagine
5 4 8 C Cysteine
9 9 0 H Histidine
6 8 0 M Methionine
8 9 0 F Phenylalanine
4 17 0 Y Tyrosine
24 20 3 A Alanine 

6XVG_1|Chains A, B, C, D, E, F|NAD-dependent protein deacetylase sirtuin-6|Homo sapiens (9606)
>6HZK_1|Chains A, B|Phosphoribulokinase|Synechococcus sp. (strain ATCC 27144 / PCC 6301 / SAUG 1402/1) (269084)
>1IKD_1|Chain A|TRNA ALA ACCEPTOR STEM|
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 \(w=f(c)\)
6XVG , Knot 139 316 0.84 40 187 306 
VNYAAGLSPYADKGKCGLPEIFDPPEELERKVWELARLVWQSSSVVFHTGAGISTASGIPDFRGPHGVWTMEERGLAPKFDTTFESARPTQTHMALVQLERVGLLRFLVSQNVDGLHVRSGFPRDKLAELHGNMFVEECAKCKTQYVRDTVVGTMGLKATGRLCTVAKARGLRACRGELRDTILDWEDSLPDRDLALADEASRNADLSITLGTSLQIRPSGNLPLATKRRGGRLVIVNLQPTKHDRHADLRIHGYVDEVMTRLMKHLGLEIPAWDGPRVLERALPPLPRPPTPKLEPKEESPTRINGSIPAGPKQE
6HZK , Knot 145 333 0.84 40 199 320 
MSKPDRVVLIGVAGDSGCGKSTFLNRLADLFGTELMTVICLDDYHSLDRKGRKEAGVTALDPRANNFDLMYEQVKALKNGETIMKPIYNHETGLIDPPEKIEPNRIIVIEGLHPLYDERVRELLDFSVYLDIDDEVKIAWKIQRDMAERGHSYEDVLASIEARRPDFKAYIEPQRGHADIVIRVMPTQLIPNDTERKVLRVQLIQREGRDGFEPAYLFDEGSTIQWTPCGRKLTCSYPGIRLAYGPDTYYGHEVSVLEVDGQFENLEEMIYVEGHLSKTDTQYYGELTHLLLQHKDYPGSNNGTGLFQVLTGLKMRAAYERLTSQAAPVAASV
1IKD , Knot 9 22 0.42 8 11 16 
GGGGCUCUUCGGAGCUCCACCA

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 \(c\).

\(|P_{f(6XVG_1)}(2) \setminus P_{f(6HZK_1)}(2)|=78\), \(|P_{f(6HZK_1)}(2) \setminus P_{f(6XVG_1)}(2)|=90\). 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 1:1001111010100100111011011001000110110111000011100111100101110101101110100011110100010010100001111010011110111000101101001110001101010111000100000010001110111010101001101011010010100011010001100011110010001010101100101010101111000011011110101000000101010101001100110011101111011011001111110110101010000100101011111000
Pair \(Z_2\) Length of longest common subsequence
6XVG_1,6HZK_1 168 4
6XVG_1,1IKD_1 186 3
6HZK_1,1IKD_1 204 2

Newick tree

 
[
	1IKD_1:10.73,
	[
		6XVG_1:84,6HZK_1:84
	]:17.73
]

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 \((0.85)(0.8)(\frac{649 }{\log_{20} 649}-\frac{316}{\log_{20}316})=92.3\)
Status Protein1 Protein2 d d1/2
Query variables 6XVG_1 6HZK_1 117 115
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]