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Parikh vectors
7ZMB_1 6LOU_1 8SBD_1 Letter Amino acid
6 6 0 D Aspartic acid
27 12 3 G Glycine
36 10 1 S Serine
1 8 2 H Histidine
28 6 3 F Phenylalanine
20 5 2 Y Tyrosine
34 11 3 V Valine
41 8 0 I Isoleucine
65 14 4 L Leucine
8 4 0 M Methionine
25 10 1 A Alanine
9 10 1 R Arginine
3 4 2 C Cysteine
7 7 1 Q Glutamine
16 6 2 T Threonine
6 2 0 W Tryptophan
11 8 1 N Asparagine
13 11 2 E Glutamic acid
6 9 1 K Lycine
16 6 1 P Proline 

7ZMB_1|Chain A[auth 1]|NADH-ubiquinone oxidoreductase chain 1|Chaetomium thermophilum var. thermophilum DSM 1495 (759272)
>6LOU_1|Chain A|Dual specificity protein phosphatase 22|Homo sapiens (9606)
>8SBD_1|Chains A[auth a], B[auth b], C[auth c], D[auth d], E[auth e], F[auth f], G[auth g], H[auth h], I[auth i], J[auth j], K[auth k], L[auth l], M[auth m], N[auth n], O[auth o], P[auth p]|Insulin B chain|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 \(w=f(c)\)
7ZMB , Knot 152 378 0.79 40 176 334 
MSYSQTINSLVEVVLVLVPSLVGIAYVTVGERKTMGSMQRRLGPNAVGIYGLLQAFADALKLLLKEYVGPTQANLVLFFLGPVITLIFSLLGYAVIPYGPGLAVNDLSTGILYMLAVSSLATYGILLAGWSANSKYAFLGSLRSTAQLISYELVLSSSILLVIMLSGSLSLTVIVESQRAIWYILPLLPVFIIFFIGSVAETNRAPFDLAEAESELVSGFMTEHAAVIFVFFFLAEYGSIVLMCILTSILFLGGYLLISLLDIIYNNLLSWIVIGKYIIFIFPFWGPVFIDLGLYEIISYLYNAPTVEGSFYGLSLGVKTSILIFVFIWTRASFPRIRFDQLMSFCWTVLLPILFALIVLVPCILYSFNIFPVNISLL
6LOU , Knot 79 157 0.84 40 129 155 
GPMGNGMNKILPGLYIGNFKDARDAEQLSKNKVTHILSVHDSARPMLEGVKYLCIPAADSPSQNLTRHFKESIKFIHECRLRGESCLVHSLAGVNRSVTLVIAYIMTVTDFGWEDALHTVRAGRSCANPNVGFQRQLQEFEKHEVHQYRQWLKEEYG
8SBD , Knot 22 30 0.83 32 26 28 
FVNQHLCGSHLVEALYLVCGERGFFYTPKT

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 \(c\).

\(|P_{f(7ZMB_1)}(2) \setminus P_{f(6LOU_1)}(2)|=110\), \(|P_{f(6LOU_1)}(2) \setminus P_{f(7ZMB_1)}(2)|=63\). 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 1:100000100110111111101111101011000011010001110111101110111011011100011100101111111111011101110111101111110010011101111001100111111101000011110100010110001110001111111010101011100001110111111111111110110000111011010001101110001111111111100101111011001111110111011011000110111110011111111111110111001100100110101010110111000111111110010110101001101010111111111111110110010111101011
Pair \(Z_2\) Length of longest common subsequence
7ZMB_1,6LOU_1 173 3
7ZMB_1,8SBD_1 172 3
6LOU_1,8SBD_1 137 2

Newick tree

 
[
	7ZMB_1:91.40,
	[
		8SBD_1:68.5,6LOU_1:68.5
	]:22.90
]

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 \((0.85)(0.8)(\frac{535 }{\log_{20} 535}-\frac{157}{\log_{20}157})=110.\)
Status Protein1 Protein2 d d1/2
Query variables 7ZMB_1 6LOU_1 133 95
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]