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Parikh vectors
5EBW_1 6ESY_1 3TJH_1 Letter Amino acid
16 43 17 G Glycine
4 7 3 H Histidine
21 31 8 V Valine
5 22 17 R Arginine
5 35 6 N Asparagine
9 19 10 Q Glutamine
6 26 3 I Isoleucine
5 37 4 F Phenylalanine
9 18 16 Y Tyrosine
8 32 17 E Glutamic acid
2 8 5 M Methionine
15 30 6 P Proline
31 35 6 S Serine
21 33 11 T Threonine
18 32 15 A Alanine
6 21 10 D Aspartic acid
4 7 3 C Cysteine
14 48 13 L Leucine
13 31 4 K Lycine
6 14 6 W Tryptophan 

5EBW_1|Chain A|Antibody Fab Fragment Light Chain|Mus musculus (10090)
>6ESY_1|Chains A, B|Cholinesterase|Homo sapiens (9606)
>3TJH_1|Chain A|H2-Ld SBM2|Mus musculus (10090)
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 \(w=f(c)\)
5EBW , Knot 99 218 0.81 40 146 204 
QVQLQQPGAELVKPGASVKLSCKASGYTFTSDWIHWVKQRPGHGLEWIGEIIPSYGRANYNEKIQKKATLTADKSSSTAFMQLSSLTSEDSAVYYCARERGDGYFAVWGAGTTVTVSSAKTTPPSVYPLAPGSAAQTNSMVTLGCLVKGYFPEPVTVTWNSGSLSSGVHTFPAVLQSDLYTLSSSVTVPSSSWPSETVTCNVAHPASSTKVDKKIVPR
6ESY , Knot 216 529 0.85 40 262 501 
EDDIIIATKNGKVRGMNLTVFGGTVTAFLGIPYAQPPLGRLRFKKPQSLTKWSDIWNATKYANSCCQNIDQSFPGFHGSEMWNPNTDLSEDCLYLNVWIPAPKPKNATVLIWIYGGGFQTGTSSLHVYDGKFLARVERVIVVSMNYRVGALGFLALPGNPEAPGNMGLFDQQLALQWVQKNIAAFGGNPKSVTLFGESAGAASVSLHLLSPGSHSLFTRAILQSGSFNAPWAVTSLYEARNRTLNLAKLTGCSRENETEIIKCLRNKDPQEILLNEAFVVPYGTPLSVNFGPTVDGDFLTDMPDILLELGQFKKTQILVGVNKDEGTAFLVYGAPGFSKDNNSIITRKEFQEGLKIFFPGVSEFGKESILFHYTDWVDDQRPENYREALGDVVGDYNFICPALEFTKKFSEWGNNAFFYYFEHRSSKLPWPEWMGVMHGYEIEFVFGLPLERRDNYTKAEEILSRSIVKRWANFAKYGNPNETQNNSTSWPVFKSTEQKYLTLNTESTRIMTKLRAQQCRFWTSFFPKV
3TJH , Knot 85 180 0.81 40 134 175 
MGPHSMRYYETATSRRGLGEPRYTSVGYVDDKEFVRFDSDAENPRYEPQVPWMEQEGPEYWERITQVAKGQEQWFRVNLRTLLGYYNQSAGGTHTLQRMYGCDVGSDGRLLRGYEQFAYDGCDYIALNEDLRTWTAADMAAQITRRKWEQAGAAEYYRAYLEGECVEWLHRYLKNGNATL

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 \(c\).

\(|P_{f(5EBW_1)}(2) \setminus P_{f(6ESY_1)}(2)|=34\), \(|P_{f(6ESY_1)}(2) \setminus P_{f(5EBW_1)}(2)|=150\). 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 1:01010011101101110101000101001000110110001101101110111001010000010001010100000011101001000001100010001010111111100101001000110101111101100001101101101011011010100101001100111110001001000101100011000100011011000010001110
Pair \(Z_2\) Length of longest common subsequence
5EBW_1,6ESY_1 184 3
5EBW_1,3TJH_1 174 3
6ESY_1,3TJH_1 194 4

Newick tree

 
[
	6ESY_1:96.91,
	[
		5EBW_1:87,3TJH_1:87
	]:9.91
]

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 \((0.85)(0.8)(\frac{747 }{\log_{20} 747}-\frac{218}{\log_{20}218})=147.\)
Status Protein1 Protein2 d d1/2
Query variables 5EBW_1 6ESY_1 190 131.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]