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Parikh vectors
4AHK_1 7BWH_1 4QFC_1 Letter Amino acid
6 7 12 K Lycine
5 7 19 V Valine
7 5 22 I Isoleucine
6 7 38 L Leucine
7 6 22 T Threonine
13 6 22 R Arginine
6 4 15 D Aspartic acid
6 1 5 C Cysteine
6 5 15 Q Glutamine
5 7 23 E Glutamic acid
8 6 31 G Glycine
6 10 13 H Histidine
8 3 22 P Proline
5 9 17 A Alanine
9 4 15 N Asparagine
9 13 15 S Serine
1 2 10 W Tryptophan
4 5 12 Y Tyrosine
1 1 5 M Methionine
5 4 14 F Phenylalanine 

4AHK_1|Chains A, B|ANGIOGENIN|HOMO SAPIENS (9606)
>7BWH_1|Chain A|Cytochrome b5 heme-binding domain-containing protein|Ramazzottius varieornatus (947166)
>4QFC_1|Chains A, B|D-amino-acid oxidase|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 \(w=f(c)\)
4AHK , Knot 63 123 0.82 40 102 120 
QDNSRYTHFLTQHYDAKPQGRDDRYCESIMRRRGLTSPCKDINTFIHGNKRSIEAICENKNGNPHRENLRISKSSFQVTTCKLHGGSPWPPCQYRATAGFRNVVVACENGLPVHLDQSIFRRP
7BWH , Knot 56 112 0.78 40 91 106 
HHHHHHSSENLYFQSLRKDKAEEQTFSWSEISQHTSANSLWVVVRDKTSPGSPLRVYDVTNFQKTHPGGHLILLKYAGTECSRAFAAVGHSKYAIKRMSQYRIGIAEADNVE
4QFC , Knot 148 347 0.83 40 210 335 
MRVVVIGAGVIGLSTALCIHERYHSVLQPLDIKVYADRFTPLTTTDVAAGLWQPYLSDPNNPQEADWSQQTFDYLLSHVHSPNAENLGLFLISGYNLFHEAIPDPSWKDTVLGFRKLTPRELDMFPDYGYGWFHTSLILEGKNYLQWLTERLTERGVKFFQRKVESFEEVAREGADVIVNCTGVWAGALQRDPLLQPGRGQIMKVDAPWMKHFILTHDPERGIYNSPYIIPGTQTVTLGGIFQLGNWSELNNIQDHNTIWEGCCRLEPTLKNARIIGERTGFRPVRPQIRLEREQLRTGPSNTEVIHNYGHGGYGLTIHWGCALEAAKLFGRILEEKKLSRMPPSHL

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 \(c\).

\(|P_{f(4AHK_1)}(2) \setminus P_{f(7BWH_1)}(2)|=69\), \(|P_{f(7BWH_1)}(2) \setminus P_{f(4AHK_1)}(2)|=58\). 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 1:000000001100000101010000000011000110010001001101000010110000010100001010000101000010110111100001011100111100011110100011001
Pair \(Z_2\) Length of longest common subsequence
4AHK_1,7BWH_1 127 3
4AHK_1,4QFC_1 192 3
7BWH_1,4QFC_1 191 3

Newick tree

 
[
	4QFC_1:10.30,
	[
		4AHK_1:63.5,7BWH_1:63.5
	]:40.80
]

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 \((0.85)(0.8)(\frac{235 }{\log_{20} 235}-\frac{112}{\log_{20}112})=39.3\)
Status Protein1 Protein2 d d1/2
Query variables 4AHK_1 7BWH_1 51 47
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]