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Parikh vectors
3QJD_1 6CTT_1 8XTN_1 Letter Amino acid
1 0 1 Q Glutamine
4 0 0 E Glutamic acid
0 0 1 I Isoleucine
11 0 0 K Lycine
2 0 0 M Methionine
7 0 3 F Phenylalanine
9 2 1 T Threonine
3 0 3 R Arginine
9 0 1 H Histidine
19 0 1 L Leucine
7 0 2 P Proline
4 0 0 N Asparagine
11 0 6 S Serine
1 0 0 W Tryptophan
3 0 1 Y Tyrosine
13 0 2 V Valine
21 3 3 A Alanine
1 7 0 C Cysteine
7 4 8 G Glycine
8 0 0 D Aspartic acid 

3QJD_1|Chains A, C|Hemoglobin subunit alpha|Homo sapiens (9606)
>6CTT_1|Chain A[auth T]|DNA (5'-D(*CP*CP*GP*AP*CP*GP*TP*CP*GP*CP*AP*TP*CP*AP*GP*C)-3')|Homo sapiens (9606)
>8XTN_1|Chain A|Keratin, type I cytoskeletal 19|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 \(w=f(c)\)
3QJD , Knot 70 141 0.82 38 100 137 
VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLSHGSAQVKGLGKKVADALTNAVAHVDDMPNALSALSDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR
6CTT , Knot 8 16 0.46 8 10 14 
CCGACGTCGCATCAGC
8XTN , Knot 20 33 0.70 26 28 31 
YRQSSATSSFGGLGGGSVRFGPGVAFRAPSIHG

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 \(c\).

\(|P_{f(3QJD_1)}(2) \setminus P_{f(6CTT_1)}(2)|=98\), \(|P_{f(6CTT_1)}(2) \setminus P_{f(3QJD_1)}(2)|=8\). 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 1:110110000101111011101100110110011101100000110101001010101110011011001110100110110110010100101011010110001110111011101011101010011101001100000
Pair \(Z_2\) Length of longest common subsequence
3QJD_1,6CTT_1 106 2
3QJD_1,8XTN_1 108 3
6CTT_1,8XTN_1 36 2

Newick tree

 
[
	3QJD_1:60.89,
	[
		6CTT_1:18,8XTN_1:18
	]:42.89
]

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 \((0.85)(0.8)(\frac{157 }{\log_{20} 157}-\frac{16}{\log_{20}16})=51.4\)
Status Protein1 Protein2 d d1/2
Query variables 3QJD_1 6CTT_1 65 36
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]