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Parikh vectors
4DET_1 7HEH_1 8TNC_1 Letter Amino acid
7 19 19 L Leucine
1 2 0 M Methionine
5 5 5 F Phenylalanine
10 11 8 S Serine
1 3 0 C Cysteine
4 6 0 H Histidine
5 6 3 I Isoleucine
4 2 5 R Arginine
7 13 3 G Glycine
10 6 14 E Glutamic acid
6 13 11 K Lycine
7 5 1 P Proline
12 15 25 A Alanine
0 3 11 Q Glutamine
10 6 12 T Threonine
2 0 1 W Tryptophan
5 7 4 Y Tyrosine
12 22 8 V Valine
3 16 7 N Asparagine
5 9 10 D Aspartic acid 

4DET_1|Chains A, B|Transthyretin|Homo sapiens (9606)
>7HEH_1|Chains A, B|Non-structural protein 3|Severe acute respiratory syndrome coronavirus 2 (2697049)
>8TNC_1|Chains A, B, C|De novo designed protein|synthetic construct (32630)
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 \(w=f(c)\)
4DET , Knot 62 116 0.84 38 94 114 
CPLMVKVLDAVRGSPAINVAVHVFRKAADDTWEPFASGKTSESGELHGLTTEEEFVEGIYKVEIDTKSYWKALGISPFHEHAEVVFTANDSGPRRYTIAALLSPYSYSTTAVVTNP
7HEH , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL
8TNC , Knot 70 147 0.79 34 103 142 
SDAQEILSRLNSVLEAAWKTILNLASATDAAEKAYKEGREEDLATYLDQAASYQSQVDQYAVETVRLLAELKKVFPDEEADRALQIAEKLLKTVQEASKTLDTAVAAAANGDEETFAKAFNQFVSLGNQADTLFTQLQRTLTNLNKK

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 \(c\).

\(|P_{f(4DET_1)}(2) \setminus P_{f(7HEH_1)}(2)|=57\), \(|P_{f(7HEH_1)}(2) \setminus P_{f(4DET_1)}(2)|=82\). 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 1:01111011011010111011101100110001011101000001010110000011011001010000010111101100010111010001100001111101000000111001
Pair \(Z_2\) Length of longest common subsequence
4DET_1,7HEH_1 139 3
4DET_1,8TNC_1 125 3
7HEH_1,8TNC_1 130 3

Newick tree

 
[
	7HEH_1:68.80,
	[
		4DET_1:62.5,8TNC_1:62.5
	]:6.30
]

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 \((0.85)(0.8)(\frac{285 }{\log_{20} 285}-\frac{116}{\log_{20}116})=53.0\)
Status Protein1 Protein2 d d1/2
Query variables 4DET_1 7HEH_1 68 58
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]