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Parikh vectors
8DIL_1 1TNJ_1 7ZQQ_1 Letter Amino acid
6 10 15 D Aspartic acid
3 12 0 C Cysteine
2 3 12 H Histidine
13 14 35 L Leucine
9 3 6 F Phenylalanine
7 10 17 T Threonine
14 18 25 V Valine
24 14 34 A Alanine
5 16 5 N Asparagine
10 15 13 I Isoleucine
7 15 5 K Lycine
9 34 12 S Serine
2 10 3 Y Tyrosine
13 25 26 G Glycine
6 2 3 M Methionine
3 4 1 W Tryptophan
14 2 23 R Arginine
9 10 7 Q Glutamine
15 4 12 E Glutamic acid
12 8 21 P Proline 

8DIL_1|Chains A, B, C, D, E, F|Putative NAD(P)H nitroreductase|Salmonella enterica subsp. enterica serovar Typhimurium str. SL1344 (216597)
>1TNJ_1|Chain A|TRYPSIN|Bos taurus (9913)
>7ZQQ_1|Chain A|Molybdenum storage protein subunit alpha|Azotobacter vinelandii (354)
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 \(w=f(c)\)
8DIL , Knot 88 183 0.83 40 135 180 
MDALELLVNRRSASRLAEPAPVGEQLQNILRAGMRVPDHKSLQPWRFFVIEGEGRDRFSAVLEQGAVAAGGDEKAIEKARNAPFRAPLIITVVAKCEENHKVPVWEQEMSAGCAVMAMQMAAIAQGFNGIWRSGALTESAIVREAFECRPQDKIVGFLYLGTPQLKASTTISTPDPTPFVRYF
1TNJ , Knot 102 229 0.80 40 144 221 
VDDDDKIVGGYTCGANTVPYQVSLNSGYHFCGGSLINSQWVVSAAHCYKSGIQVRLGEDNINVVEGNEQFISASKSIVHPSYNSNTLNNDIMLIKLKSAASLNSRVASISLPTSCASAGTQCLISGWGNTKSSGTSYPDVLKCLKAPILSDSSCKSAYPGQITSNMFCAGYLEGGKDSCQGDSGGPVVCSGKLQGIVSWGSGCAQKNKPGVYTKVCNYVSWIKQTIASN
7ZQQ , Knot 117 275 0.79 38 153 257 
TDTTNSIKHVISPLARQTLQDRDLTRPVAGKRPIRLLPWLQVVKIGGRVMDRGADAILPLVEELRKLLPEHRLLILTGAGVRARHVFSVGLDLGLPVGSLAPLAASEAGQNGHILAAMLASEGVSYVEHPTVADQLAIHLSATRAVVGSAFPPYHHHEFPGSRIPPHRADTGAFLLADAFGAAGLTIVENVDGIYTADPNGPDRGQARFLPETSATDLAKSEGPLPVDRALLDVMATARHIERVQVVNGLVPGRLTAALRGEHVGTLIRTGVRPA

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 \(c\).

\(|P_{f(8DIL_1)}(2) \setminus P_{f(1TNJ_1)}(2)|=84\), \(|P_{f(1TNJ_1)}(2) \setminus P_{f(8DIL_1)}(2)|=93\). 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 1:101101110000100110111110010011011101100001011011110101000101110011111110001100100111011111011100000001111000101101111101111101101110011100011100110001000111110110101010001001010111001
Pair \(Z_2\) Length of longest common subsequence
8DIL_1,1TNJ_1 177 5
8DIL_1,7ZQQ_1 142 3
1TNJ_1,7ZQQ_1 173 3

Newick tree

 
[
	1TNJ_1:92.35,
	[
		8DIL_1:71,7ZQQ_1:71
	]:21.35
]

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 \((0.85)(0.8)(\frac{412 }{\log_{20} 412}-\frac{183}{\log_{20}183})=67.8\)
Status Protein1 Protein2 d d1/2
Query variables 8DIL_1 1TNJ_1 87 79.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]