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Parikh vectors
8IQR_1 5PBE_1 7WGT_1 Letter Amino acid
19 11 36 S Serine
7 4 34 Y Tyrosine
9 12 14 D Aspartic acid
10 4 40 I Isoleucine
13 14 13 K Lycine
6 8 46 F Phenylalanine
8 6 23 P Proline
3 6 20 N Asparagine
11 9 16 E Glutamic acid
16 6 45 G Glycine
5 6 9 M Methionine
3 2 17 W Tryptophan
8 5 20 R Arginine
3 2 9 C Cysteine
11 2 10 Q Glutamine
8 8 6 H Histidine
8 8 27 T Threonine
5 4 50 A Alanine
17 13 63 L Leucine
9 8 38 V Valine 

8IQR_1|Chains A[auth L], C[auth l]|M9 VL-SARAH|Mus musculus (10090)
>5PBE_1|Chain A|Bromodomain adjacent to zinc finger domain protein 2B|Homo sapiens (9606)
>7WGT_1|Chain A|Sodium-dependent dopamine transporter|Drosophila melanogaster (7227)
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 \(w=f(c)\)
8IQR , Knot 84 179 0.81 40 132 168 
MSKIKGHHHHHHGGMDVLMTQTPLSLPVSLGDQASISCRSSQSIVHSNGNTYLEWYLQKPGQSPKLLIYKVSNRFSGVPDRFSGSGSGTDFTLKISRVEAEDLGVYYCFQGSHVPWTFGGGTKLEIKRGSDYEFLKSWTVEDLQKRLLALDPMMEQEIEEIRQKYQCKRQPILDAIEAK
5PBE , Knot 66 138 0.78 40 109 129 
MHHHHHHSSGVDLGTENLYFQSMSVKKPKRDDSKDLALCSMILTEMETHEDAWPFLLPVNLKLVPGYKKVIKKPMDFSTIREKLSSGQYPNLETFALDVRLVFDNCETFNEDDSDIGRAGHNMRKYFEKKWTDTFKVS
7WGT , Knot 211 536 0.82 40 243 488 
DERETWSGKVDFLLSVIGYAVGLANVWRFPYLCYKNGGGAFLVPYGIMLAVGGIPLFYMELALGQHNRKGAITCWGRLVPLFKGIGYAVVLISFYLNFYYNVIIAWSLRFFFASFTNSLPWTSCNNIWNTPNCRPFEGHVEGFQSAASEYFNRYILELNRSEGIHDLGAIKWDMALCLLIVYLICYFSLWKGISTSGKVVWFTALFPYAALLILLIRGLTLPGSFLGIQYYLTPNFSAIYKAEVWADAATQVFFSLGPGLGSLLAYASYNKYHNNVYKDALLTSFINSATSFIAGFVIFSVLGYMAHTLGVRIEDVATSGPGLVFVVYPAAIATMPASTFWALIFFMMLATLGLDSQFGTVEAIITALSDEFPKIKRNRELFVAGLFSLYFVVGLASCTQGGFYFFHLLDRYAAGYSILVAVFFEAIAVSWIYGTNRFSEDIRDMIGFPPGRYWQVCWRFVAPIFLLFITVYLLIGYEPLTYADYVYPSWANALGWCIAGSSVVMIPAVAIFKLLSTPGSLRQRFTILTTPWRDQQ

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 \(c\).

\(|P_{f(8IQR_1)}(2) \setminus P_{f(5PBE_1)}(2)|=82\), \(|P_{f(5PBE_1)}(2) \setminus P_{f(8IQR_1)}(2)|=59\). 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 1:10010100000011101110001101110110010100000001100010001010100110010111001000101110010101010010101001010011100010100111011110010100100001100101001000111101110001001000000000111011010
Pair \(Z_2\) Length of longest common subsequence
8IQR_1,5PBE_1 141 6
8IQR_1,7WGT_1 197 4
5PBE_1,7WGT_1 200 3

Newick tree

 
[
	7WGT_1:10.13,
	[
		8IQR_1:70.5,5PBE_1:70.5
	]:36.63
]

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 \((0.85)(0.8)(\frac{317 }{\log_{20} 317}-\frac{138}{\log_{20}138})=55.0\)
Status Protein1 Protein2 d d1/2
Query variables 8IQR_1 5PBE_1 66 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]