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Parikh vectors
3EVI_1 3EQX_1 8PPH_1 Letter Amino acid
8 14 3 N Asparagine
7 13 24 G Glycine
3 19 10 P Proline
9 21 16 V Valine
4 6 7 C Cysteine
5 30 10 Q Glutamine
12 50 32 L Leucine
4 16 7 Y Tyrosine
3 14 18 D Aspartic acid
4 9 9 H Histidine
5 18 16 S Serine
2 5 4 W Tryptophan
4 25 14 T Threonine
6 33 16 A Alanine
3 15 27 R Arginine
12 26 26 E Glutamic acid
13 25 10 I Isoleucine
8 18 13 K Lycine
1 6 6 M Methionine
5 10 11 F Phenylalanine 

3EVI_1|Chains A, B|Phosducin-like protein 2|Homo sapiens (9606)
>3EQX_1|Chains A, B|FIC DOMAIN CONTAINING TRANSCRIPTIONAL REGULATOR|Shewanella oneidensis (70863)
>8PPH_1|Chains A, B|Inositol-trisphosphate 3-kinase A|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 \(w=f(c)\)
3EVI , Knot 61 118 0.82 40 94 116 
KFGELREISGNQYVNEVTNAEEDVWVIIHLYRSSIPMCLLVNQHLSLLARKFPETKFVKAIVNSCIQHYHDNCLPTIFVYKNGQIEAKFIGIIECGGINLKLEELEWKLAEVGAIQTD
3EQX , Knot 159 373 0.84 40 216 350 
GMEWQAEQAYNHLPPLPLDSKLAELAETLPILKACIPARAALAELKQAGELLPNQGLLINLLPLLEAQGSSEIENIVTTTDKLFQYAQEDSQADPMTKEALRYRTALYQCFTQLSNRPLCVTTALEICSTIKSVQMDVRKVPGTSLTNQATGEVIYTPPAGESVIRDLLSNWEAFLHNQDDVDPLIKMAMAHYQFEAIHPFIDGNGRTGRVLNILYLIDQQLLSAPILYLSRYIVAHKQDYYRLLLNVTTQQEWQPWIIFILNAVEQTAKWTTHKIAAARELIAHTTEYVRQQLPKIYSHELVQVIFEQPYCRIQNLVESGLAKRQTASVYLKQLCDIGVLEEVQSGKEKLFVHPKFVTLMTKDSNQFSRYAL
8PPH , Knot 123 279 0.82 40 181 273 
GSHMSWVQLAGHTGSFKAAGTSGLILKRCSEPERYCLARLMADALRGCVPAFHGVVERDGESYLQLQDLLDGFDGPCVLDCKMGVRTYLEEELTKARERPKLRKDMYKKMLAVDPEAPTEEEHAQRAVTKPRYMQWREGISSSTTLGFRIEGIKKADGSCSTDFKTTRSREQVLRVFEEFVQGDEEVLRRYLNRLQQIRDTLEVSEFFRRHEVIGSSLLFVHDHCHRAGVWLIDFGKTTPLPDGQILDHRRPWEEGNREDGYLLGLDNLIGILASLAER

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 \(c\).

\(|P_{f(3EVI_1)}(2) \setminus P_{f(3EQX_1)}(2)|=32\), \(|P_{f(3EQX_1)}(2) \setminus P_{f(3EVI_1)}(2)|=154\). 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 1:0110100101000100100100011111010000111011100010111001100011011100010000000110111000101010111110011101010010101101111000
Pair \(Z_2\) Length of longest common subsequence
3EVI_1,3EQX_1 186 4
3EVI_1,8PPH_1 185 3
3EQX_1,8PPH_1 185 4

Newick tree

 
[
	3EQX_1:92.83,
	[
		3EVI_1:92.5,8PPH_1:92.5
	]:0.33
]

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 \((0.85)(0.8)(\frac{491 }{\log_{20} 491}-\frac{118}{\log_{20}118})=111.\)
Status Protein1 Protein2 d d1/2
Query variables 3EVI_1 3EQX_1 139 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]