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Parikh vectors
5CVP_1 4APE_1 1EIT_1 Letter Amino acid
14 5 4 E Glutamic acid
1 11 1 K Lycine
4 47 0 T Threonine
12 23 1 V Valine
6 0 0 M Methionine
11 13 3 P Proline
8 49 1 S Serine
14 1 3 R Arginine
4 6 4 N Asparagine
1 2 8 C Cysteine
10 18 1 I Isoleucine
17 19 0 L Leucine
1 5 1 W Tryptophan
18 29 0 A Alanine
11 21 2 D Aspartic acid
14 38 2 G Glycine
8 20 1 F Phenylalanine
7 13 2 Y Tyrosine
5 9 1 Q Glutamine
5 1 1 H Histidine 

5CVP_1|Chain A|Peptide deformylase|Xanthomonas oryzae pv. oryzae KACC10331 (291331)
>4APE_1|Chain A|ENDOTHIAPEPSIN|Cryphonectria parasitica (5116)
>1EIT_1|Chain A|MU-AGATOXIN-I|Agelenopsis aperta (6908)
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 \(w=f(c)\)
5CVP , Knot 82 171 0.82 40 123 166 
MIRDIIRMGDKRLLRVAPQVTNLGSAELHALVSDMFETMGAAHGVGLAAPQIAVDLQLMVFGFEASERYPEAPAVPLTALANAQIEPLSDEMENGWEGCLSIPGLRAVIPRYRYIRYRGFAPDGSPIEREAEGFHARVVQHEYDHLVGRLYPSRIENFDTFGFDDVLSYDL
4APE , Knot 132 330 0.77 38 160 297 
STGSATTTPIDSLDDAYITPVQIGTPAQTLNLDFDTGSSDLWVFSSETTASEVDGQTIYTPSKSTTAKLLSGATWSISYGDGSSSSGDVYTDTVSVGGLTVTGQAVESAKKVSSSFTEDSTIDGLLGLAFSTLNTVSPTQQKTFFDNAKASLDSPVFTADLGYHAPGTYNFGFIDTTAYTGSITYTAVSTKQGFWEWTSTGYAVGSGTFKSTSIDGIADTGTTLLYLPATVVSAYWAQVSGAKSSSSVGGYVFPCSATLPSFTFGVGSARIVIPGDYIDFGPISTGSSSCFGGIQSSAGIGINIFGDVALKAAFVVFNGATTPTLGFASK
1EIT , Knot 23 37 0.74 34 32 35 
ECVPENGHCRDWYDECCEGFYCSCRQPPKCICRNNNX

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 \(c\).

\(|P_{f(5CVP_1)}(2) \setminus P_{f(4APE_1)}(2)|=62\), \(|P_{f(4APE_1)}(2) \setminus P_{f(5CVP_1)}(2)|=99\). 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 1:110011011000110111010011010101110011001111011111110111010111111010000101111110111010101100010011010101111011110000100011110101100010110101100000011101010010010011100110001
Pair \(Z_2\) Length of longest common subsequence
5CVP_1,4APE_1 161 3
5CVP_1,1EIT_1 137 3
4APE_1,1EIT_1 184 2

Newick tree

 
[
	4APE_1:91.64,
	[
		5CVP_1:68.5,1EIT_1:68.5
	]:23.14
]

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 \((0.85)(0.8)(\frac{501 }{\log_{20} 501}-\frac{171}{\log_{20}171})=96.4\)
Status Protein1 Protein2 d d1/2
Query variables 5CVP_1 4APE_1 118 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]