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Parikh vectors
5CXJ_1 7RMQ_1 4REA_1 Letter Amino acid
7 1 13 Y Tyrosine
14 3 36 G Glycine
5 0 20 H Histidine
12 2 43 V Valine
18 1 49 A Alanine
11 0 30 D Aspartic acid
5 0 34 Q Glutamine
10 4 25 I Isoleucine
17 0 89 L Leucine
1 2 33 K Lycine
11 2 23 P Proline
8 5 44 S Serine
14 1 46 R Arginine
4 1 15 N Asparagine
1 6 18 C Cysteine
14 1 47 E Glutamic acid
6 0 12 M Methionine
8 0 28 F Phenylalanine
4 0 29 T Threonine
1 1 13 W Tryptophan 

5CXJ_1|Chain A|Peptide deformylase|Xanthomonas oryzae pv. oryzae KACC10331 (291331)
>7RMQ_1|Chain A|Cycloviolacin O2|Viola odorata (97441)
>4REA_1|Chains A, B|Fanconi-associated nuclease 1|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 \(w=f(c)\)
5CXJ , Knot 82 171 0.82 40 123 166 
MIRDIIRMGDKRLLRVAPQVTNLGSAELHALVSDMFETMGAAHGVGLAAPQIAVDLQLMVFGFEASERYPEAPAVPLTALANAQIEPLSDEMENGWEGCLSIPGLRAVIPRYRYIRYRGFAPDGSPIEREAEGFHARVVQHEYDHLVGRLYPSRIENFDTFGFDDVLSYDL
7RMQ , Knot 20 30 0.75 26 26 27 
IPCGESCVWIPCISSAIGCSCKSKVCYRNG
4REA , Knot 253 647 0.84 40 284 598 
EFPYYLRSFLVVLKTVLENEDDMLLFDEQEKGIVTKFYQLSATGQKLYVRLFQRKLSWIKMTKLEYEEIALDLTPVIEELTNAGFLQTESELQELSEVLELLSAPELKSLAKTFHLVNPNGQKQQLVDAFLKLAKQRSVCTWGKNKPGIGAVILKRAKALAGQSVRICKGPRAVFSRILLLFSLTDSMEDEDAACGGQGQLSTVLLVNLGRMEFPSYTINRKTHIFQDRDDLIRYAAATHMLSDISSAMANGNWEEAKELAQCAKRDWNRLKNHPSLRCHEDLPLFLRCFTVGWIYTRILSRFVEILQRLHMYEEAVRELESLLSQRIYCPDSRGRWWDRLALNLHQHLKRLEPTIKCITEGLADPEVRTGHRLSLYQRAVRLRESPSCKKFKHLFQQLPEMAVQDVKHVTITGRLCPQRGMCKSVFVMEAGEAADPTTVLCSVEELALAHYRRSGFDQGIHGEGSTFSTLYGLLLWDIIFMDGIPDVFRNACQAFPLDLCTDSFFTSRRPALEARLQLIHDAPEESLRAWVAATWHEQEGRVASLVSWDRFTSLQQAQDLVSCLGGPVLSGVCRHLAADFRHCRGGLPALVVWNSQSRHFKLVEVKGPNDRLSHKQMIWLAELQKLGAEVEVCHVVAVGAKSQSLS

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 \(c\).

\(|P_{f(5CXJ_1)}(2) \setminus P_{f(7RMQ_1)}(2)|=118\), \(|P_{f(7RMQ_1)}(2) \setminus P_{f(5CXJ_1)}(2)|=21\). 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
5CXJ_1,7RMQ_1 139 2
5CXJ_1,4REA_1 213 3
7RMQ_1,4REA_1 272 4

Newick tree

 
[
	4REA_1:13.21,
	[
		5CXJ_1:69.5,7RMQ_1:69.5
	]:65.71
]

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 \((0.85)(0.8)(\frac{201 }{\log_{20} 201}-\frac{30}{\log_{20}30})=59.2\)
Status Protein1 Protein2 d d1/2
Query variables 5CXJ_1 7RMQ_1 76 44.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]