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Parikh vectors
9EAF_1 7XZY_1 7SGE_1 Letter Amino acid
20 6 20 P Proline
18 13 41 K Lycine
9 3 24 M Methionine
17 4 29 F Phenylalanine
26 18 44 A Alanine
15 18 20 R Arginine
12 1 34 N Asparagine
22 4 28 D Aspartic acid
42 12 60 L Leucine
26 6 42 S Serine
3 0 9 W Tryptophan
16 3 21 Y Tyrosine
10 2 21 C Cysteine
35 8 56 G Glycine
9 3 19 H Histidine
19 7 39 I Isoleucine
11 8 22 Q Glutamine
25 7 49 E Glutamic acid
15 10 41 T Threonine
26 6 46 V Valine 

9EAF_1|Chains A, B|Carboxynorspermidine decarboxylase|[Clostridium] leptum (1535)
>7XZY_1|Chains A, E|Histone H3.1|Homo sapiens (9606)
>7SGE_1|Chain A|Josiah GPCysR4-I53-50A - nanoparticle component|synthetic construct (32630)
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 \(w=f(c)\)
9EAF , Knot 159 376 0.83 40 213 356 
MELPFSSLQTPCYVVDEALLERNLVILKQVIDRTGCKILLAQKAFSMFACYPLIGSYLNGTTASGLFEARLGKEEMGGETHIFSPAYREDEIDEILSLCDHVIFNSFSQWEKYKAKVLASGKSAGLRLNPEHSTQDHAIYDPCSPGSRLGITLKKFRPDLLDGIEGLHFHTLCEQDAAPLVETVAVVEEKFGPWLSQMKWLNFGGGHHITRPGYDIDALVSCVSRVQERYGVQVYLEPGEAVALNAGFLVSTVLDVLENSGNIAVLDTSAACHMPDVLEMPYRPPIAGGGGLGEKAYDYRLGGPTCLAGDVIGDYSFDEPLSPGSRVVFCDMAIYSMVKNNTFNGMNLPAIYLKKQDGSIQLVRKFGYEDFKTRLS
7XZY , Knot 68 139 0.80 38 107 131 
GSHMARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEACEAYLVGLFEDTNLCAIHAKRVTIMPKDIQLARRIRGERA
7SGE , Knot 257 665 0.83 40 293 603 
MGQIVTFFQEVPHVIEEVMNIVLIALSVLAVLKGLYNFATCGLVGLVTFLLLCGRSCTTSLYKGVYELQTLELNMETLNMTMPLSCTKNNSHHYIMVGNETGLELTLTNTSIINHKFCNLSDAHKKNLYDHALMSIISTFHLSIPNFNQYEAMSCDFNGGKISVQYNLSHSYAGDAANHCGTVANGVLQTFMRMAWGGSYIALDSGCGNWDCIMTSYQYLIIQNTTWEDHCQFSRPSPIGYLGLLSQRTRDIYISRRRRGTFTWTLSDSEGKDTPGGYCLTRWMLIEAELKCFGNTAVAKCNEKHDEEFCDMLRLFDFNKQAIQRLKAPAQMSIQLINKAVNALINDQLIMKNHLRDIMCIPYCNYSKYWYLNHTTTGRTSLPKCWLVSNGSYLNETHFSDDIEQQADNMITEMLQKEYMERQGGSGGSGGSGGSGGSEKAAKAEEAARKMEELFKKHKIVAVLRANSVEEAIEKAVAVFAGGVHLIEITFTVPDADTVIKALSVLKEKGAIIGAGTVTSVEQCRKAVESGAEFIVSPHLDEEISQFCKEKGVFYMPGVMTPTELVKAMKLGHDILKLFPGEVVGPEFVKAMKGPFPNVKFVPTGGVDLDNVCEWFDAGVLAVGVGDALVEGDPDEVREKAKEFVEKIRGCTEGSLEWSHPQFEK

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 \(c\).

\(|P_{f(9EAF_1)}(2) \setminus P_{f(7XZY_1)}(2)|=137\), \(|P_{f(7XZY_1)}(2) \setminus P_{f(9EAF_1)}(2)|=31\). 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 1:1011100100100110011100011110011000100111100110111001111001010010111010110001110001101100000100110100011100100100001011101001110101000000011001001100111010010101101101101001000011111001111000111110010110111100100110010111001001000011010101101111011111001101100010111100011001101101100111111111100100001111001110111000100110110011100111001100001011011110100001010110011000100010
Pair \(Z_2\) Length of longest common subsequence
9EAF_1,7XZY_1 168 4
9EAF_1,7SGE_1 176 5
7XZY_1,7SGE_1 230 4

Newick tree

 
[
	7SGE_1:10.83,
	[
		9EAF_1:84,7XZY_1:84
	]:23.83
]

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 \((0.85)(0.8)(\frac{515 }{\log_{20} 515}-\frac{139}{\log_{20}139})=110.\)
Status Protein1 Protein2 d d1/2
Query variables 9EAF_1 7XZY_1 137 92.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]