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Parikh vectors
5PMI_1 2KBD_1 8JKD_1 Letter Amino acid
25 2 24 A Alanine
26 0 43 E Glutamic acid
18 0 27 H Histidine
19 0 16 F Phenylalanine
19 0 14 Y Tyrosine
18 0 20 R Arginine
20 0 21 N Asparagine
27 6 44 G Glycine
23 0 41 K Lycine
20 4 46 T Threonine
8 0 12 W Tryptophan
14 0 28 D Aspartic acid
15 0 16 Q Glutamine
24 0 48 L Leucine
18 0 25 P Proline
18 0 55 S Serine
7 4 26 C Cysteine
20 0 37 I Isoleucine
11 0 12 M Methionine
14 0 36 V Valine 

5PMI_1|Chain A|Lysine-specific demethylase 4D|Homo sapiens (9606)
>2KBD_1|Chain A|DNA (5'-D(*CP*TP*GP*GP*GP*GP*AP*CP*TP*TP*TP*CP*CP*AP*GP*G)-3')|
>8JKD_1|Chains A, B, C|Glycoprotein C|Crimean-Congo hemorrhagic fever virus strain IbAr10200 (652961)
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 \(w=f(c)\)
5PMI , Knot 160 364 0.86 40 229 347 
MHHHHHHSSGVDLGTENLYFQSMETMKSKANCAQNPNCNIMIFHPTKEEFNDFDKYIAYMESQGAHRAGLAKIIPPKEWKARETYDNISEILIATPLQQVASGRAGVFTQYHKKKKAMTVGEYRHLANSKKYQTPPHQNFEDLERKYWKNRIYNSPIYGADISGSLFDENTKQWNLGHLGTIQDLLEKECGVVIEGVNTPYLYFGMWKTTFAWHTEDMDLYSINYLHLGEPKTWYVVPPEHGQRLERLARELFPGSSRGCGAFLRHKVALISPTVLKENGIPFNRITQEAGEFMVTFPYGYHAGFNHGFNCAEAINFATPRWIDYGKMASQCSCGEARVTFSMDAFVRILQPERYDLWKRGQDR
2KBD , Knot 8 16 0.46 8 10 13 
CTGGGGACTTTCCAGG
8JKD , Knot 238 591 0.85 40 285 550 
MKNLLNSTSLETSLSIEAPWGAINVQSTYKPTVSTANIALSWSSVEHRGNKILVSGRSESIMKLEERTGISWDLGVEDASESKLLTVSVMDLSQMYSPVFEYLSGDRQVGEWPKATCTGDCPERCGCTSSTCLHKEWPHSRNWRCNPTWCWGVGTGCTCCGLDVKDLFTDYMFVKWKVEYIKTEAIVCVELTSQERQCSLIEAGTRFNLGPVTITLSEPRNIQQKLPPEIITLHPRIEEGFFDLMHVQKVLSASTVCKLQSCTHGVPGDLQVYHIGNLLKGDKVNGHLIHKIEPHFNTSWMSWDGCDLDYYCNMGDWPSCTYTGVTQHNHASFVNLLNIETDYTKNFHFHSKRVTAHGDTPQLDLKARPTYGAGEITVLVEVADMELHTKKIEISGLKFASLACTGCYACSSGISCKVRIHVDEPDELTVHVKSDDPDVVAASSSLMARKLEFGTDSTFKAFSAMPKTSLCFYIVEREHCKSCSEEDTKKCVNTKLEQPQSILIEHKGTIIGKQNSTCTAKSRGSGGMKQIEDKIEEILSKIYHIENEIARIKKLIGEGSGGSRGPFEGKPIPNPLLGLDSTRTGHHHHHH

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 \(c\).

\(|P_{f(5PMI_1)}(2) \setminus P_{f(2KBD_1)}(2)|=225\), \(|P_{f(2KBD_1)}(2) \setminus P_{f(5PMI_1)}(2)|=6\). 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 1:1000000001101100010100100100010010010001111010000100100011010001100111101111001010000001001111011001101011110000000011011000011000000011000100100001000100011011010101100000010110110100110000111101100101011110001110000101001001011010010111100100100110011110001011110001111010110001111001000110111011010011100110010110110101100101100000101010101011101101000011001000
Pair \(Z_2\) Length of longest common subsequence
5PMI_1,2KBD_1 231 2
5PMI_1,8JKD_1 174 6
2KBD_1,8JKD_1 279 3

Newick tree

 
[
	2KBD_1:13.08,
	[
		5PMI_1:87,8JKD_1:87
	]:52.08
]

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 \((0.85)(0.8)(\frac{380 }{\log_{20} 380}-\frac{16}{\log_{20}16})=118.\)
Status Protein1 Protein2 d d1/2
Query variables 5PMI_1 2KBD_1 157 81.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]