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Parikh vectors
7WGV_1 2FJM_1 8IDV_1 Letter Amino acid
10 12 7 M Methionine
94 13 7 T Threonine
9 6 3 W Tryptophan
59 23 11 D Aspartic acid
63 14 5 Q Glutamine
79 14 6 G Glycine
16 9 4 H Histidine
99 27 22 L Leucine
90 17 7 V Valine
76 13 3 A Alanine
93 24 10 S Serine
53 10 7 Y Tyrosine
89 10 24 N Asparagine
30 6 2 C Cysteine
47 28 12 E Glutamic acid
71 16 23 I Isoleucine
57 24 19 K Lycine
74 15 11 F Phenylalanine
54 12 1 P Proline
41 17 6 R Arginine 

7WGV_1|Chains A, B, C|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
>2FJM_1|Chains A, B|Tyrosine-protein phosphatase, non-receptor type 1|Homo sapiens (9606)
>8IDV_1|Chains A, B, C, D|Cell filamentation protein Fic|Mycoplasma mycoides subsp. capri (40477)
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 \(w=f(c)\)
7WGV , Knot 429 1204 0.84 40 321 1045 
QCVNLTTRTQLPPAYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLGVYYHKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLVRDLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQDVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEHVNNSYECDIPIGAGICASYQTQTNSRSVASQSIIAYTMSLGAENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLNRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKDFGGFNFSQILPDPSKPSKRSFIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGAALQIPFAMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTASALGKLQDVVNQNAQALNTLVKQLSSNFGAISSVLNDILSRLDKVEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELDSFKEELDKYFKNHTSPDVDLGDISGINASVVNIQKEIDRLNEVAKNLNESLIDLQELGKYEQYIKGSGRENLYFQ
2FJM , Knot 139 310 0.85 40 202 302 
MDYKDDDDKLEFMEMEKEFEQIDKSGSWAAIYQDIRHEASDFPCRVAKLPKNKNRNRYRDVSPFDHSRIKLHQEDNDYINASLIKMEEAQRSYILTQGPLPNTCGHFWEMVWEQKSRGVVMLNRVMEKGSVKCAQYWPQKEEKEMIFEDTNLKLTLISEDIKSYYTVRQLELENLTTQETREILHFHYTTWPDFGVPESPASFLNFLFKVRESGSLSPEHGPVVVHCSAGIGRSGTFCLADTCLLLMDKRKDPSSVDIKKVLLEMRKFRMGLIQTADQLRFSYLAVIEGAKFIMGDSSVQDQWKELSHED
8IDV , Knot 85 190 0.78 40 122 183 
MKANFLEEEFEINLSVKHLLELWDKNLLNTFEIGTFKGLSQIHSYMFKDIFDFNGQIRNVNISKNNSMFCLARYLKQNLEIIDNMKHDTFDQIIDKYVEMNICHPFREGNGRSMRIWLDLILKKQLNVVVNWTNINKDEYLLAMINSLIDSTNLKLLIKNNLTNKITDRNVYIKSIIKSYEYEGFKINIK

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 \(c\).

\(|P_{f(7WGV_1)}(2) \setminus P_{f(2FJM_1)}(2)|=148\), \(|P_{f(2FJM_1)}(2) \setminus P_{f(7WGV_1)}(2)|=29\). 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 1:0010100000111100001001100100110001100000111111001011011010100100010011111001101100000011011111001000000111100100111010010100011111000000001100010100010000100100111101010010100100111001010101000001101100110110110111011111010010011110000101100001101111100110101001110000010100110011011000000100101001100000101010001101101001011101101001101011000010001100011000101001000110100100101001010011101001001111001011000001100101011110000100011100001001100001011000100010011001001101100011100011010011100100111101011011101011000001100001010101101011100000011110011001100001100100101101010011110110110000001111000100001111101001010101000100110001101111001000000011111110100000000001100011100101110001100000111100101010001111010000100010101000000011100101000100110111100000000111010010001110011110100111010010000110011100101101111000100110111001101001011011111100011100001111101001101111111011111011001011110001100000111001001110100010001011101001100010110011001000111100110011001001010101001101010010001000110110101010111001000111000010101010011011001101111101001110000100111100010101100111100100111000010010110000011010001111110001001101010010001000100000101011010110101101000100100110010001101001100000101010001010
Pair \(Z_2\) Length of longest common subsequence
7WGV_1,2FJM_1 177 4
7WGV_1,8IDV_1 225 4
2FJM_1,8IDV_1 186 5

Newick tree

 
[
	8IDV_1:10.66,
	[
		7WGV_1:88.5,2FJM_1:88.5
	]:19.16
]

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 \((0.85)(0.8)(\frac{1514 }{\log_{20} 1514}-\frac{310}{\log_{20}310})=311.\)
Status Protein1 Protein2 d d1/2
Query variables 7WGV_1 2FJM_1 394 247
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]