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Parikh vectors
5YEW_1 6WYV_1 9FRA_1 Letter Amino acid
17 0 0 T Threonine
32 0 0 V Valine
17 0 0 R Arginine
22 0 4 N Asparagine
20 912 524 G Glycine
33 762 320 A Alanine
39 0 0 E Glutamic acid
42 0 0 L Leucine
34 0 0 K Lycine
11 0 0 M Methionine
33 0 0 S Serine
4 0 0 W Tryptophan
24 0 0 D Aspartic acid
6 639 416 C Cysteine
20 0 0 I Isoleucine
23 0 0 F Phenylalanine
11 0 0 P Proline
4 0 0 Y Tyrosine
17 0 0 Q Glutamine
12 0 0 H Histidine 

5YEW_1|Chain A|Mitofusin-1,Mitofusin-1 fusion protein|Homo sapiens (9606)
>6WYV_1|Chain A[auth I]|23S ribosomal RNA|Escherichia coli (562)
>9FRA_1|Chain A[auth 2]|rRNA 16S|Saccharolobus solfataricus P2 (273057)
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 \(w=f(c)\)
5YEW , Knot 175 421 0.83 40 217 395 
MAEPVSPLKHFVLAKKAITAIFDQLLEFVTEGSHFVEATYKNPELDRIATEDDLVEMQGYKDKLSIIGEVLSRRHMKVAFFGRTSSGKSSVINAMLWDKVLPSGIGHITNCFLSVEGTDGDKAYLMTEGSDEKKSVKVNNQLAHALHMDKDLKAGCLVRVFWPKAKCALLRDDLVLVDSPGTDVTTELDSWIDKFCLDADVFVLVANSESTLMNTEKHFFHKVNERLSKPNIFILNNRWDASASEPEYMEDVRRQHMERCLHFLVEELKVVNALEAQNRIFFVSAKEVLSARKQKAQGMPESGVALAEGFHARLQEFQNFEQIFEECISQSAVKTKFEQHTIRAKQILATVKNIMDSVNLAAEDGSGSGSGGSEIARLPKEIDQLEKIQNNSKLLRNKAVQLENELENFTKQFLPSSNEES
6WYV , Knot 489 2904 0.44 10 18 67 
GGUUAAGCGACUAAGCGUACACGGUGGAUGCCCUGGCAGUCAGAGGCGAUGAAGGACGUGCUAAUCUGCGAUAAGCGUCGGUAAGGUGAUAUGAACCGUUAUAACCGGCGAUUUCCGAAUGGGGAAACCCAGUGUGUUUCGACACACUAUCAUUAACUGAAUCCAUAGGUUAAUGAGGCGAACCGGGGGAACUGAAACAUCUAAGUACCCCGAGGAAAAGAAAUCAACCGAGAUUCCCCCAGUAGCGGCGAGCGAACGGGGAGCAGCCCAGAGCCUGAAUCAGUGUGUGUGUUAGUGGAAGCGUCUGGAAAGGCGCGCGAUACAGGGUGACAGCCCCGUACACAAAAAUGCACAUGCUGUGAGCUCGAUGAGUAGGGCGGGACACGUGGUAUCCUGUCUGAAUAUGGGGGGACCAUCCUCCAAGGCUAAAUACUCCUGACUGACCGAUAGUGAACCAGUACCGUGAGGGAAAGGCGAAAAGAACCCCGGCGAGGGGAGUGAAAAAGAACCUGAAACCGUGUACGUACAAGCAGUGGGAGCACGCUUAGGCGUGUGACUGCGUACCUUUUGUAUAAUGGGUCAGCGACUUAUAUUCUGUAGCAAGGUUAACCGAAUAGGGGAGCCGAAGGGAAACCGAGUCUUAACUGGGCGUUAAGUUGCAGGGUAUAGACCCGAAACCCGGUGAUCUAGCCAUGGGCAGGUUGAAGGUUGGGUAACACUAACUGGAGGACCGAACCGACUAAUGUUGAAAAAUUAGCGGAUGACUUGUGGCUGGGGGUGAAAGGCCAAUCAAACCGGGAGAUAGCUGGUUCUCCCCGAAAGCUAUUUAGGUAGCGCCUCGUGAAUUCAUCUCCGGGGGUAGAGCACUGUUUCGGCAAGGGGGUCAUCCCGACUUACCAACCCGAUGCAAACUGCGAAUACCGGAGAAUGUUAUCACGGGAGACACACGGCGGGUGCUAACGUCCGUCGUGAAGAGGGAAACAACCCAGACCGCCAGCUAAGGUCCCAAAGUCAUGGUUAAGUGGGAAACGAUGUGGGAAGGCCCAGACAGCCAGGAUGUUGGCUUAGAAGCAGCCAUCAUUUAAAGAAAGCGUAAUAGCUCACUGGUCGAGUCGGCCUGCGCGGAAGAUGUAACGGGGCUAAACCAUGCACCGAAGCUGCGGCAGCGACGCUUAUGCGUUGUUGGGUAGGGGAGCGUUCUGUAAGCCUGCGAAGGUGUGCUGUGAGGCAUGCUGGAGGUAUCAGAAGUGCGAAUGCUGACAUAAGUAACGAUAAAGCGGGUGAAAAGCCCGCUCGCCGGAAGACCAAGGGUUCCUGUCCAACGUUAAUCGGGGCAGGGUGAGUCGACCCCUAAGGCGAGGCCGAAAGGCGUAGUCGAUGGGAAACAGGUUAAUAUUCCUGUACUUGGUGUUACUGCGAAGGGGGGACGGAGAAGGCUAUGUUGGCCGGGCGACGGUUGUCCCGGUUUAAGCGUGUAGGCUGGUUUUCCAGGCAAAUCCGGAAAAUCAAGGCUGAGGCGUGAUGACGAGGCACUACGGUGCUGAAGCAACAAAUGCCCUGCUUCCAGGAAAAGCCUCUAAGCAUCAGGUAACAUCAAAUCGUACCCCAAACCGACACAGGUGGUCAGGUAGAGAAUACCAAGGCGCUUGAGAGAACUCGGGUGAAGGAACUAGGCAAAAUGGUGCCGUAACUUCGGGAGAAGGCACGCUGAUAUGUAGGUGAGGUCCCUCGCGGAUGGAGCUGAAAUCAGUCGAAGAUACCAGCUGGCUGCAACUGUUUAUUAAAAACACAGCACUGUGCAAACACGAAAGUGGACGUAUACGGUGUGACGCCUGCCCGGUGCCGGAAGGUUAAUUGAUGGGGUUAGCGCAAGCGAAGCUCUUGAUCGAAGCCCCGGUAAACGGCGGCCGUAACXAUAACGGUCCUAAGGUAGCGAAAUUCCUUGUCGGGUAAGUUCCGACCUGCACGAAUGGCGUAAUGAUGGCCAGGCUGUCUCCACCCGAGACUCAGUGAAAUUGAACUCGCUGUGAAGAUGCAGUGUACCCGCGGCAAGACGGAAAGACCCCGUGAACCUUUACUAUAGCUUGACACUGAACAUUGAGCCUUGAUGUGUAGGAUAGGUGGGAGGCUUUGAAGUGUGGACGCCAGUCUGCAUGGAGCCGACCUUGAAAUACCACCCUUUAAUGUUUGAUGUUCUAACGUUGACCCGUAAUCCGGGUUGCGGACAGUGUCUGGUGGGUAGUUUGACUGGGGCGGUCUCCUCCUAAAGAGUAACGGAGGAGCACGAAGGUUGGCUAAUCCUGGUCGGACAUCAGGAGGUUAGUGCAAUGGCAUAAGCCAGCUUGACUGCGAGCGUGACGGCGCGAGCAGGUGCGAAAGCAGGUCAUAGUGAUCCGGUGGUUCUGAAUGGAAGGGCCAUCGCUCAACGGAUAAAAGGUACUCCGGGGAUAACAGGCUGAUACCGCCCAAGAGUUCAUAUCGACGGCGGUGUUUGGCACCUCGAUGUCGGCUCAUCACAUCCUGGGGCUGAAGUAGGUCCCAAGGGUAUGGCUGUUCGCCAUUUAAAGUGGUACGCGAGCUGGGUUUAGAACGUCGUGAGACAGUUCGGUCCCUAUCUGCCGUGGGCGCUGGAGAACUGAGGGGGGCUGCUCCUAGUACGAGAGGACCGGAGUGGACGCAUCACUGGUGUUCGGGUUGUCAUGCCAAUGGCACUGCCCGGUAGCUAAAUGCGGAAGAGAUAAGUGCUGAAAGCAUCUAAGCACGAAACUUGCCCCGAGAUGAGUUCUCCCUGACCCUUUAAGGGUCCUGAAGGAACGUUGAAGACGACGACGUUGAUAGGCCGGGUGUGUAAGCGCAGCGAUGCGUUGAGCUAACCGGUACUAAUGAACCGUGAGGCUUAACCUU
9FRA , Knot 268 1497 0.43 12 23 75 
AAAUCCGGUUGAUCCUGCCGGACCCGACCGCUAUCGGGGUGGGGCUAAGCCAUGGGAGUCGUACGCUCCCGGGCAAGGGAGCGUGGCGGACGGCUGAGUAACACGUGGCUAACCUACCCUGAGGAGGGAGAUAACCCCGGGAAACUGGGGAUAAUCUCCCAUAGGCGAGGAGUCCUGGAACGGUUCCUCGCUGAAAGGCUCAUGGGCUAUUCCCCGCUCAUGAGCGCCUCAGGAUGGGGCUGCGGCCCAUCAGGUAGUUGGGGGGGUAAGGGCCCCCCAAGCCUAUAACGGGUAGGGGCCGUGAGAGCGGGAGCCCCCAGUUGGGCACUGAGACAAGGGCCCAGGCCCUACGGGGCGCACCAGGCGCGAAACGUCCCCAAUGCGCGGAAGCGUGAGGGCGCCACCCCGAGUGCUCCCGUAAGGGAGCUUUUCCCCGCUCUACAAAGGCGGGGGAAUAAGCGGGGGGCAAGUCUGGUGUCAGCCGCCGCGGUAAUACCAGCCCCGCGAGUGGUCGGGACUCUUACUGGGCCUAAAGCGCCCGUAGCCGGCCCGACAAGUCACUCCUUAAAGACCCCGGCUCAACCGGGGGAAUGGGGGUGAUACUGUCGGGCUAGGGGGCGGGAGAGGCCAGCGGUACUCCCGGAGUAGGGGCGAAAUCCUCAGAUCUCGGGAGGACCACCAGUGGCGAAAGCGGCUGGCUAGAACGCGCCCGACGGUGAGGGGCGAAAGCCGGGGCAGCAAAAGGGAUUAGAUACCCCUGUAGUCCCGGCUGUAAACAAUGCAGGCUAGGUGUCACAUGGGCUUAGAGCCCAUGUGGUGCCGCAGGGAAGCCGUUAAGCCUGCCGCCUGGGGAGUACGGUCGCAAGACUGAAACUUAAAGGAAUUGGCGGGGGAGCACCACAAGGGGUGGAACCUGCGGCUCAAUUGGAGXCAACGCCUGGAAUCUUACUAGGGGAGACCGCAGGAUGACGGCCAGGCUAACGACCUUGCCUGACUCGCGGAGAGGAGGUGCAUGGCCGUCGCCAGCUCGUGUUGUGAAAUGUCCUGUUAAGUCAGGCAACGAGCGAGACCCCCACCACUAGUUGGUAUCCUGGUCUCCGGGCCGGGACCACACUAGUGGGACUGCCGGCGUAAGCCGGAGGAGGGAGGGGGCCACGGCAGGUCAGCAUGCCCCGAAACCCCUGGGCCGCACGCGGGUUACAAUGGCAGGGACAGCGGGAUUCCGACCCCGAAAGGGGAAGGUAAUCCCUUAAACCCUGCCGCAGUUGGGAUCGAGGGCUGAAACUCGCCCUCGUGAACGAGGAAUCCCUAGUAACCGCAGAUCAACAAUCUGCGGUGAAUACGUCCCUGCUCCUUGCACACACCGCCCGUCGCUCCACCCGAGUAGGAGAGGGGUGAGGCCCCUUGCCUUUGGGUGGGGGGUCGAGCUUCUCUCCUGCAAGGGGGGAGAAGUCGUAACAAGGUAGNNGUAGGGGAANNUGCGGCUGGAUCACCUCC

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 \(c\).

\(|P_{f(5YEW_1)}(2) \setminus P_{f(6WYV_1)}(2)|=212\), \(|P_{f(6WYV_1)}(2) \setminus P_{f(5YEW_1)}(2)|=13\). 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 1:1101101100111100110111001101100100110100001010011000011010100001011101100001011111000010001101111001110111010001101010010010110010000001010001101101000101101101111010011100011110011001000100110010101011111100000110000011001000100101111000101010010010010000100010111001011011010001111010011010000101110011111011010100100100110001000110001000010100111010011001011100101010110011011001001001000001100011010001001000111000000
Pair \(Z_2\) Length of longest common subsequence
5YEW_1,6WYV_1 225 3
5YEW_1,9FRA_1 226 3
6WYV_1,9FRA_1 9 11

Newick tree

 
[
	5YEW_1:13.16,
	[
		6WYV_1:4.5,9FRA_1:4.5
	]:12.66
]

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 \((0.85)(0.8)(\frac{3325 }{\log_{20} 3325}-\frac{421}{\log_{20}421})=693.\)
Status Protein1 Protein2 d d1/2
Query variables 5YEW_1 6WYV_1 485 328
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]