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Parikh vectors
6VWH_1 7OCN_1 8CED_1 Letter Amino acid
17 30 0 H Histidine
58 50 0 I Isoleucine
75 85 0 L Leucine
63 39 0 S Serine
45 51 383 A Alanine
39 9 365 C Cysteine
27 49 0 Q Glutamine
55 34 491 G Glycine
55 30 0 T Threonine
14 3 0 W Tryptophan
17 25 0 M Methionine
30 28 0 F Phenylalanine
50 22 0 P Proline
48 29 0 Y Tyrosine
57 32 0 R Arginine
45 41 0 D Aspartic acid
81 59 0 E Glutamic acid
55 41 0 K Lycine
53 38 0 V Valine
68 32 0 N Asparagine 

6VWH_1|Chains A, B|Leucine-zippered human type 1 insulin-like growth factor receptor ectodomain|Homo sapiens (9606)
>7OCN_1|Chains A, B|HAD hydrolase, family IA, variant 3|Acinetobacter baumannii (strain ATCC 19606 / DSM 30007 / CIP 70.34 / JCM 6841 / NBRC 109757 / NCIMB 12457 / NCTC 12156 / 81) (575584)
>8CED_1|Chain A|16S rRNA|Bacillus subtilis subsp. subtilis str. 168 (224308)
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 \(w=f(c)\)
6VWH , Knot 356 952 0.85 40 327 854 
EICGPGIDIRNDYQQLKRLENCTVIEGYLHILLISKAEDYRSYRFPKLTVITEYLLLFRVAGLESLGDLFPNLTVIRGWKLFYNYALVIFEMTNLKDIGLYNLRNITRGAIRIEKNADLCYLSTVDWSLILDAVSNNYIVGNKPPKECGDLCPGTMEEKPMCEKTTINNEYNYRCWTTNRCQKMCPSTCGKRACTENNECCHPECLGSCSAPDNDTACVACRHYYYAGVCVPACPPNTYRFEGWRCVDRDFCANILSAESSDSEGFVIHDGECMQECPSGFIRNGSQSMYCIPCEGPCPKVCEEEKKTKTIDSVTSAQMLQGCTIFKGNLLINIRRGNNIASELENFMGLIEVVTGYVKIRHSHALVSLSFLKNLRLILGEEQLEGNYSFYVLDNQNLQQLWDWDHRNLTIKAGKMYFAFNPKLCVSEIYRMEEVTGTKGRQSKGDINTRNNGERASCESDVLHFTSTTTSKNRIIITWHRYRPPDYRDLISFTVYYKEAPFKNVTEYDGQDACGSNSWNMVDVDLPPNKDVEPGILLHGLKPWTQYAVYVKAVTLTMVENDHIRGAKSEILYIRTNASVPSIPLDVLSASNSSSQLIVKWNPPSLPNGNLSYYIVRWQRQPQDGYLYRHNYCSKDKIPIRKYADGTIDIEEVTENPKTEVCGGEKGPCCACPKTEAEKQAEKEEAEYRKVFENFLHNSIFVPRPERKRRDVMQVANTTMSSRSRNTTAADTYNITDPEELETEYPFFESRVDNKERTVISNLRPFTLYRIDIHSCNHEAEKLGCSASNFVFARTMPAEGADDIPGPVTWEPRPENSIFLKWPEPENPNGLILMYEIKYGSQVEDQRECVSRQEYRKYGGAKLNRLNPGNYTARIQATSLSGNGSWTDPVFFYVQAKTGYENFIHRMKQLEDKVEELLSKNYHLENEVARLKKLVGERSSSEQKLISEEDLN
7OCN , Knot 279 727 0.84 40 294 671 
MVLIFHGKPVHGAIFDMDGTMFDTERLRFQTLQQASQELIGQEFSHEYLMQCLGLSATTAEKLAQRLYGVDVPYKEIRKRADEMELEHIRKHGVPIKKGLVQVLERLRKSGLRMAVATSSRRAIAEEYLINANVYKFFDVITCGDEVEQGKPHPEIFLKAASQLHLDANQCLMFEDSENGLTSAHTSKGLTILLKDIKEPNDEMLEKAHFYYDQMYDFLTDLDQFIPVMDMPEMQEPFPQSLNQLTVGIHGFGAIGGGYIAQILSHWDGYTKPKRIIASTRNSLFREAVNAFGTYSIRYGQFSYDERIENMSIVDSDNEQQMLEMYTHSSLIALCLPEQAIESESKIIAKGLYARFNSQLETCIEPLTFLIILNKVGAKYLVMKHLKEALLELTNDEDVTEHILKEHYFCDTVVNRMVSKLSNQNLYRQLRIKHNFLEQHLEDVEQEDQIEIEDCNKLTPDQLNQASIYVDNMRRNFQPGHILQSMDLILFHSETDMPIYVEKGSPLLEKLRQVVLVDQITDIQLIKNRLWNGVHAMLAWYASLMGYESIGVAMGDHLVKAFAENLIAEVKQGLAIVLPNYAKDLDRMSQSFLDSCEYAFKDPCQRVARDPLRKLNHNERVMASIAVNIRHDLPYKNLLKGAALGYAYAIQFLEIEETKAVEHLQQQIQNLDLSTAQRRQLEAELVQLIQYLFSEQGKQPLDIKSNNTKTTSTQYVAAALEHHHHHH
8CED , Knot 288 1554 0.45 8 16 64 
UUUAUCGGAGAGUUUGAUCCUGGCUCAGGACGAACGCUGGCGGCGUGCCUAAUACAUGCAAGUCGAGCGGACAGAUGGGAGCUUGCUCCCUGAUGUUAGCGGCGGACGGGUGAGUAACACGUGGGUAACCUGCCUGUAAGACUGGGAUAACUCCGGGAAACCGGGGCUAAUACCGGAUGGUUGUUUGAACCGCAUGGUUCAAACAUAAAAGGUGGCUUCGGCUACCACUUACAGAUGGACCCGCGGCGCAUUAGCUAGUUGGUGAGGUAACGGCUCACCAAGGCGACGAUGCGUAGCCGACCUGAGAGGGUGAUCGGCCACACUGGGACUGAGACACGGCCCAGACUCCUACGGGAGGCAGCAGUAGGGAAUCUUCCGCAAUGGACGAAAGUCUGACGGAGCAACGCCGCGUGAGUGAUGAAGGUUUUCGGAUCGUAAAGCUCUGUUGUUAGGGAAGAACAAGUGCCGUUCGAAUAGGGCGGUACCUUGACGGUACCUAACCAGAAAGCCACGGCUAACUACGUGCCAGCAGCCGCGGUAAUACGUAGGUGGCAAGCGUUGUCCGGAAUUAUUGGGCGUAAAGGGCUCGCAGGCGGUUUCUUAAGUCUGAUGUGAAAGCCCCCGGCUCAACCGGGGAGGGUCAUUGGAAACUGGGGAACUUGAGUGCAGAAGAGGAGAGUGGAAUUCCACGUGUAGCGGUGAAAUGCGUAGAGAUGUGGAGGAACACCAGUGGCGAAGGCGACUCUCUGGUCUGUAACUGACGCUGAGGAGCGAAAGCGUGGGGAGCGAACAGGAUUAGAUACCCUGGUAGUCCACGCCGUAAACGAUGAGUGCUAAGUGUUAGGGGGUUUCCGCCCCUUAGUGCUGCAGCUAACGCAUUAAGCACUCCGCCUGGGGAGUACGGUCGCAAGACUGAAACUCAAAGGAAUUGACGGGGGCCCGCACAAGCGGUGGAGCAUGUGGUUUAAUUCGAAGCAACGCGAAGAACCUUACCAGGUCUUGACAUCCUCUGACAAUCCUAGAGAUAGGACGUCCCCUUCGGGGGCAGAGUGACAGGUGGUGCAUGGUUGUCGUCAGCUCGUGUCGUGAGAUGUUGGGUUAAGUCCCGCAACGAGCGCAACCCUUGAUCUUAGUUGCCAGCAUUCAGUUGGGCACUCUAAGGUGACUGCCGGUGACAAACCGGAGGAAGGUGGGGAUGACGUCAAAUCAUCAUGCCCCUUAUGACCUGGGCUACACACGUGCUACAAUGGACAGAACAAAGGGCAGCGAAACCGCGAGGUUAAGCCAAUCCCACAAAUCUGUUCUCAGUUCGGAUCGCAGUCUGCAACUCGACUGCGUGAAGCUGGAAUCGCUAGUAAUCGCGGAUCAGCAUGCCGCGGUGAAUACGUUCCCGGGCCUUGUACACACCGCCCGUCACACCACGAGAGUUUGUAACACCCGAAGUCGGUGAGGUAACCUUUUAGGAGCCAGCCGCCGAAGGUGGGACAGAUGAUUGGGGUGAAGUCGUAACAAGGUAGCCGUAUCGGAAGGUGCGGCUGGAUCACCUCCUUUCUA

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 \(c\).

\(|P_{f(6VWH_1)}(2) \setminus P_{f(7OCN_1)}(2)|=73\), \(|P_{f(7OCN_1)}(2) \setminus P_{f(6VWH_1)}(2)|=40\). 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 1:0101111010000001001000011010101111001000000011010110001111011110011011101011011011000111110100100111001001001110100010100100101011101100001110011000101011010001100000100000000100000001010001001000000000100110001100001011000000111011101100001011001000101011010000001111001001000101110010001001100110101000000000100100101101001101011101001001100100111110110101010000111010110010111100010100010110000100110100001010110101110101010010010010100100001010000010010000011010000000001110100001100001101010000111001000010010100010110101110001011111011011000110101101011000010110001101000101101110110100000011101011011010100011010001001010000000000111000101010100100010001011001100101000100010000100001100110001111010000001101100010000000011000010010010000111000100000011001011010010100000010011001001111001110110011111010101000111011010010111110010010010000001000000001110100101100010101001010101001111010100100011001001000100110000010001101001110000000011000010
Pair \(Z_2\) Length of longest common subsequence
6VWH_1,7OCN_1 113 4
6VWH_1,8CED_1 325 4
7OCN_1,8CED_1 302 3

Newick tree

 
[
	8CED_1:17.15,
	[
		6VWH_1:56.5,7OCN_1:56.5
	]:12.65
]

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 \((0.85)(0.8)(\frac{1679 }{\log_{20} 1679}-\frac{727}{\log_{20}727})=235.\)
Status Protein1 Protein2 d d1/2
Query variables 6VWH_1 7OCN_1 307 268.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]