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Parikh vectors
6ABN_1 1YIT_1 3QMP_1 Letter Amino acid
7 0 14 D Aspartic acid
6 0 2 W Tryptophan
12 754 33 A Alanine
2 0 5 E Glutamic acid
1 0 4 H Histidine
6 0 11 I Isoleucine
6 0 8 K Lycine
2 0 5 M Methionine
3 0 6 F Phenylalanine
10 0 36 S Serine
3 0 7 Q Glutamine
8 736 5 C Cysteine
12 893 33 G Glycine
8 0 14 L Leucine
2 0 9 P Proline
3 0 17 Y Tyrosine
6 0 19 V Valine
11 0 12 R Arginine
7 0 22 T Threonine
14 0 17 N Asparagine 

6ABN_1|Chain A|Lysozyme C|Gallus gallus (9031)
>1YIT_1|Chain A[auth 0]|23S RIBOSOMAL RNA|HALOARCULA MARISMORTUI (2238)
>3QMP_1|Chain A|Proteinase K|Engyodontium album (37998)
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 \(w=f(c)\)
6ABN , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
1YIT , Knot 492 2922 0.44 8 16 64 
GUUGGCUACUAUGCCAGCUGGUGGAUUGCUCGGCUCAGGCGCUGAUGAAGGACGUGCCAAGCUGCGAUAAGCUGUGGGGAGCCGCACGGAGGCGAAGAACCACAGAUUUCCGAAUGAGAAUCUCUCUAACAAUUGCUUCGCGCAAUGAGGAACCCCGAGAACUGAAACAUCUCAGUAUCGGGAGGAACAGAAAACGCAACGUGAUGUCGUUAGUAACCGCGAGUGAACGCGAUACAGCCCAAACCGAAGCCCUCACGGGCAAUGUGGUGUCAGGGCUACCUCUCAUCAGCCGACCGUCUUCACGAAGUCUCUUGGAAUAGAGCGUGAUACAGGGUGACAACCCCGUACUGAAGACCAGUACGCUGUGCGGUAGUGCCAGAGUAGCGGGGGUUGGAUAUCCCUCGCGAAUAACGCAGGCAUCGACUGCGAAGGCUAAACACAACCUGAGACCGAUAGUGAACAAGUAGUGUGAACGAACGCUGCAAAGUACCCUCAGAAGGGAGGCGAAAUAGAGCAUGAAAUCAGUUGGCGAUCGAGCGACAGGGCAUACAAGGUCCCUUGACGAAUGACCGAGACGCGAGUCUCCAGUAAGACUCACGGGAAGCCGAUGUUCUGUCGUACGUUUUGAAAAACGAGCCAGGGAGUGUGUCUGUAUGGCAAGUCUAACCGGAGUAUCCGGGGAGGCACAGGGAAACCGACAUGGCCGCAGGGCUUUGCCCGAGGGCCGCCGUCUUCAAGGGCGGGGAGCCAUGUGGACACGACCCGAAUCCGGACGAUCUACGCAUGGACAAGAUGAAGCGUGCCGAAAGGCACGUGGAAGUCUGUUAGAGUUGGUGUCCUACAAUACCCUCUCGUGAUCUAUGUGUAGGGGUGAAAGGCCCAUCGAGUCCGGCAACAGCUGGUUCCAAUCGAAACAUGUCGAAGCAUGACCUCCGCCGAGGUAGUCUGUGAGGUAGAGCGACCGAUUGGUGUGUCCGCCUCCGAGAGGAGUCGGCACACCUGUCAAACUCCAAACUUACAGACGCUGUUUGACGCGGGGAUUCCGGUGCGCGGGGUAAGCCUGUGUACCAGGAGGGGAACAACCCAGAGAUAGGUUAAGGUCCCCAAGUGUGGAUUAAGUGUAAUCCUCUGAAGGUGGUCUCGAGCCCUAGACAGCCGGGAGGUGAGCUUAGAAGCAGCUACCCUCUAAGAAAAGCGUAACAGCUUACCGGCCGAGGUUUGAGGCGCCCAAAAUGAUCGGGACUCAAAUCCACCACCGAGACCUGUCCGUACCACUCAUACUGGUAAUCGAGUAGAUUGGCGCUCUAAUUGGAUGGAAGCAGGGGCGAGAGCUCCUGUGGACCGAUUAGUGACGAAAAUCCUGGCCAUAGUAGCAGCGAUAGUCGGGUGAGAACCCCGACGGCCUAAUGGAUAAGGGUUCCUCAGCACUGCUGAUCAGCUGAGGGUUAGCCGGUCCUAAGUCUCACCGCAACUCGACUGAGACGAAAUGGGAAACAGGUUAAUAUUCCUGUGCCAUCAUGCAGUGAAAGUUGACGCCCUGGGGUCGAUCACGCCGGGCAUUCGCCCGGUCGAACCGUCCAACUCCGUGGAAGCCGUAAUGGCAGGAAGCGGACGAACGGCGGCAUAGGGAAACGUGAUUCAACCUGGGGCCCAUGAAAAGACGAGCAUGAUGUCCGUACCGAGAACCGACACAGGUGUCCAUGGCGGCGAAAGCCAAGGCCUGUCGGGAGCAACCAACGUUAGGGAAUUCGGCAAGUUAGUCCCGUACCUUCGGAAGAAGGGAUGCCUGCUCCGGAACGGAGCAGGUCGCAGUGACUCGGAAGCUCGGACUGUCUAGUAACAACAUAGGUGACCGCAAAUCCGCAAGGACUCGUACGGUCACUGAAUCCUGCCCAGUGCAGGUAUCUGAACACCUCGUACAAGAGGACGAAGGACCUGUCAACGGCGGGGGUAACUAUGACCCUCUUAAGGUAGCGUAGUACCUUGCCGCAUCAGUAGCGGCUUGCAUGAAUGGAUUAACCAGAGCUUCACUGUCCCAACGUUGGGCCCGGUGAACUGUACAUUCCAGUGCGGAGUCUGGAGACACCCAGGGGGAAGCGAAGACCCUAUGGAGCUUUACUGCAGGCUGUCGCUGAGACGUGGUCGCCGAUGUGCAGCAUAGGUAGGAGUCGUUACAGAGGUACCCGCGCUAGCGGGCCACCCAGACAACAGUGAAAUACUACCCGUCGGUGACUGCGACUCUCACUCCGGGAGGAGGACACCGAUAGCCGGGCAGUUUGACUGGGGCGGUACGCGCUCGAAAAGAUAUCGAGCGCGCCCUAUGGUCAUCUCAGCCGGGACAGAGACCCGGCGAAGAGUGCAAGAGCAAAAGAUGACUUGACAGUGUUCUUCCCAACGAGGAACGCUGACGCGAAAGCGUGGUCUAGCGAACCAAUUAGCCUGCUUGAUGCGGGCAAUUGAUGACAGAAAAGCUACCCUAGGGAUAACAGAGUCGUCACUCGCAAGAGCACAUAUCGACCGAGUGGCUUGCUACCUCGAUGUCGGUUCCCUCCAUCCUGCCCGUGCAGAAGCGGGCAAGGGUGAGGUUGUUCGCCUAUUAAAGGAGGUCGUGAGCUGGGUUUAGACCGUCGUGAGACAGGUCGGCUGCUAUCUACUGGGUGUGUAAUGGUGUCUGACAAGAACGACCGUAUAGUACGAGAGGAACUACGGUUGGUGGCCACUGGUGUACCGGUUGUUCGAGAGAGCACGUGCCGGGUAGCCACGCCACACGGGGUAAGAGCUGAACGCAUCUAAGCUCGAAACCCACUUGGAAAAGAGACACCGCCGAGGUCCCGCGUACAAGACGCGGUCGAUAGACUCGGGGUGUGCGCGUCGAGGUAACGAGACGUUAAGCCCACGAGCACUAACAGACCAAAGCCAUCA
3QMP , Knot 120 279 0.80 40 170 266 
AAQTNAPWGLARISSTSPGTSTYYYDESAGQGSCVYVIDTGIEASHPEFEGRAQMVKTYYYSSRDGNGHGTHCAGTVGSRTYGVAKKTQLFGVKVLDDNGSGQYSTIIAGMDFVASDKNNRNCPKGVVASLSLGGGYSSSVNSAAARLQSSGVMVAVAAGNNNADARNYSPASEPSVCTVGASDRYDRRSSFSNYGSVLDIFGPGTDILSTWIGGSTRSISGTSMATPHVAGLAAYLMTLGKTTAASACRYIADTANKGDLSNIPFGTVNLLAYNNYQA

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 \(c\).

\(|P_{f(6ABN_1)}(2) \setminus P_{f(1YIT_1)}(2)|=101\), \(|P_{f(1YIT_1)}(2) \setminus P_{f(6ABN_1)}(2)|=13\). 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 1:011100011111000110000100110110110100010001000000100001110100011000100110001001100111000101010010011001011011111000001001011101001
Pair \(Z_2\) Length of longest common subsequence
6ABN_1,1YIT_1 114 3
6ABN_1,3QMP_1 146 4
1YIT_1,3QMP_1 174 3

Newick tree

 
[
	3QMP_1:86.69,
	[
		6ABN_1:57,1YIT_1:57
	]:29.69
]

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 \((0.85)(0.8)(\frac{3051 }{\log_{20} 3051}-\frac{129}{\log_{20}129})=720.\)
Status Protein1 Protein2 d d1/2
Query variables 6ABN_1 1YIT_1 491 276.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]