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Parikh vectors
6WTW_1 5PSM_1 7BHP_1 Letter Amino acid
51 11 797 A Alanine
2 1 1696 C Cysteine
30 7 0 S Serine
31 5 0 T Threonine
15 5 0 Y Tyrosine
7 10 0 H Histidine
27 6 0 K Lycine
22 6 0 P Proline
23 7 0 M Methionine
5 14 0 R Arginine
16 4 0 N Asparagine
8 13 0 D Aspartic acid
9 8 0 Q Glutamine
48 5 0 I Isoleucine
54 18 0 L Leucine
13 13 0 E Glutamic acid
43 7 1824 G Glycine
26 6 0 F Phenylalanine
19 0 0 W Tryptophan
42 10 0 V Valine 

6WTW_1|Chains A, B|DASS family sodium-coupled anion symporter|Lactobacillus acidophilus (1579)
>5PSM_1|Chains A, B|Bromodomain-containing protein 1|Homo sapiens (9606)
>7BHP_1|Chain A[auth L5]|28S ribosomal RNA|Homo sapiens (9606)
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 \(w=f(c)\)
6WTW , Knot 195 491 0.82 40 221 449 
SNAMKTLEKVNYKGFIWPLAVGIVLWLITPWRPGGLSVQAWEMFAIFVATIVGCITKPLPIGGTTLLGMVVTVLVGLAPVKDVVNSKGVVIQTGILSSFGNSAAWLIAMAFIMAHGISKTGLGNRVAYVMIEKFGKRSIGIGYAITGLELMMGALIPSNSARTGGVTWPVVESISKSYDSKPNDPSRKKIGAYLDFMAFHANILSTALFITGAAPNLVAQQMAAQKGYQMSWVSWFWAALVPVLVATVIIPLVIYKMYPPEVKETPNAKNWADDKLKEMGPISKPEKIMATVFCLAILLWVLSGFFKIPQLDSAFVAFLAVTLLLITGVLSMEDALHETGAWNILIWLSILIFMAGKLISYGFIAWFAKFIQSEVHGINWGLVLVVLILLMFYTHYFFASGTAHMTALYLPFLTVATAMGAPLGLSAMLLAFTGVINASTTHYANGPASILATTGYVKQSEWWKMNFILGLIYMVIFGIVGTIWMKIIGIW
5PSM , Knot 74 156 0.79 38 120 151 
MHHHHHHSSGVDLGTENLYFQSMEQVAMELRLTELTRLLRSVLDQLQDKDPARIFAQPVSLKEVPDYLDHIKHPMDFATMRKRLEAQGYKNLHEFEEDFDLIIDNCMKYNARDTVFYRAAVRLRDQGGVVLRQARREVDSIGLEEASGMHLPERPA
7BHP , Knot 747 5070 0.41 8 16 64 
CGCGACCUCAGAUCAGACGUGGCGACCCGCUGAAUUUAAGCAUAUUAGUCAGCGGAGGAGAAGAAACUAACCAGGAUUCCCUCAGUAACGGCGAGUGAACAGGGAAGAGCCCAGCGCCGAAUCCCCGCCCCGCGGCGGGGCGCGGGACAUGUGGCGUACGGAAGACCCGCUCCCCGGCGCCGCUCGUGGGGGGCCCAAGUCCUUCUGAUCGAGGCCCAGCCCGUGGACGGUGUGAGGCCGGUAGCGGCCCCCGGCGCGCCGGGCCCGGGUCUUCCCGGAGUCGGGUUGCUUGGGAAUGCAGCCCAAAGCGGGUGGUAAACUCCAUCUAAGGCUAAAUACCGGCACGAGACCGAUAGUCAACAAGUACCGUAAGGGAAAGUUGAAAAGAACUUUGAAGAGAGAGUUCAAGAGGGCGUGAAACCGUUAAGAGGUAAACGGGUGGGGUCCGCGCAGUCCGCCCGGAGGAUUCAACCCGGCGGCGGGUCCGGCCGUGUCGGCGGCCCGGCGGAUCUUUCCCGCCCCCCGUUCCUCCCGACCCCUCCACCCGCCCUCCCUUCCCCCGCCGCCCCUCCUCCUCCUCCCCGGAGGGGGCGGGCUCCGGCGGGUGCGGGGGUGGGCGGGCGGGGCCGGGGGUGGGGUCGGCGGGGGACCGUCCCCCGACCGGCGACCGGCCGCCGCCGGGCGCAUUUCCACCGCGGCGGUGCGCCGCGACCGGCUCCGGGACGGCUGGGAAGGCCCGGCGGGGAAGGUGGCUCGGGGGGCCCCGUCCGUCCGUCCGUCCGUCCUCCUCCUCCCCCGUCUCCGCCCCCCGGCCCCGCGUCCUCCCUCGGGAGGGCGCGCGGGUCGGGGCGGCGGCGGCGGCGGCGGUGGCGGCGGCGGCGGCGGCGGCGGGACCGAAACCCCCCCCGAGUGUUACAGCCCCCCCGGCAGCAGCACUCGCCGAAUCCCGGGGCCGAGGGAGCGAGACCCGUCGCCGCGCUCUCCCCCCUCCCGGCGCCCACCCCCGCGGGGAAUCCCCCGCGAGGGGGGUCUCCCCCGCGGGGGCGCGCCGGCGUCUCCUCGUGGGGGGGCCGGGCCACCCCUCCCACGGCGCGACCGCUCUCCCACCCCUCCUCCCCGCGCCCCCGCCCCGGCGACGGGGGGGGUGCCGCGCGCGGGUCGGGGGGCGGGGCGGACUGUCCCCAGUGCGCCCCGGGCGGGUCGCGCCGUCGGGCCCGGGGGAGGUUCUCUCGGGGCCACGCGCGCGUCCCCCGAAGAGGGGGACGGCGGAGCGAGCGCACGGGGUCGGCGGCGACGUCGGCUACCCACCCGACCCGUCUUGAAACACGGACCAAGGAGUCUAACACGUGCGCGAGUCGGGGGCUCGCACGAAAGCCGCCGUGGCGCAAUGAAGGUGAAGGCCGGCGCGCUCGCCGGCCGAGGUGGGAUCCCGAGGCCUCUCCAGUCCGCCGAGGGCGCACCACCGGCCCGUCUCGCCCGCCGCGCCGGGGAGGUGGAGCACGAGCGCACGUGUUAGGACCCGAAAGAUGGUGAACUAUGCCUGGGCAGGGCGAAGCCAGAGGAAACUCUGGUGGAGGUCCGUAGCGGUCCUGACGUGCAAAUCGGUCGUCCGACCUGGGUAUAGGGGCGAAAGACUAAUCGAACCAUCUAGUAGCUGGUUCCCUCCGAAGUUUCCCUCAGGAUAGCUGGCGCUCUCGCAGACCCGACGCACCCCCGCCACGCAGUUUUAUCCGGUAAAGCGAAUGAUUAGAGGUCUUGGGGCCGAAACGAUCUCAACCUAUUCUCAAACUUUAAAUGGGUAAGAAGCCCGGCUCGCUGGCGUGGAGCCGGGCGUGGAAUGCGAGUGCCUAGUGGGCCACUUUUGGUAAGCAGAACUGGCGCUGCGGGAUGAACCGAACGCCGGGUUAAGGCGCCCGAUGCCGACGCUCAUCAGACCCCAGAAAAGGUGUUGGUUGAUAUAGACAGCAGGACGGUGGCCAUGGAAGUCGGAAUCCGCUAAGGAGUGUGUAACAACUCACCUGCCGAAUCAACUAGCCCUGAAAAUGGAUGGCGCUGGAGCGUCGGGCCCAUACCCGGCCGUCGCCGGCAGUCGAGAGUGGACGGGAGCGGCGGCGGCGGCGCGCGCGCGCGCGCGUGUGGUGUGCGUCGGAGGGCGGCGGCGGCGGCGGCGGCGGGGGUGUGGGGUCCUUCCCCCGCCCCCCCCCCCACGCCUCCUCCCCUCCUCCCGCCCACGCCCCGCUCCCCGCCCCCGGAGCCCCGCGGACGCUACGCCGCGACGAGUAGGAGGGCCGCUGCGGUGAGCCUUGAAGCCUAGGGCGCGGGCCCGGGUGGAGCCGCCGCAGGUGCAGAUCUUGGUGGUAGUAGCAAAUAUUCAAACGAGAACUUUGAAGGCCGAAGUGGAGAAGGGUUCCAUGUGAACAGCAGUUGAACAUGGGUCAGUCGGUCCUGAGAGAUGGGCGAGCGCCGUUCCGAAGGGACGGGCGAUGGCCUCCGUUGCCCUCGGCCGAUCGAAAGGGAGUCGGGUUCAGAUCCCCGAAUCCGGAGUGGCGGAGAUGGGCGCCGCGAGGCGUCCAGUGCGGUAACGCGACCGAUCCCGGAGAAGCCGGCGGGAGCCCCGGGGAGAGUUCUCUUUUCUUUGUGAAGGGCAGGGCGCCCUGGAAUGGGUUCGCCCCGAGAGAGGGGCCCGUGCCUUGGAAAGCGUCGCGGUUCCGGCGGCGUCCGGUGAGCUCUCGCUGGCCCUUGAAAAUCCGGGGGAGAGGGUGUAAAUCUCGCGCCGGGCCGUACCCAUAUCCGCAGCAGGUCUCCAAGGUGAACAGCCUCUGGCAUGUUGGAACAAUGUAGGUAAGGGAAGUCGGCAAGCCGGAUCCGUAACUUCGGGAUAAGGAUUGGCUCUAAGGGCUGGGUCGGUCGGGCUGGGGCGCGAAGCGGGGCUGGGCGCGCGCCGCGGCUGGACGAGGCGCCGCCGCCCCCCCCACGCCCGGGGCACCCCCCUCGCGGCCCUCCCCCGCCCCACCCCGCGCGCGCCGCUCGCUCCCUCCCCGCCCCGCGCCCUCUCUCUCUCUCUCUCCCCCGCUCCCCGUCCUCCCCCCUCCCCGGGGGAGCGCCGCGUGGGGGCGGCGGCGGGGGGAGAAGGGUCGGGGCGGCAGGGGCCGGCGGCGGCCCGCCGCGGGGCCCCGGCGGCGGGGGCACGGUCCCCCGCGAGGGGGGCCCGGGCACCCGGGGGGCCGGCGGCGGCGGCGACUCUGGACGCGAGCCGGGCCCUUCCCGUGGAUCGCCCCAGCUGCGGCGGGCGUCGCGGCCGCCCCCGGGGAGCCCGGCGGGCGCCGGCGCGCCCCCCCCCCCACCCCACGUCUCGUCGCGCGCGCGUCCGCUGGGGGCGGGGAGCGGUCGGGCGGCGGCGGUCGGCGGGCGGCGGGGCGGGGCGGUUCGUCCCCCCGCCCUACCCCCCCGGCCCCGUCCGCCCCCCGUUCCCCCCUCCUCCUCGGCGCGCGGCGGCGGCGGCGGCAGGCGGCGGAGGGGCCGCGGGCCGGUCCCCCCCGCCGGGUCCGCCCCCGGGGCCGCGGUUCCGCGCGGCGCCUCGCCUCGGCCGGCGCCUAGCAGCCGACUUAGAACUGGUGCGGACCAGGGGAAUCCGACUGUUUAAUUAAAACAAAGCAUCGCGAAGGCCCGCGGCGGGUGUUGACGCGAUGUGAUUUCUGCCCAGUGCUCUGAAUGUCAAAGUGAAGAAAUUCAAUGAAGCGCGGGUAAACGGCGGGAGUAACUAUGACUCUCUUAAGGUAGCCAAAUGCCUCGUCAUCUAAUUAGUGACGCGCAUGAAUGGAUGAACGAGAUUCCCACUGUCCCUACCUACUAUCCAGCGAAACCACAGCCAAGGGAACGGGCUUGGCGGAAUCAGCGGGGAAAGAAGACCCUGUUGAGCUUGACUCUAGUCUGGCACGGUGAAGAGACAUGAGAGGUGUAGAAUAAGUGGGAGGCCCCCGGCGCCCCCCCGGUGUCCCCGCGAGGGGCCCGGGGCGGGGUCCGCCGGCCCUGCGGGCCGCCGGUGAAAUACCACUACUCUGAUCGUUUUUUCACUGACCCGGUGAGGCGGGGGGGCGAGCCCCGAGGGGCUCUCGCUUCUGGCGCCAAGCGCCCGGCCGCGCGCCGGCCGGGCGCGACCCGCUCCGGGGACAGUGCCAGGUGGGGAGUUUGACUGGGGCGGUACACCUGUCAAACGGUAACGCAGGUGUCCUAAGGCGAGCUCAGGGAGGACAGAAACCUCCCGUGGAGCAGAAGGGCAAAAGCUCGCUUGAUCUUGAUUUUCAGUACGAAUACAGACCGUGAAAGCGGGGCCUCACGAUCCUUCUGACCUUUUGGGUUUUAAGCAGGAGGUGUCAGAAAAGUUACCACAGGGAUAACUGGCUUGUGGCGGCCAAGCGUUCAUAGCGACGUCGCUUUUUGAUCCUUCGAUGUCGGCUCUUCCUAUCAUUGUGAAGCAGAAUUCACCAAGCGUUGGAUUGUUCACCCACUAAUAGGGAACGUGAGCUGGGUUUAGACCGUCGUGAGACAGGUUAGUUUUACCCUACUGAUGAUGUGUUGUUGCCAUGGUAAUCCUGCUCAGUACGAGAGGAACCGCAGGUUCAGACAUUUGGUGUAUGUGCUUGGCUGAGGAGCCAAUGGGGCGAAGCUACCAUCUGUGGGAUUAUGACUGAACGCCUCUAAGUCAGAAUCCCGCCCAGGCGGAACGAUACGGCAGCGCCGCGGAGCCUCGGUUGGCCUCGGAUAGCCGGUCCCCCGCCUGUCCCCGCCGGCGGGCCGCCCCCCCCCUCCACGCGCCCCGCGCGCGCGGGAGGGCGCGUGCCCCGCCGCGCGCCGGGACCGGGGUCCGGUGCGGAGUGCCCUUCGUCCUGGGAAACGGGGCGCGGCCGGAGAGGCGGCCGCCCCCUCGCCCGUCACGCACCGCACGUUCGUGGGGAACCUGGCGCUAAACCAUUCGUAGACGACCUGCUUCUGGGUCGGGGUUUCGUACGUAGCAGAGCAGCUCCCUCGCUGCGAUCUAUUGAAAGUCAGCCCUCGACACAAGGGUUUGUC

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 \(c\).

\(|P_{f(6WTW_1)}(2) \setminus P_{f(5PSM_1)}(2)|=153\), \(|P_{f(5PSM_1)}(2) \setminus P_{f(6WTW_1)}(2)|=52\). 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 1:00110010010001111111111111110110111101011011111110111010011111100111111011111111001100011110011100110011111111111101100011100110111001100011110110110111111110001001110111100100000001001000011101011110101100111101111011100111001001011011111111111101111111001011010001010011000100111100100111011011111111011101101001111111101111011101001100011101111101111111011001111111011000101101111111111111000011101010101101111011011111111011111101110100000101110111001010000110101111110111111110111011111
Pair \(Z_2\) Length of longest common subsequence
6WTW_1,5PSM_1 205 3
6WTW_1,7BHP_1 227 3
5PSM_1,7BHP_1 132 2

Newick tree

 
[
	6WTW_1:11.91,
	[
		5PSM_1:66,7BHP_1:66
	]:52.91
]

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 \((0.85)(0.8)(\frac{647 }{\log_{20} 647}-\frac{156}{\log_{20}156})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 6WTW_1 5PSM_1 175 116
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]