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Parikh vectors
2RBH_1 7WBH_1 7XHE_1 Letter Amino acid
2 16 6 H Histidine
11 65 5 I Isoleucine
13 89 14 L Leucine
5 10 5 M Methionine
7 70 6 F Phenylalanine
8 58 11 P Proline
11 71 4 A Alanine
8 51 9 D Aspartic acid
3 9 3 W Tryptophan
8 50 6 Y Tyrosine
4 40 8 R Arginine
10 81 4 N Asparagine
4 29 1 C Cysteine
17 38 8 E Glutamic acid
16 76 5 G Glycine
16 49 11 K Lycine
9 57 9 Q Glutamine
14 86 6 S Serine
11 90 4 T Threonine
11 85 8 V Valine 

2RBH_1|Chains A, B|Gamma-glutamyl cyclotransferase|Homo sapiens (9606)
>7WBH_1|Chain A|Spike glycoprotein|Severe acute respiratory syndrome-related coronavirus (694009)
>7XHE_1|Chains A, B|CREB-binding protein|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 \(w=f(c)\)
2RBH , Knot 95 188 0.88 40 150 185 
MANSGCKDVTGPDEESFLYFAYGSNLLTERIHLRNPSAAFFCVARLQDFKLDFGNSQGKTSQTWHGGIATIFQSPGDEVWGVVWKMNKSNLNSLDEQAGVKSGMYVVIEVKVATQEGKEITCRSYLMTNYESAPPSPQYKKIICMGAKENGLPLEYQEKLKAIEPNDYTGKVSEEIEDIIKKGETQTL
7WBH , Knot 409 1120 0.85 40 317 991 
AYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLHVYYHKNNKSWMEGEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLVRGLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGNIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVKGFNCYFPLQSYGFQPTYGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQGVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEHVNNSYECDIPIGAGICASYQTQTNSPRRARSVASQSIIAYTMSLGVENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLNRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKDFGGFNFSQILPDPSKPSKRSPIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGPALQIPFPMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTPSALGKLQDVVNQNAQALNTLVKQLSSNFGAISSVLNDILSRLDPPEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELD
7XHE , Knot 64 133 0.78 40 108 128 
MKKGHHHHHHLVPRGSRKKIFKPEELRQALMPTLEALYRQDPESLPFRQPVDPQLLGIPDYFDIVKNPMDLSTIKRKLDTGQYQEPWQYVDDVWLMFNNAWLYNRKTSRVYKFCSKLAEVFEQEIDPVMQSLG

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 \(c\).

\(|P_{f(2RBH_1)}(2) \setminus P_{f(7WBH_1)}(2)|=15\), \(|P_{f(7WBH_1)}(2) \setminus P_{f(2RBH_1)}(2)|=182\). 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 1:11001000101100001101101001100010100101111011010010101100010000010111101100110011111101000010010001110011011101011000100100000110000011101000011011100011110000010110100001010001001100100001
Pair \(Z_2\) Length of longest common subsequence
2RBH_1,7WBH_1 197 4
2RBH_1,7XHE_1 164 3
7WBH_1,7XHE_1 231 3

Newick tree

 
[
	7WBH_1:11.54,
	[
		2RBH_1:82,7XHE_1:82
	]:32.54
]

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 \((0.85)(0.8)(\frac{1308 }{\log_{20} 1308}-\frac{188}{\log_{20}188})=298.\)
Status Protein1 Protein2 d d1/2
Query variables 2RBH_1 7WBH_1 373 216
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]