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Parikh vectors
2EIT_1 6DLQ_1 7DAV_1 Letter Amino acid
22 0 24 T Threonine
14 0 21 N Asparagine
1 25 12 C Cysteine
10 0 14 Q Glutamine
39 0 29 L Leucine
6 0 10 M Methionine
16 0 16 S Serine
62 22 17 A Alanine
56 0 9 E Glutamic acid
47 38 26 G Glycine
5 0 7 H Histidine
26 0 11 K Lycine
29 0 13 P Proline
54 0 27 V Valine
15 0 17 D Aspartic acid
22 0 11 I Isoleucine
27 0 17 F Phenylalanine
8 0 3 W Tryptophan
20 0 11 Y Tyrosine
37 0 11 R Arginine 

2EIT_1|Chains A, B|1-pyrroline-5-carboxylate dehydrogenase|Thermus thermophilus (300852)
>6DLQ_1|Chain A|PRPP Riboswitch|Syntrophothermus lipocalidus DSM 12680 (643648)
>7DAV_1|Chain A|COVID-19 MAIN PROTEASE|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
2EIT , Knot 201 516 0.81 40 220 465 
MTVEPFRNEPIETFQTEEARRAMREALRRVREEFGRHYPLYIGGEWVDTKERMVSLNPSAPSEVVGTTAKAGKAEAEAALEAAWKAFKTWKDWPQEDRSRLLLKAAALMRRRKRELEATLVYEVGKNWVEASADVAEAIDFIEYYARAALRYRYPAVEVVPYPGEDNESFYVPLGAGVVIAPWNFPVAIFTGMIVGPVAVGNTVIAKPAEDAVVVGAKVFEIFHEAGFPPGVVNFLPGVGEEVGAYLVEHPRIRFINFTGSLEVGLKIYEAAGRLAPGQTWFKRAYVETGGKDAIIVDETADFDLAAEGVVVSAYGFQGQKCSAASRLILTQGAYEPVLERVLKRAERLSVGPAEENPDLGPVVSAEQERKVLSYIEIGKNEGQLVLGGKRLEGEGYFIAPTVFTEVPPKARIAQEEIFGPVLSVIRVKDFAEALEVANDTPYGLTGGVYSRKREHLEWARREFHVGNLYFNRKITGALVGVQPFGGFKLSGTNAKTGALDYLRLFLEMKAVAERF
6DLQ , Knot 31 107 0.45 8 16 53 
GGAAAGUGUGUCUAGGGUUCCGCGUGCUUCGGCACGGACUGGUCCAAGUGACACAGACGCAUUCGUGCGUUACACCGGAGGGAUAGAAGCCCAGGCGGGUAGGUUUC
7DAV , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ

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 \(c\).

\(|P_{f(2EIT_1)}(2) \setminus P_{f(6DLQ_1)}(2)|=216\), \(|P_{f(6DLQ_1)}(2) \setminus P_{f(2EIT_1)}(2)|=12\). 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 1:101011000110010000100110011001000110001101110110000011010101100111001011010101110111011001001100000011101111100000010101100110011010101101101100010111000011101110110000010111111111111011111101111111111001110110011111101101100111111110111111001110110010101101010101110100111011110011001010011001111000101011101111010110100001100111001100111001100100101111000101111101000001100101100010111110010101011110110011101011000111111011010011011011000101101110000000101100010110101000101111110111110101001001110010111010111001
Pair \(Z_2\) Length of longest common subsequence
2EIT_1,6DLQ_1 228 3
2EIT_1,7DAV_1 174 4
6DLQ_1,7DAV_1 200 3

Newick tree

 
[
	6DLQ_1:11.17,
	[
		2EIT_1:87,7DAV_1:87
	]:26.17
]

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 \((0.85)(0.8)(\frac{623 }{\log_{20} 623}-\frac{107}{\log_{20}107})=150.\)
Status Protein1 Protein2 d d1/2
Query variables 2EIT_1 6DLQ_1 198 113.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]