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Parikh vectors
8STC_1 5ANT_1 7GRV_1 Letter Amino acid
12 8 13 P Proline
22 8 24 T Threonine
28 14 27 V Valine
2 2 12 C Cysteine
3 10 7 H Histidine
7 9 11 K Lycine
6 4 11 Y Tyrosine
42 4 17 A Alanine
9 9 11 R Arginine
7 5 10 M Methionine
12 10 16 S Serine
7 1 21 N Asparagine
17 11 14 Q Glutamine
11 12 9 E Glutamic acid
18 17 29 L Leucine
8 11 17 F Phenylalanine
1 4 3 W Tryptophan
7 12 17 D Aspartic acid
24 19 26 G Glycine
13 5 11 I Isoleucine 

8STC_1|Chains A, B, C, D, E, F|Pyridinium-3,5-biscarboxylic acid mononucleotide synthase|Lactiplantibacillus plantarum WCFS1 (220668)
>5ANT_1|Chains A, B, C|7,8-DIHYDRO-8-OXOGUANINE TRIPHOSPHATASE|HOMO SAPIENS (9606)
>7GRV_1|Chains A, B|3C-like proteinase nsp5|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 \(w=f(c)\)
8STC , Knot 109 256 0.78 40 150 242 
MATTAEILQQVAAGQLSPTAAAQQLEAGKTAALGFANVDLDRQRRNGFPEVIYGAGKTATQIVGIVQALSQQTLPILTTRLSAEKFAALQPALPTAVYHATAQCMTVGEQPAPKTPGYIAVVTAGTADQPVAEEAAVTAETFGNRVERVYDVGVAGIHRLFAKLDVIRGARVVIVIAGMEGALASVVGGLVDKPVIAVPTSVGYGTSFQGMTALLTMLNSCASGITVVNIDNGFGAAYSASMVNQMASWSHPQFEK
5ANT , Knot 81 175 0.79 40 127 166 
GSSHHHHHHSSGLVPRGSHMGASRLYTLVLVLQPQRVLLGMKKRGFGAGRWNGFGGKVQEGETIEDGARRELQEESGLTVDALHKVGQIVFEFVGEPELMDVHVFCTDSIQGTPVESDEMRPCWFQLDQIPFKDMWPDDSYWFPLLLQKKKFHGYFKFQGQDTILDYTLREVDTV
7GRV , 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 \(c\).

\(|P_{f(8STC_1)}(2) \setminus P_{f(5ANT_1)}(2)|=94\), \(|P_{f(5ANT_1)}(2) \setminus P_{f(8STC_1)}(2)|=71\). 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 1:1100101100111101010111001011001111110101000000111011011100100111110110000111100010100111101111011001010010110011100110111101101001110011101001100100100111111001110101101101111111101111011111100111111001101001011011101100010110110100111110010110011010010100
Pair \(Z_2\) Length of longest common subsequence
8STC_1,5ANT_1 165 4
8STC_1,7GRV_1 166 4
5ANT_1,7GRV_1 187 3

Newick tree

 
[
	7GRV_1:90.28,
	[
		8STC_1:82.5,5ANT_1:82.5
	]:7.78
]

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 \((0.85)(0.8)(\frac{431 }{\log_{20} 431}-\frac{175}{\log_{20}175})=75.7\)
Status Protein1 Protein2 d d1/2
Query variables 8STC_1 5ANT_1 92 78
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]