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Parikh vectors
8ZVT_1 2ZHW_1 4MAU_1 Letter Amino acid
32 1 16 A Alanine
34 4 14 G Glycine
53 5 17 L Leucine
14 0 1 M Methionine
14 2 8 F Phenylalanine
18 1 10 Y Tyrosine
3 1 5 C Cysteine
30 3 32 S Serine
19 3 7 R Arginine
19 0 7 N Asparagine
20 3 8 D Aspartic acid
17 0 12 Q Glutamine
22 1 12 P Proline
29 0 14 V Valine
24 6 13 E Glutamic acid
14 0 4 H Histidine
17 1 8 I Isoleucine
24 3 13 K Lycine
24 2 15 T Threonine
9 0 2 W Tryptophan 

8ZVT_1|Chain A|Citrate synthase, mitochondrial|Homo sapiens (9606)
>2ZHW_1|Chain A[auth L]|Thrombin light chain|Homo sapiens (9606)
>4MAU_1|Chain A[auth L]|C2244 light chain|Mus musculus (10090)
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 \(w=f(c)\)
8ZVT , Knot 181 436 0.84 40 240 421 
ASSTNLKDILADLIPKEQARIKTFRQQHGKTVVGQITVDMMYGGMRGMKGLVYETSVLDPDEGIRFRGFSIPECQKLLPKAKGGEEPLPEGLFWLLVTGHIPTEEQVSWLSKEWAKRAALPSHVVTMLDNFPTNLHPMSQLSAAVTALNSESNFARAYAQGISRTKYWELIYEDSMDLIAKLPCVAAKIYRNLYREGSGIGAIDSNLDWSHNFTNMLGYTDHQFTELTRLYLTIHSDHEGGNVSAHTSHLVGSALSDPYLSFAAAMNGLAGPLHGLANQEVLVWLTQLQKEVGKDVSDEKLRDYIWNTLNSGRVVPGYGHAVLRKTDPRYTCQREFALKHLPNDPMFKLVAQLYKIVPNVLLEQGKAKNPWPNVDAHSGVLLQYYGMTEMNYYTVLFGVSRALGVLAQLIWSRALGFPLERPKSMSTEGLMKFVDS
2ZHW , Knot 24 36 0.79 28 34 34 
TFGSGEADCGLRPLFEKKSLEDKTERELLESYIDGR
4MAU , Knot 104 218 0.85 40 158 211 
DIVLTQSPASLAISLGQRATISCRASKSVSTSGSSYMFWYQQKPGQPPKLLIYLASNLESGVPARFSGSGSGTDFTLNIHPVEEEDAAAYYCQHSREIPYTFGGGTKLEIKRTVAAPSVFIFPPSDEQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGEC

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 \(c\).

\(|P_{f(8ZVT_1)}(2) \setminus P_{f(2ZHW_1)}(2)|=215\), \(|P_{f(2ZHW_1)}(2) \setminus P_{f(8ZVT_1)}(2)|=9\). 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 1:1000010011101110001010010000100111010101101110110111000011010011010110110000111010110011101111111010110000101100011001111001101100110010110010111011000001101010110000010110000101110110111010001000101111100010100010011100000100100101010000011010100001110110010101111101111110111000111110010001100100001000110010010111101011100001000000011100110011101110100111011100101001110101001111000110010000111110011111101110011111100100100011101100
Pair \(Z_2\) Length of longest common subsequence
8ZVT_1,2ZHW_1 224 3
8ZVT_1,4MAU_1 172 3
2ZHW_1,4MAU_1 156 3

Newick tree

 
[
	8ZVT_1:10.13,
	[
		4MAU_1:78,2ZHW_1:78
	]:28.13
]

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 \((0.85)(0.8)(\frac{472 }{\log_{20} 472}-\frac{36}{\log_{20}36})=135.\)
Status Protein1 Protein2 d d1/2
Query variables 8ZVT_1 2ZHW_1 175 94
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]