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Parikh vectors
5JDV_1 5YXO_1 1JML_1 Letter Amino acid
13 43 9 A Alanine
19 33 3 D Aspartic acid
26 38 3 L Leucine
11 19 4 F Phenylalanine
17 17 2 S Serine
22 35 5 G Glycine
1 9 2 M Methionine
8 3 1 W Tryptophan
8 15 3 Y Tyrosine
17 30 4 V Valine
13 20 6 E Glutamic acid
9 23 3 I Isoleucine
24 25 7 K Lycine
12 52 8 T Threonine
7 12 0 R Arginine
10 26 4 N Asparagine
1 0 0 C Cysteine
11 29 1 Q Glutamine
12 17 6 H Histidine
17 19 1 P Proline 

5JDV_1|Chain A[auth B]|Carbonic anhydrase 2|Homo sapiens (9606)
>5YXO_1|Chain A|Pilus assembly protein|Lactobacillus rhamnosus GG (568703)
>1JML_1|Chain A|Protein L|Finegoldia magna (334413)
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 \(w=f(c)\)
5JDV , Knot 110 258 0.79 40 174 247 
HHWGYGKHNGPEHWHKDFPIAKGERQSPVDIDTHTAKYDPSLKPLSVSYDQATSLRILNNGHAFNVEFDDSQDKAVLKGGPLDGTYRLIQFHFHWGSLDGQGSEHTVDKKKYAAELHLVHWNTKYGDWGKAVQQPDGLAVLGIFLKVGSAKPGLQKVVDVLDSIKTKGKSADFTNFDPRGLLPESLDYWTYPGSLTTPPLLECVTWIVLKEPISVSSEQVLKFRKLNFNGEGEPEELMVDNWRPAQPLKNRQIKASFK
5YXO , Knot 188 465 0.82 38 227 434 
MGRDPNSTTTVDFTLHKIEQTSDEQIQNTGHDLGLTGRKPVQGAQFKIFNVTDAFYQLLENHDKTTAASMISQNLGQYVNLQDPNAATVTTDADGLAAFKGLAAKTNGRHSVYAFHEAVTPQPYQKAADMIVSLPVRQDDGSDLTNIHLYPKDSLVTKNLTEINEQAVATKDLHDVAVGDVLTYQVQFQIPHDIGALADHSQDTFKYNQFKVLDYMTKEGLTFKALTAITVDGQDILKALTGKMAFMSSNDAAWQQTHNYPFGFELDFLGGTDPDAVRNLLTQYAGKRVTVAYTGIVNEKMIPDQKVGNTAEVSFDPDSKITVNGPEIQTGGIRFFKHEAGSSKSLANATFILQRMNGNVREYAVLEGVNGMAGTYQPTKITWTTNQDAATRLKTSGAETANLTIQGLLPGRYTLVETAAPEGYEILDPTTDFEVIAGTWGTKTIRIANTPVNQLLPLEHHHHHH
1JML , Knot 36 72 0.71 36 57 66 
MHHHHHHGMEEVTIKANLIFANGSTQTAEFKGTFEKATSEAYAYADTLKKDNGEWTVDVVPKAYTLNIKFAG

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 \(c\).

\(|P_{f(5JDV_1)}(2) \setminus P_{f(5YXO_1)}(2)|=54\), \(|P_{f(5YXO_1)}(2) \setminus P_{f(5JDV_1)}(2)|=107\). 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 1:001101000110010001111010000110100001000101011010000100101100101101010000001110111101000110101011010101000010000011010110100001011011001011111111101101011100110110010001001010010101111001001001101001111001011110011010000110100101010101001110010110110000101010
Pair \(Z_2\) Length of longest common subsequence
5JDV_1,5YXO_1 161 4
5JDV_1,1JML_1 165 3
5YXO_1,1JML_1 204 6

Newick tree

 
[
	1JML_1:96.50,
	[
		5JDV_1:80.5,5YXO_1:80.5
	]:16.00
]

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 \((0.85)(0.8)(\frac{723 }{\log_{20} 723}-\frac{258}{\log_{20}258})=129.\)
Status Protein1 Protein2 d d1/2
Query variables 5JDV_1 5YXO_1 161 124
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]