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Parikh vectors
5WVD_1 2DRU_1 7UXK_1 Letter Amino acid
14 6 19 P Proline
10 9 10 Y Tyrosine
21 6 19 A Alanine
14 6 16 I Isoleucine
14 5 16 F Phenylalanine
20 11 14 S Serine
10 4 3 C Cysteine
8 4 10 H Histidine
24 6 17 G Glycine
23 14 21 K Lycine
12 15 17 T Threonine
4 4 4 W Tryptophan
18 8 16 D Aspartic acid
16 9 9 Q Glutamine
26 15 17 E Glutamic acid
29 16 39 L Leucine
4 7 5 M Methionine
22 15 23 V Valine
13 9 16 R Arginine
8 11 8 N Asparagine 

5WVD_1|Chains A, B|MAP kinase interacting serine/threonine kinase 1|Homo sapiens (9606)
>2DRU_1|Chain A|chimera of CD48 antigen and T-cell surface antigen CD2|Rattus norvegicus (10116)
>7UXK_1|Chain A|Cyclin-dependent kinase 2|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 \(w=f(c)\)
5WVD , Knot 131 310 0.80 40 195 297 
GPLGSTDSLPGKFEDMYKLTSELLGEGAYAKVQGAVSLQNGKEYAVKIIEKQAGHSRSRVFREVETLYQCQGNKNILELIEFFEDDTRFYLVFEKLQGGSILAHIQKQKHFNEREASRVVRDVAAALDFLHTKGIAHRDLKPENILCESPEKVSPVKICDFDLGSGMKLNNSCTPITTPELTTPCGSAEYMAPEVVEVFTDQATFYDKRCDLWSLGVVLYIMLSGYPPFVGHCGADCGWDRGEVCRVCQNKLFESIQEGKYEFPDKDWAHISSEAKDLISKLLVRDAKQRLSAAQVLQHPWVQGQAPEKG
2DRU , Knot 83 180 0.79 40 131 174 
FQDQSVPNVNAITGSNVTLTILKHPLASYQRLTWLHTTNQKILEYFPNGKKTVFESVFKDRVDLDKTNGALRIYNVSKEDRGDYYMRMLHETEDQWKITMEVYEMVSKPMIYWECSNATLTCEVLEGTDVELKLYQGKEHLRSLRQKTMSYQWTNLRAPFKCKAVNRVSQESEMEVVNCP
7UXK , Knot 134 299 0.85 40 192 285 
GMENFQKVEKIGEGTYGVVYKARNKLTGEVVALKKIRLDTETEGVPSTAIREISLLKELNHPNIVKLLDVIHTENKLYLVFEFLHQDLKKFMDASALTGIPLPLIKSYLFQLLQGLAFCHSHRVLHRDLKPQNLLINTEGAIKLADFGLARAFGVPVRTYTHEVVTLWYRAPEILLGCKYYSTAVDIWSLGCIFAEMVTRRALFPGDSEIDQLFRIFRTLGTPDEVVWPGVTSMPDYKPSFPKWARQDFSKVVPPLDEDGRSLLSQMLHYDPNKRISAKAALAHPFFQDVTKPVPHLRL

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 \(c\).

\(|P_{f(5WVD_1)}(2) \setminus P_{f(2DRU_1)}(2)|=129\), \(|P_{f(2DRU_1)}(2) \setminus P_{f(5WVD_1)}(2)|=65\). 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 1:1111000011101001001000111011010101110100100011011000110000011001001000010001101101100000101110010110111010000010000100110011111011000111000101001100010010110100101101101000001100101001010100111011011000101000000110111110111010111110011001100101001000011001001000110001101000100110011100100010110110011101011001
Pair \(Z_2\) Length of longest common subsequence
5WVD_1,2DRU_1 194 3
5WVD_1,7UXK_1 179 6
2DRU_1,7UXK_1 177 3

Newick tree

 
[
	5WVD_1:94.87,
	[
		7UXK_1:88.5,2DRU_1:88.5
	]:6.37
]

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 \((0.85)(0.8)(\frac{490 }{\log_{20} 490}-\frac{180}{\log_{20}180})=90.5\)
Status Protein1 Protein2 d d1/2
Query variables 5WVD_1 2DRU_1 115 91
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]