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Parikh vectors
5XZQ_1 4PAD_1 8QLA_1 Letter Amino acid
8 11 32 L Leucine
10 4 20 F Phenylalanine
5 13 23 S Serine
5 13 16 Q Glutamine
5 28 36 G Glycine
10 12 27 I Isoleucine
8 10 19 K Lycine
9 10 20 P Proline
9 18 34 V Valine
10 14 36 A Alanine
4 12 21 R Arginine
6 8 29 T Threonine
1 7 12 C Cysteine
11 7 37 E Glutamic acid
11 2 13 H Histidine
3 0 10 M Methionine
3 5 4 W Tryptophan
7 19 19 Y Tyrosine
9 13 16 N Asparagine
6 6 27 D Aspartic acid 

5XZQ_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|Hydroxynitrile lyase|Passiflora edulis (78168)
>4PAD_1|Chain A|PAPAIN|Carica papaya (3649)
>8QLA_1|Chain A|Tubulin alpha-1B chain|Bos taurus (9913)
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 \(w=f(c)\)
5XZQ , Knot 69 140 0.81 40 112 135 
MNHKVHHHHHHIEGRHMELNPPEIVRHIVFNRYKSQLSQKQIDQIIADYGNLQNIAPEMKEWKWGTDLGPAVEDRADGFTHAYESTFHSVADFLNFFYSPPALEFAKEFFPACEKIVVLNYIINETFPYTWALPNKYVVT
4PAD , Knot 99 212 0.83 38 141 203 
IPEYVDWRQKGAVTPVKNQGSCGSCWAFSAVVTIEGIIKIRTGNLNQYSEQELLDCDRRSYGCNGGYPWSALQLVAQYGIHYRNTYPYEGVQRYCRSREKGPYAAKTDGVRQVQPYNQGALLYSIANQPVSVVLQAAGKDFQLYRGGIFVGPCGNKVDHAVAAVGYGPNYILIKNSWGTGWGENGYIRIKRGTGNSYGVCGLYTSSFYPVKN
8QLA , Knot 192 451 0.86 40 258 426 
MRECISIHVGQAGVQIGNACWELYCLEHGIQPDGQMPSDKTIGGGDDSFNTFFSETGAGKHVPRAVFVDLEPTVIDEVRTGTYRQLFHPEQLITGKEDAANNYARGHYTIGKEIIDLVLDRIRKLADQCTGLQGFLVFHSFGGGTGSGFTSLLMERLSVDYGKKSKLEFSIYPAPQVSTAVVEPYNSILTTHTTLEHSDCAFMVDNEAIYDICRRNLDIERPTYTNLNRLISQIVSSITASLRFDGALNVDLTEFQTNLVPYPRIHFPLATYAPVISAEKAYHEQLSVAEITNACFEPANQMVKCDPRHGKYMACCLLYRGDVVPKDVNAAIATIKTKRSIQFVDWCPTGFKVGINYQPPTVVPGGDLAKVQRAVCMLSNTTAIAEAWARLDHKFDLMYAKRAFVHWYVGEGMEEGEFSEAREDMAALEKDYEEVGVDSVEGEGEEEGEEY

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 \(c\).

\(|P_{f(5XZQ_1)}(2) \setminus P_{f(4PAD_1)}(2)|=67\), \(|P_{f(4PAD_1)}(2) \setminus P_{f(5XZQ_1)}(2)|=96\). 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 1:10001000000101001010110110011100000010000100111001010011101001011001111100010110010000100110110110011110110011110001111001100011001111000110
Pair \(Z_2\) Length of longest common subsequence
5XZQ_1,4PAD_1 163 3
5XZQ_1,8QLA_1 222 3
4PAD_1,8QLA_1 191 4

Newick tree

 
[
	8QLA_1:10.90,
	[
		5XZQ_1:81.5,4PAD_1:81.5
	]:28.40
]

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 \((0.85)(0.8)(\frac{352 }{\log_{20} 352}-\frac{140}{\log_{20}140})=64.5\)
Status Protein1 Protein2 d d1/2
Query variables 5XZQ_1 4PAD_1 83 68.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]