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Parikh vectors
9GDJ_1 7FQP_1 1PYL_1 Letter Amino acid
12 11 2 H Histidine
21 19 8 R Arginine
20 18 7 D Aspartic acid
2 4 2 C Cysteine
12 14 4 Q Glutamine
19 22 8 P Proline
13 30 5 E Glutamic acid
24 29 5 L Leucine
3 23 4 K Lycine
8 11 0 M Methionine
32 13 7 A Alanine
23 14 9 G Glycine
21 13 7 T Threonine
4 6 1 W Tryptophan
11 9 7 Y Tyrosine
16 17 7 V Valine
3 11 5 N Asparagine
8 18 2 I Isoleucine
15 14 3 F Phenylalanine
24 25 4 S Serine 

9GDJ_1|Chains A, B, C|Methyltransferase|Streptomyces griseoviridis (45398)
>7FQP_1|Chain A|Tyrosine-protein phosphatase non-receptor type 1|Homo sapiens (9606)
>1PYL_1|Chains A, B|ribonuclease|Streptomyces aureofaciens (1894)
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 \(w=f(c)\)
9GDJ , Knot 127 291 0.82 40 176 274 
MGSSHHHHHHSSGLVPRGSHMSSQTVTPDPYGNLAESYDRLAQWAIDQQQESPRDRVGDFLQTFWQSQDRPVRTVLEICCGTGLMLAELARRGYVVTGLDRSAAMLEQARARMGGKTTLIRAELPDIPAPAGEFDAVVSAAGGLNYLSESQISATFGAVARLLPAGGTFTFDVFGQGFYAKFFDPSAPRVMALELDDISYIWTFTKPAEAPFVDMSYTQFSPASRAVDGEPAFIRTRDLHRYYPLPHATVLRLAAEHGFTDARAHDNYSSDPSGPHTLYDTWTMVRTGSLE
7FQP , Knot 141 321 0.84 40 205 309 
MEMEKEFEQIDKSGSWAAIYQDIRHEASDFPSRVAKLPKNKNRNRYRDVSPFDHSRIKLHQEDNDYINASLIKMEEAQRSYILTQGPLPNTVGHFWEMVWEQKSRGVVMLNRVMEKGSLKCAQYWPQKEEKEMIFEDTNLKLTLISEDIKSYYTVRQLELENLTTQETREILHFHYTTWPDFGVPESPASFLNFLFKVRESGSLSPEHGPVVVHCSAGIGRSGTFCLADTCLLLMDKRKDPSSVDIKKVLLEMRKFRMGLIQTADQLRFSYLAVIEGAKFIMGDSSVQDQWKELSHEDLEPPPEHIPPPPRPPKRILEPHN
1PYL , Knot 51 97 0.80 38 84 94 
ADPALADVCRTKLPSQAQDTLALIAKNGPYPYNRDGVVFENRESRLPKKGNGYYHEFTVVTPGSNDRGTRRVVTGGYGEQYWSPDHYATFQEIDPRC

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 \(c\).

\(|P_{f(9GDJ_1)}(2) \setminus P_{f(7FQP_1)}(2)|=68\), \(|P_{f(7FQP_1)}(2) \setminus P_{f(9GDJ_1)}(2)|=97\). 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 1:110000000000111101001000010101010110000011011100000010001101100110000011001101001011111011001011011000111100101011100011010110111111010111011111001000010101111101111110101011101101011010110111101001001101001101111010000101100110101111000010000111010110111001100101000000010110010001011001010
Pair \(Z_2\) Length of longest common subsequence
9GDJ_1,7FQP_1 165 4
9GDJ_1,1PYL_1 148 4
7FQP_1,1PYL_1 189 3

Newick tree

 
[
	7FQP_1:93.08,
	[
		9GDJ_1:74,1PYL_1:74
	]:19.08
]

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 \((0.85)(0.8)(\frac{612 }{\log_{20} 612}-\frac{291}{\log_{20}291})=89.8\)
Status Protein1 Protein2 d d1/2
Query variables 9GDJ_1 7FQP_1 115 107.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]