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Parikh vectors
8EZS_1 7MXT_1 4YSB_1 Letter Amino acid
6 23 18 D Aspartic acid
10 24 17 G Glycine
7 28 9 I Isoleucine
7 29 4 K Lycine
3 9 3 M Methionine
5 30 20 A Alanine
11 36 23 L Leucine
4 12 19 T Threonine
7 15 6 Y Tyrosine
9 22 22 V Valine
3 19 17 R Arginine
0 11 2 C Cysteine
4 16 11 Q Glutamine
8 20 12 E Glutamic acid
7 14 8 F Phenylalanine
5 12 10 P Proline
2 16 9 N Asparagine
1 7 10 H Histidine
3 14 13 S Serine
0 1 0 W Tryptophan 

8EZS_1|Chain A|HipS(Lp)|Legionella pneumophila (446)
>7MXT_1|Chain A[auth Z]|Exonuclease 1|Homo sapiens (9606)
>4YSB_1|Chains A, B|Metallo-beta-lactamase family protein|Myxococcus xanthus (strain DK 1622) (246197)
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 \(w=f(c)\)
8EZS , Knot 52 102 0.78 36 81 100 
MRKAYVSVSGIKAGILEELQGGTYQFTYFEDYHGAPVSLTMPLKNKVYDFDVFPPFFEGLLPEGIMLEALLRKYKIDKNDYFGQLILVGQDVVGAVTIEEIR
7MXT , Knot 152 358 0.83 40 211 344 
MGIQGLLQFIKEASEPIHVRKYKGQVVAVDTYCWLHKGAIACAEKLAKGEPTDRYVGFCMKFVNMLLSHGIKPILVFDGCTLPSKKEVERSRRERRQANLLKGKQLLREGKVSEARECFTRSINITHAMAHKVIKAARSQGVDCLVAPYEADAQLAYLNKAGIVQAIITEDSDLLAFGCKKVILKMDQFGNGLEIDQARLGMCRQLGDVFTEEKFRYMCILSGCDYLSSLRGIGLAKACKVLRLANNPDIVKVIKKIGHYLKMNITVPEDYINGFIRANNTFLYQLVFDPIKRKLIPLNAYEDDVDPETLSYAGQYVDDSIALQIALGNKDINTFEQIDDYNPDTAMPAHSRENLYFQ
4YSB , Knot 105 233 0.81 38 154 225 
MIFRQLFDSESSTYTYLIGDEATRQAVLIDPVLEQVDRDLQMVAELDLTLTHVFDTHVHADHITASGALRERTQATVVGSVNGASCANVQVRHGDEVRVGQLVFQVLATPGHTDDSISYLLGDRVFTGDALLVRGNGRTDFQNGNASQLYDSLTRVLFTLPDETLVYPGHDYKGRTVTSIAEEKRHNPRVAGKSREEFIHIMENLNLPRPKLIDAAVPANRACGHTAPSPQGA

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 \(c\).

\(|P_{f(8EZS_1)}(2) \setminus P_{f(7MXT_1)}(2)|=24\), \(|P_{f(7MXT_1)}(2) \setminus P_{f(8EZS_1)}(2)|=154\). 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 1:100101010110111100101100010010000111101011100010010111111011110111101110000100000110111110011111010010
Pair \(Z_2\) Length of longest common subsequence
8EZS_1,7MXT_1 178 4
8EZS_1,4YSB_1 159 3
7MXT_1,4YSB_1 161 4

Newick tree

 
[
	7MXT_1:86.56,
	[
		8EZS_1:79.5,4YSB_1:79.5
	]:7.06
]

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 \((0.85)(0.8)(\frac{460 }{\log_{20} 460}-\frac{102}{\log_{20}102})=107.\)
Status Protein1 Protein2 d d1/2
Query variables 8EZS_1 7MXT_1 136 86
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]