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Parikh vectors
5EZI_1 7QYR_1 2YSX_1 Letter Amino acid
6 22 10 E Glutamic acid
7 24 4 I Isoleucine
5 8 5 F Phenylalanine
15 14 5 P Proline
34 18 12 S Serine
12 6 6 Y Tyrosine
14 29 5 A Alanine
6 8 3 Q Glutamine
2 14 2 H Histidine
3 12 3 M Methionine
17 25 8 V Valine
21 11 7 T Threonine
6 0 1 W Tryptophan
5 23 7 R Arginine
8 10 7 D Aspartic acid
5 3 3 C Cysteine
20 33 9 G Glycine
8 9 5 N Asparagine
17 29 11 L Leucine
11 16 6 K Lycine 

5EZI_1|Chain A[auth H]|Fab c12 heavy chain|Homo sapiens (9606)
>7QYR_1|Chains A, B, C, D, E, F, G, H|Probable alpha-L-glutamate ligase|Pseudomonas aeruginosa PAO1 (208964)
>2YSX_1|Chain A|Signaling inositol polyphosphate phosphatase SHIP II|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 \(w=f(c)\)
5EZI , Knot 104 222 0.84 40 149 209 
NVNLLESGGGLVQPGGSLNLSCAASGFDFSRYWMSWARQAPGKGQEWIGEINPGSSTIKYTPSLKDKFIISRDNAKNTLYLQMSKVSSEDTALYYCARYGSYVYAMDYWGPGTSVTVSSAKTTAPSVYPLAPVCGDTTGSSVTLGCLVKGYFPEPVTLTWNSGSLSSGVHTFPAVLQSDLYTLSSSVTVTSSTWPSQSITCNVAHPASSTKVDKKIEPRGPT
7QYR , Knot 135 314 0.82 38 191 294 
MKIAVLSRNPRLYSTRRLVEAGRERGHEMVVIDTLRAYMNIASHKPQIHYRGQPLEGFDAVIPRIGASVTFYGCAVLRQFEMMGVFPLNESVAIARSRDKLRSLQLLSRKGIGLPVTGFAHSPDDVPDLIEMVGGAPLVIKLLEGTQGIGVVLCETEKAAESVLEAFMGLKHNIMVQEYIKEAGGADIRCFVVGDKVIASMKRQAAPGEFRSNLHRGGSASLIKITPEERMTAIRAARVMGLNVAGVDILRSNHGPLVMEVNSSPGLEGIESTTGKDIAGIIIQYLEKNGGPHLARTKGKGKLAAALEHHHHHH
2YSX , Knot 63 119 0.84 40 100 114 
GSSGSSGMVPCWNHGNITRSKAEELLSRTGKDGSFLVRASESISRAYALCVLYRNCVYTYRILPNEDDKFTVQASEGVSMRFFTKLDQLIEFYKKENMGLVTHLQYPVPLEEEDTGDDP

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 \(c\).

\(|P_{f(5EZI_1)}(2) \setminus P_{f(7QYR_1)}(2)|=68\), \(|P_{f(7QYR_1)}(2) \setminus P_{f(5EZI_1)}(2)|=110\). 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 1:010110011111011101010011011010001101100111010011101011000100010100011100001000101010010000011000100100101100111100101001000110101111101000100101101101011011010100101001100111110001001000101000011000100011011000010001010110
Pair \(Z_2\) Length of longest common subsequence
5EZI_1,7QYR_1 178 3
5EZI_1,2YSX_1 161 3
7QYR_1,2YSX_1 169 4

Newick tree

 
[
	7QYR_1:88.77,
	[
		5EZI_1:80.5,2YSX_1:80.5
	]:8.27
]

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 \((0.85)(0.8)(\frac{536 }{\log_{20} 536}-\frac{222}{\log_{20}222})=90.0\)
Status Protein1 Protein2 d d1/2
Query variables 5EZI_1 7QYR_1 117 98
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]