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Parikh vectors
7OLN_1 7NIS_1 7CZO_1 Letter Amino acid
14 13 8 G Glycine
8 7 13 L Leucine
5 3 4 K Lycine
13 10 8 S Serine
11 9 1 T Threonine
2 3 1 W Tryptophan
15 8 4 V Valine
4 3 4 N Asparagine
1 2 0 C Cysteine
3 11 6 Q Glutamine
3 3 3 M Methionine
14 16 3 A Alanine
6 5 6 D Aspartic acid
9 3 5 I Isoleucine
5 5 10 F Phenylalanine
3 8 6 R Arginine
2 6 5 H Histidine
8 5 6 P Proline
6 6 5 Y Tyrosine
2 6 8 E Glutamic acid 

7OLN_1|Chain A[auth AAA]|Lectin|Burkholderia cenocepacia (strain ATCC BAA-245 / DSM 16553 / LMG 16656 / NCTC 13227 / J2315 / CF5610) (216591)
>7NIS_1|Chain A[auth F]|Nanobody8192 core|Camelidae mixed library (1579311)
>7CZO_1|Chain A|Uncharacterized protein HI_0666|Haemophilus influenzae (strain ATCC 51907 / DSM 11121 / KW20 / Rd) (71421)
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 \(w=f(c)\)
7OLN , Knot 66 134 0.80 40 108 131 
GHMPLLSASIVSAPVVTSETYVDIPGLYLDVAKAGIRDGKLQVILNVPTPYATGNNFPGIYFAIATNQGVVADGCFTYSSKVPESTGRMPFTLVATIDVGSGVTFVKGQWKSVRGSAMHIDSYASLSAIWGTAA
7NIS , Knot 62 132 0.76 40 99 123 
QVQLQESGGGLVQAGASLRLSCAASGRTFMGWFRQAPGQEREFVAAIDAFGINTYYADSAKGRFTISRDSAKNTVYLQMNSLKPEDTAVYYCAATLRGTQPGAVMQWRPDYWGQGTQVTVSSHHHHHHEPEA
7CZO , Knot 56 106 0.82 38 96 104 
MRDLVRSGKVFLYGEFIGLLREDHRGFHFSYNPDYQGIPLSLSFPIEQSPFHSDTLFPYFASLVPEGWLKHKYALHQRIDESDMFRFLLNNGENMLGAVQIQEEKQ

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 \(c\).

\(|P_{f(7OLN_1)}(2) \setminus P_{f(7NIS_1)}(2)|=64\), \(|P_{f(7NIS_1)}(2) \setminus P_{f(7OLN_1)}(2)|=55\). 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 1:10111101011011110000010111101011011100101011101101010100111101111000111101010000011000101110111010110110110101001010110100010101111011
Pair \(Z_2\) Length of longest common subsequence
7OLN_1,7NIS_1 119 3
7OLN_1,7CZO_1 142 3
7NIS_1,7CZO_1 135 3

Newick tree

 
[
	7CZO_1:72.23,
	[
		7OLN_1:59.5,7NIS_1:59.5
	]:12.73
]

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 \((0.85)(0.8)(\frac{266 }{\log_{20} 266}-\frac{132}{\log_{20}132})=41.9\)
Status Protein1 Protein2 d d1/2
Query variables 7OLN_1 7NIS_1 53 50.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]