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Parikh vectors
2PQY_1 1ZWF_1 6XII_1 Letter Amino acid
15 3 9 E Glutamic acid
4 3 4 H Histidine
4 2 2 M Methionine
8 0 2 Y Tyrosine
27 1 7 A Alanine
20 1 12 G Glycine
19 6 3 L Leucine
15 3 10 K Lycine
12 1 5 F Phenylalanine
17 2 8 R Arginine
8 0 0 C Cysteine
10 2 6 Q Glutamine
15 1 3 S Serine
4 1 1 W Tryptophan
11 3 1 N Asparagine
13 1 3 D Aspartic acid
7 1 7 I Isoleucine
13 0 1 P Proline
13 0 5 T Threonine
10 3 14 V Valine 

2PQY_1|Chain A|Ribonuclease I|Escherichia coli (562)
>1ZWF_1|Chain A|PARATHYROID HORMONE|Homo sapiens (9606)
>6XII_1|Chain A[auth 0]|50S ribosomal protein L21|Escherichia coli (562)
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 \(w=f(c)\)
2PQY , Knot 109 245 0.81 40 168 239 
LALQAKQYGDFDRYVLALSWQTGFCQSQHDRNRNERDECRLQTETTNKADFLTVHGLWPGLPKSVAARGVDERRWMRFGCATRPIPNLPEARASRMCSSPETGLSLETAAKLSEVMPGAGGRSCLERYEYAKHGACFGFDPDAYFGTMVRLNQEIKESEAGKFLADNYGKTVSRRDFDAAFAKSWGKENVKAVKLTCQGNPAYLTEIQISIKADAINAPLSANSFLPQPHPGNCGKTFVIDKAGY
1ZWF , Knot 24 35 0.81 34 33 33 
XEIQLMHNLGKHLNSMERVEWLRKKLQDVHNFVAL
6XII , Knot 53 103 0.79 38 82 98 
MYAVFQSGGKQHRVSEGQTVRLEKLDIATGETVEFAEVLMIANGEEVKIGVPFVDGGVIKAEVVAHGRGEKVKIVKFRRRKHYRKQQGHRQWFTDVKITGISA

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 \(c\).

\(|P_{f(2PQY_1)}(2) \setminus P_{f(1ZWF_1)}(2)|=154\), \(|P_{f(1ZWF_1)}(2) \setminus P_{f(2PQY_1)}(2)|=19\). 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 1:11101000101000111101001100000000000000001000000010110101111111001110110000110110100111011010100100010011010011010011111110001000001001101110101011011010001000011011100010010000101111001100010110100010110100101010101101110100111010110010011100110
Pair \(Z_2\) Length of longest common subsequence
2PQY_1,1ZWF_1 173 3
2PQY_1,6XII_1 172 3
1ZWF_1,6XII_1 95 2

Newick tree

 
[
	2PQY_1:95.74,
	[
		6XII_1:47.5,1ZWF_1:47.5
	]:48.24
]

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 \((0.85)(0.8)(\frac{280 }{\log_{20} 280}-\frac{35}{\log_{20}35})=81.1\)
Status Protein1 Protein2 d d1/2
Query variables 2PQY_1 1ZWF_1 105 59.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]