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Parikh vectors
6CQQ_1 2LJJ_1 5EIM_1 Letter Amino acid
8 5 13 A Alanine
15 0 5 F Phenylalanine
13 0 6 T Threonine
19 0 10 E Glutamic acid
7 7 9 G Glycine
9 0 11 K Lycine
6 0 18 S Serine
4 0 3 W Tryptophan
4 0 7 Y Tyrosine
8 0 11 R Arginine
9 0 8 N Asparagine
12 0 10 D Aspartic acid
3 0 3 Q Glutamine
15 0 8 L Leucine
3 0 7 M Methionine
2 10 3 C Cysteine
6 0 5 H Histidine
9 0 15 I Isoleucine
13 0 2 P Proline
17 0 9 V Valine 

6CQQ_1|Chains A, F|HLA class II histocompatibility antigen, DR alpha chain|Homo sapiens (9606)
>2LJJ_1|Chain A|IV-B RNA|null
>5EIM_1|Chains A, B|YTH domain-containing protein mmi1|Schizosaccharomyces pombe 972h- (284812)
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 \(w=f(c)\)
6CQQ , Knot 86 182 0.82 40 141 178 
IKEEHVIIQAEFYLNPDQSGEFMFDFDGDEIFHVDMAKKETVWRLEEFGRFASFEAQGALANIAVDKANLEIMTKRSNYTPITNVPPEVTVLTNSPVELREPNVLICFIDKFTPPVVNVTWLRNGKPVTTGVSETVFLPREDHLFRKFHYLPFLPSTEDVYDCRVEHWGLDEPLLKHWEFDT
2LJJ , Knot 11 27 0.44 8 11 23 
GGCCUCAGCACUACCCCAGUGUAGGUC
5EIM , Knot 79 163 0.82 40 127 157 
NEKGERISMINPRVVLDENGISHRSRYFIMLCDNETAIAHAKKTSIWAVKKDSSKRISDAYKKASVYFIFVAQQTYNALGYAQVVSDLNSTELPFWSDSSHAGGVRIKWIKTCNLFSAEISEIVSHMDHGSEARDGMEMMYDEGSRLCTLINYAIMKRIGRDR

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 \(c\).

\(|P_{f(6CQQ_1)}(2) \setminus P_{f(2LJJ_1)}(2)|=141\), \(|P_{f(2LJJ_1)}(2) \setminus P_{f(6CQQ_1)}(2)|=11\). 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 1:10000111010101010001011101010011010110000110100110110101011110111001010110000000110011101011000110100101110110010111101011001011001100011110000110010011111000010000100111001110010100
Pair \(Z_2\) Length of longest common subsequence
6CQQ_1,2LJJ_1 152 1
6CQQ_1,5EIM_1 174 3
2LJJ_1,5EIM_1 134 3

Newick tree

 
[
	6CQQ_1:86.02,
	[
		2LJJ_1:67,5EIM_1:67
	]:19.02
]

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 \((0.85)(0.8)(\frac{209 }{\log_{20} 209}-\frac{27}{\log_{20}27})=63.0\)
Status Protein1 Protein2 d d1/2
Query variables 6CQQ_1 2LJJ_1 85 48
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]