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Parikh vectors
1YCY_1 6TFY_1 6LXY_1 Letter Amino acid
10 33 27 L Leucine
1 12 11 Q Glutamine
8 26 25 E Glutamic acid
0 6 5 C Cysteine
5 25 19 I Isoleucine
2 8 12 F Phenylalanine
3 18 20 S Serine
0 13 9 Y Tyrosine
2 8 14 N Asparagine
6 21 21 D Aspartic acid
8 21 20 G Glycine
6 23 22 K Lycine
2 6 1 W Tryptophan
1 21 22 A Alanine
1 17 10 R Arginine
0 18 9 P Proline
2 12 17 T Threonine
8 22 21 V Valine
2 9 9 H Histidine
4 14 11 M Methionine 

1YCY_1|Chains A, B, C, D|Conserved hypothetical protein|Pyrococcus furiosus (2261)
>6TFY_1|Chains A, B|Epidermal growth factor receptor|Homo sapiens (9606)
>6LXY_1|Chains A, B, C[auth D], D[auth E]|Interleukin-1 receptor-associated kinase 4|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 \(w=f(c)\)
1YCY , Knot 38 71 0.76 34 58 67 
MGMESLLEKVLKEWKGHKVAVSVGGDHSFTGTLEDFDEEVILLKDVVDVIGNRGKQMLIGLEDINWIMLLE
6TFY , Knot 148 333 0.86 40 213 326 
GSHMASGEAPNQALLRILKETEFKKIKVLGSGAFGTVYKGLWIPEGEKVKIPVAIKELREATSPKANKEILDEAYVMASVDNPHVCRLLGICLTSTVQLIMQLMPFGCLLDYVREHKDNIGSQYLLNWCVQIAKGMNYLEDRRLVHRDLAARNVLVKTPQHVKITDFGLAKLLGAEEKEYHAEGGKVPIKWMALESILHRIYTHQSDVWSYGVTVWELMTFGSKPYDGIPASEISSILEKGERLPQPPICTIDVYMIMRKCWMIDADSRPKFRELIIEFSKMARDPQRYLVIQGDERMHLPSPTDSNFYRALMDEEDMDDVVDADEYLIPQQG
6LXY , Knot 134 305 0.83 40 192 292 
GAMGVSDTRFHSFSFYELKNVTNNFDERPISVGGNKMGEGGFGVVYKGYVNNTTVAVKKLAAMVDITTEELKQQFDQEIKVMAKCQHENLVELLGFSSDGDDLCLVYVYMPNGSLLDRLSCLDGTPPLSWHMRCKIAQGAANGINFLHENHHIHRDIKSANILLDEAFTAKISDFGLARASEKFAQTVMTSRIVGTTAYMAPEALRGEITPKSDIYSFGVVLLEIITGLPAVDEHREPQLLLDIKEEIEDEEKTIEDYIDKKMNDADSTSVEAMYSVASQCLHEKKNKRPDIKKVQQLLQEMTAS

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 \(c\).

\(|P_{f(1YCY_1)}(2) \setminus P_{f(6TFY_1)}(2)|=25\), \(|P_{f(6TFY_1)}(2) \setminus P_{f(1YCY_1)}(2)|=180\). 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 1:11100110011001010011101110001010100100011110011011100100111110010111110
Pair \(Z_2\) Length of longest common subsequence
1YCY_1,6TFY_1 205 4
1YCY_1,6LXY_1 178 4
6TFY_1,6LXY_1 161 5

Newick tree

 
[
	1YCY_1:10.62,
	[
		6LXY_1:80.5,6TFY_1:80.5
	]:20.12
]

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 \((0.85)(0.8)(\frac{404 }{\log_{20} 404}-\frac{71}{\log_{20}71})=103.\)
Status Protein1 Protein2 d d1/2
Query variables 1YCY_1 6TFY_1 136 81
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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