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Parikh vectors
6DFL_1 1JCG_1 5BQY_1 Letter Amino acid
25 26 17 A Alanine
35 20 20 R Arginine
30 32 26 L Leucine
5 9 3 M Methionine
16 15 10 D Aspartic acid
6 3 7 Q Glutamine
12 20 18 K Lycine
6 18 24 S Serine
21 29 23 E Glutamic acid
8 6 4 H Histidine
9 34 21 I Isoleucine
12 12 18 P Proline
6 1 8 W Tryptophan
7 4 12 Y Tyrosine
4 11 26 N Asparagine
2 0 9 C Cysteine
16 38 26 G Glycine
10 6 11 F Phenylalanine
12 24 22 T Threonine
17 36 19 V Valine 

6DFL_1|Chain A|Lipopolysaccharide core heptose(I) kinase RfaP|Pseudomonas aeruginosa (287)
>1JCG_1|Chain A|ROD SHAPE-DETERMINING PROTEIN MREB|Thermotoga maritima (2336)
>5BQY_1|Chains A, C, E|HEMAGGLUTININ HA1 CHAIN|Influenza A virus (A/chicken/Guangdong/S1312/2010(H6N2)) (1454273)
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 \(w=f(c)\)
6DFL , Knot 117 259 0.83 40 165 248 
MRLVLEEPFKRLWNGRDPFEAVEALQGKVYRELEGRRTLRTEVDGRGYFVKIHRGIGWGEIAKNLLTAKLPVLGARQEWQAIRRLHEAGVATMTAVAYGERGSDPARQHSFIVTEELAPTVDLEVFSQDWRERPPPPRLKRALVEAVARMVGDMHRAGVNHRDCYICHFLLHTDKPVSADDFRLSVIDLHRAQTRDATPKRWRNKDLAALYFSALDIGLTRRDKLRFLRTYFRRPLREILRDEAGLLAWMERKAEKLYE
1JCG , Knot 145 344 0.82 38 168 314 
MLRKDIGIDLGTANTLVFLRGKGIVVNEPSVIAIDSTTGEILKVGLEAKNMIGKTPATIKAIRPMRDGVIADYTVALVMLRYFINKAKGGMNLFKPRVVIGVPIGITDVERRAILDAGLEAGASKVFLIEEPMAAAIGSNLNVEEPSGNMVVDIGGGTTEVAVISLGSIVTWESIRIAGDEMDEAIVQYVRETYRVAIGERTAERVKIEIGNVFPSKENDELETTVSGIDLSTGLPRKLTLKGGEVREALRSVVVAIVESVRTTLEKTPPELVSDIIERGIFLTGGGSLLRGLDTLLQKETGISVIRSEEPLTAVAKGAGMVLDKVNILKKLQGAGGSHHHHHH
5BQY , Knot 143 324 0.85 40 204 311 
DKICIGYHANNSTTKVDTILEKNVTVTHSVELLENQKEERFCKISNKAPLDLRDCTLEGWILGNPRCGILLADQSWSYIVERPNARNGICYPGTLNEAEELKALIGSGERVERFEMFPKSTWTGVNTESGVSSACPLGNGPSFYRNLLWIIKLKSSEYPVIRGTFNNTGDKSILYFWGVHHPPVTTEQNALYGSGDRYVRMGTESMNFARSPEIAARPAVNGQRGRIDYFWSILKPGETLNVESNGNLIAPWYAYRFVNKDSKGAIFRSNLPIENCDATCQTTEGVIRTNKTFQNVSPLWIGECPKYVKSKSLRLATGLRNVPQ

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 \(c\).

\(|P_{f(6DFL_1)}(2) \setminus P_{f(1JCG_1)}(2)|=68\), \(|P_{f(1JCG_1)}(2) \setminus P_{f(6DFL_1)}(2)|=71\). 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 1:1011100110011010011011011010100010100010001010101101001111101100110101111110001011001001111010111010010011000011100011101010110001000111101001110111011101001110000001001110000110100101011010010000101001000011110101101110000010110001001100110001111111000100100
Pair \(Z_2\) Length of longest common subsequence
6DFL_1,1JCG_1 139 4
6DFL_1,5BQY_1 177 3
1JCG_1,5BQY_1 144 4

Newick tree

 
[
	5BQY_1:84.06,
	[
		6DFL_1:69.5,1JCG_1:69.5
	]:14.56
]

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 \((0.85)(0.8)(\frac{603 }{\log_{20} 603}-\frac{259}{\log_{20}259})=96.9\)
Status Protein1 Protein2 d d1/2
Query variables 6DFL_1 1JCG_1 113 102
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]