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Parikh vectors
1BLD_1 7RNA_1 6TFN_1 Letter Amino acid
14 11 17 K Lycine
11 11 20 R Arginine
3 3 12 H Histidine
3 4 10 M Methionine
9 3 21 P Proline
12 10 18 S Serine
2 5 4 C Cysteine
16 11 25 G Glycine
5 10 16 I Isoleucine
14 11 38 L Leucine
8 7 18 F Phenylalanine
1 0 7 W Tryptophan
7 7 19 V Valine
10 3 44 A Alanine
5 10 7 N Asparagine
7 10 24 D Aspartic acid
4 1 12 Q Glutamine
10 11 22 E Glutamic acid
7 10 16 T Threonine
7 3 22 Y Tyrosine 

1BLD_1|Chain A|BASIC FIBROBLAST GROWTH FACTOR|Homo sapiens (9606)
>7RNA_1|Chains A, C|Caspase-3 subunit p17|Homo sapiens (9606)
>6TFN_1|Chains A, B, C, D, E, F, G, H, I, J|Linalool dehydratase-isomerase protein LDI|Castellaniella defragrans 65Phen (1437824)
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 \(w=f(c)\)
1BLD , Knot 75 155 0.81 40 121 151 
MAEGEITTLPALPEDGGSGAFPPGHFKDPKRLYCKNGGFFLRIHPDGRVDGVREKSDPHIKLQLQAEERGVVSIKGVSANRYLAMKEDGRLLASKSVTDECFFFERLESNNYNTYRSRKYTSWYVALKRTGQYKLGSKTGPGQKAILFLPMSAKS
7RNA , Knot 71 141 0.83 38 112 138 
DNSYKMDYPEMGLCIIINNKNFHKSTGMTSRSGTDVDAANLRETFRNLKYEVRNKNDLTREEIVELMRDVSKEDHSKRSSFVCVLLSHGEEGIIFGTNGPVDLKKITNFFRGDRCRSLTGKPKLFIIQACRGTELDCGIET
6TFN , Knot 160 372 0.84 40 221 352 
MAELPPGRLATTEDYFAQQAKQAVTPDVMAQLAYMNYIDFISPFYSRGCSFEAWELKHTPQRVIKYSIAFYAYGLASVALIDPKLRALAGHDLDIAVSKMKCKRVWGDWEEDGFGTDPIEKENIMYKGHLNLMYGLYQLVTGSRRYEAEHAHLTRIIHDEIAANPFAGIVCEPDNYFVQCNSVAYLSLWVYDRLHGTDYRAATRAWLDFIQKDLIDPERGAFYLSYHPESGAVKPWISAYTTAWTLAMVHGMDPAFSERYYPRFKQTFVEVYDEGRKARVRETAGTDDADGGVGLASAFTLLLAREMGDQQLFDQLLNHLEPPAKPSIVSASLRYEHPGSLLFDELLFLAKVHAGFGALLRMPPPAAKLAGK

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 \(c\).

\(|P_{f(1BLD_1)}(2) \setminus P_{f(7RNA_1)}(2)|=84\), \(|P_{f(7RNA_1)}(2) \setminus P_{f(1BLD_1)}(2)|=75\). 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 1:11010100111110011011111101001001000011111010101010110000010101010100011101011010001110001011100010000111001000000000000000101110001000110001110011111110100
Pair \(Z_2\) Length of longest common subsequence
1BLD_1,7RNA_1 159 3
1BLD_1,6TFN_1 176 3
7RNA_1,6TFN_1 191 3

Newick tree

 
[
	6TFN_1:95.58,
	[
		1BLD_1:79.5,7RNA_1:79.5
	]:16.08
]

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 \((0.85)(0.8)(\frac{296 }{\log_{20} 296}-\frac{141}{\log_{20}141})=47.9\)
Status Protein1 Protein2 d d1/2
Query variables 1BLD_1 7RNA_1 63 60
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]