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Parikh vectors
7FXF_1 6UUR_1 5KEE_1 Letter Amino acid
11 4 8 D Aspartic acid
9 3 12 E Glutamic acid
5 2 11 L Leucine
12 2 9 T Threonine
11 9 10 G Glycine
2 5 2 H Histidine
1 5 4 P Proline
17 4 8 V Valine
6 7 15 A Alanine
2 0 0 C Cysteine
10 6 4 S Serine
14 4 21 K Lycine
5 6 4 M Methionine
6 2 5 F Phenylalanine
2 1 1 W Tryptophan
6 5 5 R Arginine
4 7 7 N Asparagine
2 3 6 Q Glutamine
8 2 4 I Isoleucine
2 8 7 Y Tyrosine 

7FXF_1|Chain A|Fatty acid-binding protein, adipocyte|Homo sapiens (9606)
>6UUR_1|Chains A, B, C, D, E, F, G, H, I, J|Major prion protein|Homo sapiens (9606)
>5KEE_1|Chain A|Thermonuclease|Staphylococcus aureus (1280)
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 \(w=f(c)\)
7FXF , Knot 69 135 0.83 40 104 129 
GSHMCDAFVGTWKLVSSENFDDYMKEVGVGFATRKVAGMAKPNMIISVNGDVITIKSESTFKNTEISFILGQEFDEVTADDRKVKSTITLDGGVLVHVQKWDGKSTTIKRKREDDKLVVECVMKGVTSTRVYERA
6UUR , Knot 45 85 0.78 38 70 80 
GTHSQWNKPSKPKTNMKHMAGAAAAGAVVGGLGGYMLGSAMSRPIIHFGSDYEDRYYRENMHRYPNQVYYRPMDEYSNQNNFVHD
5KEE , Knot 67 143 0.77 38 103 133 
ATSTKKLHKEPATLIKAIDGDTVKKMYKGQPMTFRLLLVDTPEFNEKYGPEASAFTKKMVENAKKIEVEFDKGQRTDKYGRGLAYFYADGKMVNEALVRQGLAKVAYVYKGNNTHEQLLRKAEAQAKKEKLNIWSEDNADSGQ

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 \(c\).

\(|P_{f(7FXF_1)}(2) \setminus P_{f(6UUR_1)}(2)|=78\), \(|P_{f(6UUR_1)}(2) \setminus P_{f(7FXF_1)}(2)|=44\). 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 1:100100111101011000010001001111110001111101011101010110100000100001011110010010100001000101011111010010100001000000001110011011000010001
Pair \(Z_2\) Length of longest common subsequence
7FXF_1,6UUR_1 122 2
7FXF_1,5KEE_1 143 3
6UUR_1,5KEE_1 157 2

Newick tree

 
[
	5KEE_1:79.22,
	[
		7FXF_1:61,6UUR_1:61
	]:18.22
]

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 \((0.85)(0.8)(\frac{220 }{\log_{20} 220}-\frac{85}{\log_{20}85})=44.1\)
Status Protein1 Protein2 d d1/2
Query variables 7FXF_1 6UUR_1 57 45.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]