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Parikh vectors
2GIW_1 4JRT_1 7HLX_1 Letter Amino acid
4 0 7 Y Tyrosine
6 0 8 A Alanine
2 1 4 C Cysteine
12 9 14 G Glycine
6 0 12 L Leucine
2 0 6 M Methionine
4 0 11 F Phenylalanine
3 0 10 Q Glutamine
9 0 7 E Glutamic acid
3 0 10 H Histidine
10 0 10 T Threonine
1 0 6 W Tryptophan
2 0 9 R Arginine
3 0 10 D Aspartic acid
19 0 7 K Lycine
0 0 15 S Serine
5 0 10 N Asparagine
6 0 9 I Isoleucine
4 0 9 P Proline
3 0 14 V Valine 

2GIW_1|Chain A|CYTOCHROME C|Equus caballus (9796)
>4JRT_1|Chain A|RNA (5'-R(P*GP*GP*GP*UP*GP*GP*UP*GP*CP*GP*GP*G)-3')|null
>7HLX_1|Chain A[auth B]|E3 ubiquitin-protein ligase TRIM21|Mus musculus (10090)
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 \(w=f(c)\)
2GIW , Knot 53 104 0.79 38 86 99 
GDVEKGKKIFVQKCAQCHTVEKGGKHKTGPNLHGLFGRKTGQAPGFTYTDANKNKGITWKEETLMEYLENPKKYIPGTKMIFAGIKKKTEREDLIAYLKKATNE
4JRT , Knot 4 12 0.27 6 5 7 
GGGUGGUGCGGG
7HLX , Knot 91 188 0.84 40 148 179 
MHHHHHHMVHITLDRNTANSWLIISKDRRQVRMGDTHQNVSDNKERFSNYPMVLGAQRFSSGKMYWEVDVTQKEAWDLGVCRDSVQRKGQFSLSPENGFWTIWLWQDSYEAGTSPQTTLHIQVPPCQIGIFVDYEAGVVSFYNITDHGSLIYTFSECVFAGPLRPFFNVGFNYSGGNAAPLKLCPLKM

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 \(c\).

\(|P_{f(2GIW_1)}(2) \setminus P_{f(4JRT_1)}(2)|=85\), \(|P_{f(4JRT_1)}(2) \setminus P_{f(2GIW_1)}(2)|=4\). 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 1:10100100111000100001001100001101011110001011110000100001101000011001001000111001111110000000011101001000
Pair \(Z_2\) Length of longest common subsequence
2GIW_1,4JRT_1 89 2
2GIW_1,7HLX_1 166 3
4JRT_1,7HLX_1 151 2

Newick tree

 
[
	7HLX_1:87.93,
	[
		2GIW_1:44.5,4JRT_1:44.5
	]:43.43
]

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 \((0.85)(0.8)(\frac{116 }{\log_{20} 116}-\frac{12}{\log_{20}12})=39.8\)
Status Protein1 Protein2 d d1/2
Query variables 2GIW_1 4JRT_1 52 27.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]