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Parikh vectors
2FVA_1 9GVY_1 9GPM_1 Letter Amino acid
7 7 9 I Isoleucine
9 15 9 V Valine
9 14 16 K Lycine
2 6 6 F Phenylalanine
5 8 8 S Serine
0 3 4 Y Tyrosine
9 6 8 A Alanine
10 5 7 D Aspartic acid
0 3 0 C Cysteine
0 1 3 H Histidine
3 4 2 Q Glutamine
10 17 10 E Glutamic acid
4 12 6 T Threonine
1 4 2 M Methionine
0 3 6 P Proline
0 3 1 W Tryptophan
0 4 3 R Arginine
2 7 4 N Asparagine
4 9 15 G Glycine
7 10 9 L Leucine 

2FVA_1|Chain A|Acyl Carrier Protein|Spinacia oleracea (3562)
>9GVY_1|Chain A|Cellular retinoic acid-binding protein 2|Homo sapiens (9606)
>9GPM_1|Chains A, B|Peptidyl-prolyl cis-trans isomerase FKBP5|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 \(w=f(c)\)
2FVA , Knot 41 82 0.73 28 61 76 
AKKETIDKVSDIVKEKLALGADVVVTADSEFSKLGADSLDTVEIVMNLEEEFGINVDEDKAQDISTIQQAADVIEGLLEKKA
9GVY , Knot 70 141 0.82 40 113 136 
GSHMPNFSGNWKIIRSENFEELLKVLGVNVMLRKIAVAAASKYAVEIKQEGDTFYIKVSTTVYTTEINFKVGEEFEEQTVDGRPCKSLVKWESENKMVCEQKLLKGEGPKTSWTKELTNDGELILTMTADDVVCTQVFVRE
9GPM , Knot 64 128 0.80 38 103 125 
GAPATVTEQGEDITSKKDRGVLKIVKRVGNGEETPMIGDKVYVHYKGKLSNGKKFDSSHDRNEPFVFSLGKGQVIKAWDIGVATMKKGEIAHLLIKPEYAYGSAGSLPKIPSNATLFFEIELLDFKGE

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 \(c\).

\(|P_{f(2FVA_1)}(2) \setminus P_{f(9GVY_1)}(2)|=33\), \(|P_{f(9GVY_1)}(2) \setminus P_{f(2FVA_1)}(2)|=85\). 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 1:1000010010011000111110111010001001110010010111010001110100001001001001101101110001
Pair \(Z_2\) Length of longest common subsequence
2FVA_1,9GVY_1 118 3
2FVA_1,9GPM_1 116 3
9GVY_1,9GPM_1 138 3

Newick tree

 
[
	9GVY_1:66.13,
	[
		2FVA_1:58,9GPM_1:58
	]:8.13
]

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 \((0.85)(0.8)(\frac{223 }{\log_{20} 223}-\frac{82}{\log_{20}82})=46.1\)
Status Protein1 Protein2 d d1/2
Query variables 2FVA_1 9GVY_1 59 44
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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