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Parikh vectors
4FCP_1 3HGX_1 3SKZ_1 Letter Amino acid
8 10 0 R Arginine
27 9 0 E Glutamic acid
4 1 0 H Histidine
1 3 0 W Tryptophan
7 3 0 Y Tyrosine
15 19 18 A Alanine
8 1 0 N Asparagine
16 7 0 D Aspartic acid
11 4 0 Q Glutamine
6 5 0 P Proline
16 2 0 S Serine
19 3 0 T Threonine
15 5 16 G Glycine
18 6 0 L Leucine
17 3 0 K Lycine
10 3 0 F Phenylalanine
11 4 0 V Valine
0 1 17 C Cysteine
20 9 0 I Isoleucine
7 3 0 M Methionine 

4FCP_1|Chains A, B|Heat shock protein HSP 90-alpha|Homo sapiens (9606)
>3HGX_1|Chains A, B|Salicylate biosynthesis protein pchB|Pseudomonas aeruginosa (287)
>3SKZ_1|Chains A, B|RNA (68-MER)|null
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 \(w=f(c)\)
4FCP , Knot 104 236 0.80 38 157 227 
MPEETQTQDQPMEEEEVETFAFQAEIAQLMSLIINTFYSNKEIFLRELISNSSDALDKIRYESLTDPSKLDSGKELHINLIPNKQDRTLTIVDTGIGMTKADLINNLGTIAKSGTKAFMEALQAGADISMIGQFGVGFYSAYLVAEKVTVITKHNDDEQYAWESSAGGSFTVRTDTGEPMGRGTKVILHLKEDQTEYLEERRIKEIVKKHSQFIGYPITLFVEKERDKEVSDDEAE
3HGX , Knot 53 101 0.80 40 81 97 
MKTPEDCTGLADIREAIDRIDLDIVQALGRRMDYVKAASRFAASEAAIPAPERVAAMLPERARWAEENGLDAPFVEGLFAQIIHWYIAEQIKYWRQTRGAA
3SKZ , Knot 23 68 0.47 8 16 45 
GGCCUUAUACAGGGUAGCAUAAUGGGCUACUGACCCCGCCUUCAAACCUAUUUGGAGACUAUAAGGUC

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 \(c\).

\(|P_{f(4FCP_1)}(2) \setminus P_{f(3HGX_1)}(2)|=119\), \(|P_{f(3HGX_1)}(2) \setminus P_{f(4FCP_1)}(2)|=43\). 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 1:11000000001100001001110101101101110010000011100110000011001000010010010010010101110000001011001111001011001101100100111011011101011101111100101110010110000000001100011101010000101110100111010000000100001001100000111011011100000001000010
Pair \(Z_2\) Length of longest common subsequence
4FCP_1,3HGX_1 162 3
4FCP_1,3SKZ_1 167 3
3HGX_1,3SKZ_1 93 2

Newick tree

 
[
	4FCP_1:91.11,
	[
		3HGX_1:46.5,3SKZ_1:46.5
	]:44.61
]

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 \((0.85)(0.8)(\frac{337 }{\log_{20} 337}-\frac{101}{\log_{20}101})=73.3\)
Status Protein1 Protein2 d d1/2
Query variables 4FCP_1 3HGX_1 92 65
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]