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Parikh vectors
5EOV_1 5QQE_1 6LWZ_1 Letter Amino acid
26 11 5 G Glycine
5 10 2 I Isoleucine
1 3 1 M Methionine
5 6 1 F Phenylalanine
7 13 1 T Threonine
27 16 5 V Valine
18 7 2 R Arginine
2 5 6 C Cysteine
3 2 1 W Tryptophan
13 8 0 S Serine
30 13 3 A Alanine
3 6 2 N Asparagine
9 9 2 E Glutamic acid
11 2 2 H Histidine
5 13 5 K Lycine
12 11 2 P Proline
11 12 3 D Aspartic acid
6 5 4 Q Glutamine
24 18 2 L Leucine
2 8 4 Y Tyrosine 

5EOV_1|Chain A|16S/23S rRNA (cytidine-2'-O)-methyltransferase TlyA|Mycobacterium tuberculosis (83331)
>5QQE_1|Chain A|Ras-related C3 botulinum toxin substrate 1|Homo sapiens (9606)
>6LWZ_1|Chains A, B|Bacteriocin|Brevibacillus sp. SKDU10 (1247872)
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 \(w=f(c)\)
5EOV , Knot 98 220 0.80 40 129 211 
MHHHHHHASGLVPRGSRGAHKLVGALEAFAIAVAGRRCLDAGASTGGFTEVLLDRGAAHVVAADVGYGQLAWSLRNDPRVVVLERTNARGLTPEAIGGRVDLVVADLSFISLATVLPALVGCASRDADIVPLVKPQFEVGKGQVGPGGVVHDPQLRARSVLAVARRAQELGWHSVGVKASPLPGPSGNVEYFLWLRTQTDRALSAKGLEDAVHRAISEGP
5QQE , Knot 84 178 0.81 40 140 171 
SMQAIKCVVVGDGAVGKTCLLISYTTNAFPGEYIPTVFDNYSANVMVDGKPVNLGLWDTAGQEDYDRLRPLSYPQTDVFLICFSLVSPASFENVRAKWYPEVRHHCPNTPIILVGTKLDLRDDKDTIEKLKEKKLTPITYPQGLAMAKEIGAVKYLECSALTQRGLKTVFDEAIRAVL
6LWZ , Knot 32 53 0.80 38 51 51 
ACVNQCPDAIDRFIVKDKGCHGVEKKYYKQVYVACMNGQHLYCRTEWGGPCQL

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 \(c\).

\(|P_{f(5EOV_1)}(2) \setminus P_{f(5QQE_1)}(2)|=67\), \(|P_{f(5QQE_1)}(2) \setminus P_{f(5EOV_1)}(2)|=78\). 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 1:1000000101111010011001111101111111100010111001110011100111011110110101110100010111100001011010111101011110101101101111111010001011111010101101011111110010101001111100100111001110101111101010011110000001101011001100110011
Pair \(Z_2\) Length of longest common subsequence
5EOV_1,5QQE_1 145 3
5EOV_1,6LWZ_1 144 2
5QQE_1,6LWZ_1 167 3

Newick tree

 
[
	5QQE_1:80.15,
	[
		5EOV_1:72,6LWZ_1:72
	]:8.15
]

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 \((0.85)(0.8)(\frac{398 }{\log_{20} 398}-\frac{178}{\log_{20}178})=65.4\)
Status Protein1 Protein2 d d1/2
Query variables 5EOV_1 5QQE_1 82 74
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]