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Parikh vectors
5QQN_1 6RXB_1 5XSE_1 Letter Amino acid
3 4 7 M Methionine
2 3 1 W Tryptophan
16 11 22 V Valine
7 17 7 R Arginine
6 6 5 N Asparagine
10 4 10 I Isoleucine
18 26 22 L Leucine
5 6 4 Q Glutamine
6 11 8 F Phenylalanine
11 8 15 P Proline
13 13 8 T Threonine
11 10 18 G Glycine
13 7 13 K Lycine
8 13 8 S Serine
2 12 1 H Histidine
8 3 1 Y Tyrosine
13 26 34 A Alanine
12 14 10 D Aspartic acid
5 2 4 C Cysteine
9 18 10 E Glutamic acid 

5QQN_1|Chain A|Ras-related C3 botulinum toxin substrate 1|Homo sapiens (9606)
>6RXB_1|Chains A[auth B], B[auth D]|Tetracycline repressor protein class G|Acinetobacter baumannii (strain AYE) (509173)
>5XSE_1|Chains A, B, C|KHG/KDPG aldolase|Zymomonas mobilis subsp. mobilis (strain ATCC 31821 / ZM4 / CP4) (264203)
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 \(w=f(c)\)
5QQN , Knot 84 178 0.81 40 140 171 
SMQAIKCVVVGDGAVGKTCLLISYTTNAFPGEYIPTVFDNYSANVMVDGKPVNLGLWDTAGQEDYDRLRPLSYPQTDVFLICFSLVSPASFENVRAKWYPEVRHHCPNTPIILVGTKLDLRDDKDTIEKLKEKKLTPITYPQGLAMAKEIGAVKYLECSALTQRGLKTVFDEAIRAVL
6RXB , Knot 94 214 0.78 40 139 199 
MTKLDKGTVIAAALELLNEVGMDSLTTRKLAERLKVQQPALYWHFQNKRALLDALAEAMLAERHTRSLPEENEDWRVFLKENALSFRTALLSYRDGARIHAGTRPTEPNFGTAETAIRFLCAEGFCPKRAVWALRAVSHYVVGSVLEQQASDADERVPDRPDVSEQAPSSFLHDLFHELETDGMDAAFNFGLDSLIAGFERLRSSTTDHHHHHH
5XSE , Knot 96 208 0.82 40 128 201 
MRDIDSVMRLAPVMPVLVIEDIADAKPIAEALVAGGLNVLEVTLRTPCALEAIKIMKEVPGAVVGAGTVLNAKMLDQAQEAGCEFFVSPGLTADLGKHAVAQKAALLPGVANAADVMLGLDLGLDRFKFFPAENIGGLPALKSMASVFRQVRFCPTGGITPTSAPKYLENPSILCVGGSWVVPAGKPDVAKITALAKEASAFKRAAVA

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 \(c\).

\(|P_{f(5QQN_1)}(2) \setminus P_{f(6RXB_1)}(2)|=80\), \(|P_{f(6RXB_1)}(2) \setminus P_{f(5QQN_1)}(2)|=79\). 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 1:0101100111101111000111000001111001101100001011101011011110011000000101100100011110101101101001010101010000100111111001010000001001000010110010111110011110010001100011001100110111
Pair \(Z_2\) Length of longest common subsequence
5QQN_1,6RXB_1 159 4
5QQN_1,5XSE_1 136 4
6RXB_1,5XSE_1 139 3

Newick tree

 
[
	6RXB_1:76.76,
	[
		5QQN_1:68,5XSE_1:68
	]:8.76
]

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 \((0.85)(0.8)(\frac{392 }{\log_{20} 392}-\frac{178}{\log_{20}178})=63.7\)
Status Protein1 Protein2 d d1/2
Query variables 5QQN_1 6RXB_1 78 72.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]