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Parikh vectors
5YKW_1 3LHA_1 8TIR_1 Letter Amino acid
2 21 0 R Arginine
3 1 11 C Cysteine
11 27 0 K Lycine
4 14 0 F Phenylalanine
5 24 0 S Serine
1 1 0 W Tryptophan
6 21 8 G Glycine
9 17 5 T Threonine
4 14 0 N Asparagine
4 12 0 Q Glutamine
5 33 0 E Glutamic acid
1 17 0 H Histidine
9 26 0 I Isoleucine
3 17 0 Y Tyrosine
6 24 0 V Valine
6 11 8 A Alanine
8 17 0 D Aspartic acid
10 26 0 L Leucine
3 8 0 M Methionine
6 9 0 P Proline 

5YKW_1|Chain A|Thioredoxin-3, mitochondrial|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>3LHA_1|Chains A, B|Vacuolar protein sorting-associated protein 26B|Mus musculus (10090)
>8TIR_1|Chain A|DNA (5'-D(A*CP*CP*CP*GP*GP*AP*CP*CP*TP*GP*TP*GP*AP*CP*AP*AP*AP*TP*TP*GP*CP*CP*CP*TP*CP*AP*GP*AP*CP*GP*G)-3')|Escherichia coli (562)
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 \(w=f(c)\)
5YKW , Knot 53 106 0.77 40 88 103 
SSYTSITKLTNLTEFRNLIKQNDKLVIDFYATWCGPSKMMQPHLTKLIQAYPDVRFVKCDVDESPDIAKECEVTAMPTFVLGKDGQLIGKIIGANPTALEKGIKDL
3LHA , Knot 146 340 0.83 40 199 324 
MGSHHHHHHMGQSVEVEILLNDAESRKRAEHKTEDGKKEKYFLFYDGETVSGKVSLSLKNPNKRLEHQGIKIEFIGQIELYYDRGNHHEFVSLVKDLARPGEITQSQAFDFEFTHVEKPYESYTGQNVKLRYFLRATISRRLNDVVKEMDIVVHTLSTYPELNSSIKMEVGIEDCLHIEFEYNKSKYHLKDVIVGKIYFLSVEIKIKHMEIDIIKRETTGTGPNVYHENDTIAKYEIMDGAPVRGSSIPIRLFLAGYELTPTMRDINKKFSVRYYLNLVLIDEEERRYFKQQEVVLWRKGDIVRKSMSHQAAIASQRFEGTTSLGEVRTPGQLSDNNSRQ
8TIR , Knot 13 32 0.46 8 15 24 
ACCCGGACCTGTGACAAATTGCCCTCAGACGG

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 \(c\).

\(|P_{f(5YKW_1)}(2) \setminus P_{f(3LHA_1)}(2)|=30\), \(|P_{f(3LHA_1)}(2) \setminus P_{f(5YKW_1)}(2)|=141\). 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 1:0000010010010010011000001110101010110011010100110101010110001000101100001011101111001011101111010110011001
Pair \(Z_2\) Length of longest common subsequence
5YKW_1,3LHA_1 171 3
5YKW_1,8TIR_1 97 2
3LHA_1,8TIR_1 200 4

Newick tree

 
[
	3LHA_1:10.71,
	[
		5YKW_1:48.5,8TIR_1:48.5
	]:55.21
]

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 \((0.85)(0.8)(\frac{446 }{\log_{20} 446}-\frac{106}{\log_{20}106})=102.\)
Status Protein1 Protein2 d d1/2
Query variables 5YKW_1 3LHA_1 127 82.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]