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Parikh vectors
2MER_1 6DJL_1 5XDH_1 Letter Amino acid
0 15 3 E Glutamic acid
5 12 10 G Glycine
0 5 1 H Histidine
0 17 7 L Leucine
0 6 4 P Proline
0 15 6 T Threonine
0 14 10 D Aspartic acid
0 7 5 Q Glutamine
0 4 2 M Methionine
0 7 4 F Phenylalanine
0 17 5 S Serine
0 8 2 Y Tyrosine
5 16 4 A Alanine
0 15 2 R Arginine
5 2 2 C Cysteine
0 15 1 I Isoleucine
0 12 9 K Lycine
0 2 0 W Tryptophan
0 17 5 V Valine
0 13 4 N Asparagine 

2MER_1|Chain A|RNA_(5'-R(P*GP*GP*CP*CP*GP*(PSU)P*AP*AP*CP*(PSU)P*AP*(PSU)P*AP*AP*CP*GP*GP*UP*C)-3')|
>6DJL_1|Chains A, F, G, H|Ras-related protein Rab-11A|Homo sapiens (9606)
>5XDH_1|Chains A, B, C, D|Putative cytochrome c|Candidatus Jettenia caeni (247490)
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 \(w=f(c)\)
2MER , Knot 9 19 0.46 8 11 15 
GGCCGUAACUAUAACGGUC
6DJL , Knot 102 219 0.83 40 158 215 
GSHMGTRDDEYDYLFKVVLIGDSGVGKSNLLSRFTRNEFNLESKSTIGVEFATRSIQVDGKTIKAQIWDTAGLERYRAITSAYYRGAVGALLVYDIAKHLTYENVERWLKELRDHADSNIVIMLVGNKSDLRHLRAVPTDEARAFAEKNGLSFIETSALDSTNVEAAFQTILTEIYRIVSQKQMSDRRENDMSPSNNVVPIHVPPTTENKPKVQCCQNI
5XDH , Knot 47 86 0.81 38 75 84 
GDIQKTYKDTCELCHGADGKGSEAGKQFGVPDFTSPDYQKSRTDAQMKESMTNGTKNPNFVKLSDLGVDLADLDPLVQLVRGFNGK

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 \(c\).

\(|P_{f(2MER_1)}(2) \setminus P_{f(6DJL_1)}(2)|=9\), \(|P_{f(6DJL_1)}(2) \setminus P_{f(2MER_1)}(2)|=156\). 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 1:1100101100101101100
Pair \(Z_2\) Length of longest common subsequence
2MER_1,6DJL_1 165 2
2MER_1,5XDH_1 86 1
6DJL_1,5XDH_1 149 3

Newick tree

 
[
	6DJL_1:87.30,
	[
		2MER_1:43,5XDH_1:43
	]:44.30
]

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 \((0.85)(0.8)(\frac{238 }{\log_{20} 238}-\frac{19}{\log_{20}19})=75.4\)
Status Protein1 Protein2 d d1/2
Query variables 2MER_1 6DJL_1 100 53.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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