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Parikh vectors
2MOE_1 2WVW_1 7SUK_1 Letter Amino acid
2 14 8 N Asparagine
4 29 12 T Threonine
2 14 6 Y Tyrosine
1 9 3 W Tryptophan
2 12 7 Q Glutamine
4 29 14 E Glutamic acid
6 45 16 G Glycine
1 22 11 I Isoleucine
8 26 22 K Lycine
3 22 4 P Proline
8 19 17 S Serine
5 27 8 V Valine
2 44 23 A Alanine
3 31 3 D Aspartic acid
2 7 2 C Cysteine
1 16 4 H Histidine
6 43 10 L Leucine
6 24 7 F Phenylalanine
5 27 22 R Arginine
0 12 1 M Methionine 

2MOE_1|Chain A|Methyl-CpG-binding domain protein 4|Homo sapiens (9606)
>2WVW_1|Chains A, B, C, D, E, F, G, H|RIBULOSE BISPHOSPHATE CARBOXYLASE LARGE CHAIN|SYNECHOCOCCUS ELONGATUS (269084)
>7SUK_10|Chain J[auth L8]|40S ribosomal protein S8-A|Saccharomyces cerevisiae (4932)
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 \(w=f(c)\)
2MOE , Knot 41 71 0.82 38 64 69 
GSTECRKSVPCGWERVVKQRLFGKTAGRFDVYFISPQGLKFRSKSSLANYLHKNGETSLKPEDFDFTVLSK
2WVW , Knot 195 472 0.84 40 255 445 
MPKTQSAAGYKAGVKDYKLTYYTPDYTPKDTDLLAAFRFSPQPGVPADEAGAAIAAESSTGTWTTVWTDLLTDMDRYKGKCYHIEPVQGEENSYFAFIAYPLDLFEEGSVTNILTSIVGNVFGFKAIRSLRLEDIRFPVALVKTFQGPPHGIQVERDLLNKYGRPMLGCTIKPKLGLSAKNYGRAVYECLRGGLDFTKDDENINSQPFQRWRDRFLFVADAIHKSQAETGEIKGHYLNVTAPTCEEMMKRAEFAKELGMPIIMHDFLTAGFTANTTLAKWCRDNGVLLHIHRAMHAVIDRQRNHGIHFRVLAKCLRLSGGDHLHSGTVVGKLEGDKASTLGFVDLMREDHIEADRSRGVFFTQDWASMPGVLPVASGGIHVWHMPALVEIFGDDSVLQFGGGTLGHPWGNAPGATANRVALEACVQARNEGRDLYREGGDILREAGKWSPELAAALDLWKEIKFEFETMDKL
7SUK , Knot 92 200 0.81 40 134 194 
MGISRDSRHKRSATGAKRAQFRKKRKFELGRQPANTKIGAKRIHSVRTRGGNKKYRALRIETGNFSWASEGISKKTRIAGVVYHPSNNELVRTNTLTKAAIVQIDATPFRQWFEAHYGQTLGKKKNVKEEETVAKSKNAERKWAARAASAKIESSVESQFSAGRLYACISSRPGQSGRCDGYILEGEELAFYLRRLTAKK

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 \(c\).

\(|P_{f(2MOE_1)}(2) \setminus P_{f(2WVW_1)}(2)|=12\), \(|P_{f(2WVW_1)}(2) \setminus P_{f(2MOE_1)}(2)|=203\). 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 1:10000000110110011000111001101010110101101000001100100010001010010101100
Pair \(Z_2\) Length of longest common subsequence
2MOE_1,2WVW_1 215 3
2MOE_1,7SUK_1 144 3
2WVW_1,7SUK_1 187 3

Newick tree

 
[
	2WVW_1:10.64,
	[
		2MOE_1:72,7SUK_1:72
	]:36.64
]

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 \((0.85)(0.8)(\frac{543 }{\log_{20} 543}-\frac{71}{\log_{20}71})=141.\)
Status Protein1 Protein2 d d1/2
Query variables 2MOE_1 2WVW_1 180 102.5
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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