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Parikh vectors
2MXL_1 7NER_1 2WYO_1 Letter Amino acid
0 2 29 R Arginine
0 1 30 Q Glutamine
14 6 41 G Glycine
0 1 13 H Histidine
0 3 19 I Isoleucine
0 5 39 S Serine
0 2 25 K Lycine
0 2 25 P Proline
11 3 46 A Alanine
0 4 18 N Asparagine
0 3 27 D Aspartic acid
7 0 10 C Cysteine
0 4 37 E Glutamic acid
0 4 61 L Leucine
0 3 7 W Tryptophan
0 5 56 V Valine
0 2 24 F Phenylalanine
0 7 25 T Threonine
0 0 15 M Methionine
0 4 15 Y Tyrosine 

2MXL_1|Chain A|RNA (39-MER)|synthetic construct (32630)
>7NER_1|Chain A|v-Src SH3 domain|Gallus gallus (9031)
>2WYO_1|Chains A, B, C, D|GLUTATHIONE SYNTHETASE|TRYPANOSOMA BRUCEI (5691)
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 \(w=f(c)\)
2MXL , Knot 15 39 0.47 8 15 28 
GGAUUUGCAGGCCUACCAGAAACGGAUGGGAGUGCAGAU
7NER , Knot 35 61 0.78 36 55 58 
GGVTTFVALYDYESWIETDLSFKKGERLQIVNNTEGNWWLAHSVTTGRTGYIPSNYVAPSD
2WYO , Knot 228 562 0.85 40 258 513 
NLYFQGHMVLKLLLELGAERYAEQFAAKCHELGMVMKESAGPGRVPVPVTLQPSMISRGEFGTLCCMQPLWNEAVDNTARNFTFLRDALQETAASDVNFTGKLLNMLQEVYLSGGPFQQLMLGIFRTDYMREGVYDKMLSTTASRWKNVEINTISCSFAGLSPLITEFHQHIAAYLQVLQKARGKEDDDGVENMSWIWGKGNCRLERSVSGDVVPKAIADAVRAWVEQQKFASLRASWEQFQQNEVGSGEIHQLGVLDTAPVVLVVVQENERNTADQYALLMRVLEEHRIRFIFRTLQELHLSLKLHSISPEQPPLAVVDGHYPIAVAYFRSTYVPEDFPTDATWAARLSLERSSAIKCPSIPYHLLTFKKLQQLLCDVDRVLVPVAFCGDSDKAGLLQRHFVPQYSLNPKEVGEEAVEKVIHDVLQRPDQFVLKPQLEGGGNLLSGETMVKALKATKEGDPVTYSKVRCEYVVMSRIQFHVSTGSLLARGDVVQLERNMCSEVGIFGVILSAAKGSSVGTNGSSVLFNTFAGYTVRSKPADADDGGVMAGVAALDSLAVVP

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 \(c\).

\(|P_{f(2MXL_1)}(2) \setminus P_{f(7NER_1)}(2)|=14\), \(|P_{f(7NER_1)}(2) \setminus P_{f(2MXL_1)}(2)|=54\). 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 1:111000101110001001111101110111110101110
Pair \(Z_2\) Length of longest common subsequence
2MXL_1,7NER_1 68 2
2MXL_1,2WYO_1 261 3
7NER_1,2WYO_1 229 3

Newick tree

 
[
	2WYO_1:14.38,
	[
		2MXL_1:34,7NER_1:34
	]:10.38
]

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 \((0.85)(0.8)(\frac{100 }{\log_{20} 100}-\frac{39}{\log_{20}39})=22.5\)
Status Protein1 Protein2 d d1/2
Query variables 2MXL_1 7NER_1 33 23.5
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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