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Parikh vectors
4CRO_1 8ZZA_1 3NNC_1 Letter Amino acid
0 28 10 F Phenylalanine
0 24 8 P Proline
0 37 11 V Valine
4 36 15 A Alanine
5 21 10 G Glycine
0 64 9 I Isoleucine
0 42 12 K Lycine
0 44 7 N Asparagine
0 30 10 Q Glutamine
0 97 9 L Leucine
0 9 1 W Tryptophan
0 28 3 Y Tyrosine
0 27 11 R Arginine
4 7 6 C Cysteine
0 72 11 E Glutamic acid
0 15 4 H Histidine
0 42 8 D Aspartic acid
0 11 10 M Methionine
0 60 11 S Serine
4 32 9 T Threonine 

4CRO_1|Chains A[auth G], B[auth H], C[auth I], D[auth J], E[auth K], F[auth L]|DNA (5'-D(*TP*AP*TP*CP*AP*CP*CP*GP*CP*GP*GP*GP*TP*GP*AP*TP*A)-3')|
>8ZZA_1|Chains A, H|Nup84|null (559292)
>3NNC_1|Chain A|CUGBP Elav-like family member 1|Homo sapiens (9606)
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 \(w=f(c)\)
4CRO , Knot 9 17 0.50 8 12 15 
TATCACCGCGGGTGATA
8ZZA , Knot 278 726 0.84 40 272 657 
MELSPTYQTERFTKFSDTLKEFKIEQNNEQNPIDPFNIIREFRSAAGQLALDLANSGDESNVISSKDWELEARFWHLVELLLVFRNADLDLDEMELHPYNSRGLFEKKLMQDNKQLYQIWIVMVWLKENTYVMERPKNVPTSKWLNSITSGGLKSCDLDFPLRENTNVLDVKDKEEDHIFFKYIYELILAGAIDEALEEAKLSDNISICMILCGIQEYLNPVIDTQIANEFNTQQGIKKHSLWRRTVYSLSQQAGLDPYERAIYSYLSGAIPNQEVLQYSDWESDLHIHLNQILQTEIENYLLENNQVGTDELILPLPSHALTVQEVLNRVASRHPSESEHPIRVLMASVILDSLPSVIHSSVEMLLDVVKGTEASNDIIDKPYLLRIVTHLAICLDIINPGSVEEVDKSKLITTYISLLKLQGLYENIPIYATFLNESDCLEACSFILSSLEDPQVRKKQIETINFLRLPASNILRRTTQRVFDETEQEYSPSNEISISFDVNNIDMHLIYGVEWLIEGKLYVDAVHSIIALSRRFLLNGRVKALEQFMERNNIGEICKNYELEKIADNISKDENEDQFLEEITQYEHLIKGIREYEEWQKSVSLLSSESNIPTLIEKLQGFSKDTFELIKTFLVDLTSSNFADSADYEILYEIRALYTPFLLMELHKKLVEAAKLLKIPKFISEALAFTSLVANENDKIYLLFQSSGKLKEYLDLVARTATLSN
3NNC , Knot 87 175 0.85 40 139 168 
SDAIKMFVGQVPRTWSEKDLRELFEQYGAVYEINVLRDRSQNPPQSKGCCFVTFYTRKAALEAQNALHNMKVLPGMHHPIQMKPADSEKNNAVEDRKLFIGMISKKCTENDIRVMFSSFGQIEECRILRGPDGLSRGCAFVTFTTRAMAQTAIKAMHQAQTMEGCSSPMVVKFAD

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 \(c\).

\(|P_{f(4CRO_1)}(2) \setminus P_{f(8ZZA_1)}(2)|=5\), \(|P_{f(8ZZA_1)}(2) \setminus P_{f(4CRO_1)}(2)|=265\). 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 1:01001001011101101
Pair \(Z_2\) Length of longest common subsequence
4CRO_1,8ZZA_1 270 3
4CRO_1,3NNC_1 141 2
8ZZA_1,3NNC_1 203 3

Newick tree

 
[
	8ZZA_1:13.76,
	[
		4CRO_1:70.5,3NNC_1:70.5
	]:61.26
]

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 \((0.85)(0.8)(\frac{743 }{\log_{20} 743}-\frac{17}{\log_{20}17})=216.\)
Status Protein1 Protein2 d d1/2
Query variables 4CRO_1 8ZZA_1 275 140.5
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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