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Parikh vectors
7YCI_1 1YBN_1 8DXR_1 Letter Amino acid
0 0 26 G Glycine
0 0 74 S Serine
0 0 56 V Valine
0 2 33 A Alanine
0 0 39 N Asparagine
0 0 45 D Aspartic acid
0 0 33 Q Glutamine
0 0 48 I Isoleucine
0 0 37 P Proline
0 0 25 R Arginine
4 4 17 C Cysteine
0 0 51 E Glutamic acid
0 0 67 K Lycine
0 0 35 T Threonine
0 0 22 H Histidine
0 0 114 L Leucine
0 0 22 M Methionine
0 0 43 F Phenylalanine
0 0 9 W Tryptophan
0 0 29 Y Tyrosine 

7YCI_1|Chain A[auth B]|RNA (5'-R(*CP*CP*CP*UP*CP*U)-3')|Tetrahymena (5890)
>1YBN_1|Chains A, B, C, D|5'-D(*CP*CP*CP*CP*AP*A)-3'|synthetic construct (32630)
>8DXR_1|Chains A, B, C, D, E, F, G|Volume-regulated anion channel subunit LRRC8C,Volume-regulated anion channel subunit LRRC8A|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 \(w=f(c)\)
7YCI , Knot 3 6 0.29 4 3 4 
CCCUCU
1YBN , Knot 3 6 0.29 4 3 3 
CCCCAA
8DXR , Knot 310 825 0.84 40 295 725 
MIPVTEFRQFSEQQPAFRVLKPWWDVFTDYLSVAMLMIGVFGCTLQVMQDKIICLPKRVQPAQNHSSLSNVSQAVASTTPLPPPKPSPANPITVEMKGLKTDLDLQQYSFINQMCYERALHWYAKYFPYLVLIHTLVFMLCSNFWFKFPGSSSKIEHFISILGKCFDSPWTTRALSEVSGEDSDPKPAFSKMNGSMDKKSSTVSEDVEGSLVNSQSLKSIPEKFVVDKSTAGALDKKEGEQAKALFEKVKKFRLHVEEGDILYAMYVRQTVLKVIKFLIIIAYNSALVSKVQFTVDCNVDIQDMTGYKNFSCNHTMAHLFSKLSFCYLCFVSIYGLTCLYTLYWLFYRSLREYSFEYVRQETGIDDIPDVKNDFAFMLHMIDQYDPLYSKRFAVFLSEVSENKLKQLNLNNEWTPDKLRQKLQTNAHNRLELPLIMLSGLPDTVFEITELQSLKLEIIKNVMIPATIAQLDNLQELSLHQCSVKIHSAALSFLKENLKVLSVKFDDMRELPPWMYGLRNLEELYLVGSLSHDISRNVTLESLRDLKSLKILSIKSNVSKIPQAVVDVSSHLQKMCIHNDGTKLVMLNNLKKMTNLTELELVHCDLERIPHAVFSLLSLQELDLKENNLKSIEEIVSFQHLRKLTVLKLWHNSITYIPEHIKKLTSLERLSFSHNKIEVLPSHLFLCNKIRYLDLSYNDIRFIPPEIGVLQSLQYFSITCNVESLPDELYFCKKLKTLKIGKNSLSVLSPKIGNLLFLSYLDVKGNHFEILPPELGDCRALKRAGLVVEDALFETLPSDVREQMKTEENLYFQGAAAGDYKDDDDK

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 \(c\).

\(|P_{f(7YCI_1)}(2) \setminus P_{f(1YBN_1)}(2)|=2\), \(|P_{f(1YBN_1)}(2) \setminus P_{f(7YCI_1)}(2)|=2\). 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 1:000000
Pair \(Z_2\) Length of longest common subsequence
7YCI_1,1YBN_1 4 3
7YCI_1,8DXR_1 298 1
1YBN_1,8DXR_1 296 2

Newick tree

 
[
	8DXR_1:17.47,
	[
		7YCI_1:2,1YBN_1:2
	]:16.47
]

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 \((0.85)(0.8)(\frac{12 }{\log_{20} 12}-\frac{6}{\log_{20}6})=3.01\)
Status Protein1 Protein2 d d1/2
Query variables 7YCI_1 1YBN_1 2 2
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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