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Parikh vectors
8SPA_1 1SRI_1 1IQA_1 Letter Amino acid
6 16 13 G Glycine
1 3 10 I Isoleucine
0 3 10 K Lycine
1 0 3 M Methionine
7 2 9 F Phenylalanine
0 6 8 Y Tyrosine
4 7 10 N Asparagine
2 3 6 Q Glutamine
2 2 7 H Histidine
2 7 11 L Leucine
4 1 7 P Proline
5 9 19 S Serine
7 19 8 T Threonine
1 6 3 W Tryptophan
0 0 1 C Cysteine
1 5 5 E Glutamic acid
4 7 9 V Valine
0 4 4 R Arginine
1 4 8 D Aspartic acid
1 17 9 A Alanine 

8SPA_1|Chains A, B, C, D, E|Cytoplasmic polyadenylation element-binding protein 3|Homo sapiens (9606)
>1SRI_1|Chains A, B|STREPTAVIDIN|Streptomyces avidinii (1895)
>1IQA_1|Chains A, B, C|RECEPTOR ACTIVATOR OF NUCLEAR FACTOR KAPPA B LIGAND|Mus musculus (10090)
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 \(w=f(c)\)
8SPA , Knot 29 49 0.76 32 40 47 
LSPSFGSTWSTGTTNAVEDSFFQGITPVNGTMLFQNFPHHVNPVFGGTF
1SRI , Knot 56 121 0.74 36 83 114 
AEAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTSGTTEANAWKSTLVGHDTFTKV
1IQA , Knot 80 160 0.84 40 127 154 
GKPEAQPFAHLTINAASIPSGSHKVTLSSWYHDRGWAKISNMTLSNGKLRVNQDGFYYLYANICFRHHETSGSVPTDYLQLMVYVVKTSIKIPSSHNLMKGGSTKNWSGNSEFHFYSINVGGFFKLRAGEEISIQVSNPSLLDPDQDATYFGAFKVQDID

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 \(c\).

\(|P_{f(8SPA_1)}(2) \setminus P_{f(1SRI_1)}(2)|=26\), \(|P_{f(1SRI_1)}(2) \setminus P_{f(8SPA_1)}(2)|=69\). 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 1:1010110010010001100011011011010111001100101111101
Pair \(Z_2\) Length of longest common subsequence
8SPA_1,1SRI_1 95 3
8SPA_1,1IQA_1 141 3
1SRI_1,1IQA_1 146 3

Newick tree

 
[
	1IQA_1:78.19,
	[
		8SPA_1:47.5,1SRI_1:47.5
	]:30.69
]

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 \((0.85)(0.8)(\frac{170 }{\log_{20} 170}-\frac{49}{\log_{20}49})=41.7\)
Status Protein1 Protein2 d d1/2
Query variables 8SPA_1 1SRI_1 48 34
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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