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Parikh vectors
3HEV_1 7DTD_1 7VSQ_1 Letter Amino acid
3 6 11 R Arginine
6 15 5 E Glutamic acid
1 4 5 H Histidine
3 17 2 I Isoleucine
5 22 1 K Lycine
0 17 3 T Threonine
0 2 0 W Tryptophan
0 4 11 C Cysteine
1 2 1 M Methionine
1 3 2 Y Tyrosine
0 18 7 V Valine
1 9 15 A Alanine
1 13 6 D Aspartic acid
0 19 3 G Glycine
4 30 5 L Leucine
1 15 12 S Serine
1 12 5 N Asparagine
0 2 2 Q Glutamine
0 9 1 F Phenylalanine
0 9 5 P Proline 

3HEV_1|Chain A|alpha/beta-peptide based on the GCN4-pLI side chain sequence with an (alpha-alpha-beta) backbone and a cyclic beta-residue at position 19|null
>7DTD_1|Chain A[auth B]|Sodium channel subunit beta-4|Homo sapiens (9606)
>7VSQ_1|Chains A, B, C|Zinc finger protein CONSTANS|Arabidopsis thaliana (3702)
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 \(w=f(c)\)
3HEV , Knot 21 34 0.72 26 30 32 
XRMKXIEDKLEEIXSKXYHXENELARIKKLLXER
7DTD , Knot 103 228 0.81 40 145 214 
MPGAGDGGKAPARWLGTGLLGLFLLPVTLSLEVSVGKATDIYAVNGTEILLPCTFSSCFGFEDLHFRWTYNSSDAFKILIEGTVKNEKSDPKVTLKDDDRITLVGSTKEKMNNISIVLRDLEFSDTGKYTCHVKNPKENNLQHHATIFLQVVDRLEEVDNTVTLIILAVVGGVIGLLILILLIKKLIIFILKKTREKKKECLVSSSGNDNTENGLPGSKAEEKPPSKV
7VSQ , Knot 51 102 0.77 38 73 97 
SGSGENNRARPCDTCRSNACTVYCHADSAYLCMSCDAQVHSANRVASRHKRVRVCESCERAPAAFLCEADDASLCTACDSEVHSANPLARRHQRVPILPISG

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 \(c\).

\(|P_{f(3HEV_1)}(2) \setminus P_{f(7DTD_1)}(2)|=15\), \(|P_{f(7DTD_1)}(2) \setminus P_{f(3HEV_1)}(2)|=130\). 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 1:0010010001001000000000011010011000
Pair \(Z_2\) Length of longest common subsequence
3HEV_1,7DTD_1 145 4
3HEV_1,7VSQ_1 95 3
7DTD_1,7VSQ_1 164 3

Newick tree

 
[
	7DTD_1:85.05,
	[
		3HEV_1:47.5,7VSQ_1:47.5
	]:37.55
]

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 \((0.85)(0.8)(\frac{262 }{\log_{20} 262}-\frac{34}{\log_{20}34})=76.2\)
Status Protein1 Protein2 d d1/2
Query variables 3HEV_1 7DTD_1 94 53
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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