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Parikh vectors
6WPQ_1 6IXZ_1 6ZJG_1 Letter Amino acid
2 19 0 N Asparagine
0 5 0 Q Glutamine
0 1 0 M Methionine
1 5 0 F Phenylalanine
0 12 0 S Serine
0 3 2 R Arginine
0 19 0 D Aspartic acid
0 1 2 C Cysteine
0 12 1 H Histidine
0 19 0 I Isoleucine
0 23 1 L Leucine
0 18 1 K Lycine
0 0 0 W Tryptophan
1 12 0 Y Tyrosine
0 5 2 A Alanine
0 16 3 E Glutamic acid
1 13 5 G Glycine
0 13 0 T Threonine
0 7 1 P Proline
1 17 0 V Valine 

6WPQ_1|Chain A|Heterogeneous nuclear ribonucleoprotein A2|Homo sapiens (9606)
>6IXZ_1|Chains A, B|Sortase family protein|Clostridium perfringens (strain SM101 / Type A) (289380)
>6ZJG_1|Chain A[auth B]|CII-C-48-CIT|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 \(w=f(c)\)
6WPQ , Knot 5 6 0.49 10 5 4 
GNYNVF
6IXZ , Knot 95 220 0.77 38 139 209 
MINNKFAVSTISDYTEKINNVKDEEVDDLIKNINKYNYDLFNGTAENQLPDYLNIHEGDVLGYIEIPSINIKLPIYYGTSVDILKKGVGVLEGTSLPVGGENTHSVLSAHTGLANQKLFTDIDKLKDGDVFYLHILKKDLAYKVNQIKVVHPDEIDELKISDDKDYVTLLTCYPYGINTERLLVRGERTDLSPSNVEQVQKEISTFNHSNENLEHHHHHH
6ZJG , Knot 11 18 0.58 18 15 16 
CEAGEPGERGLKGHRGCA

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 \(c\).

\(|P_{f(6WPQ_1)}(2) \setminus P_{f(6IXZ_1)}(2)|=1\), \(|P_{f(6IXZ_1)}(2) \setminus P_{f(6WPQ_1)}(2)|=135\). 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 1:100011
Pair \(Z_2\) Length of longest common subsequence
6WPQ_1,6IXZ_1 136 2
6WPQ_1,6ZJG_1 20 1
6IXZ_1,6ZJG_1 142 3

Newick tree

 
[
	6IXZ_1:80.06,
	[
		6WPQ_1:10,6ZJG_1:10
	]:70.06
]

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 \((0.85)(0.8)(\frac{226 }{\log_{20} 226}-\frac{6}{\log_{20}6})=78.1\)
Status Protein1 Protein2 d d1/2
Query variables 6WPQ_1 6IXZ_1 93 47.5
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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