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Parikh vectors
7MKT_1 4KAB_1 2NDP_1 Letter Amino acid
0 11 2 F Phenylalanine
0 21 5 S Serine
0 11 1 Y Tyrosine
0 16 17 K Lycine
0 10 2 M Methionine
0 20 5 E Glutamic acid
0 5 1 H Histidine
0 18 9 I Isoleucine
0 27 10 L Leucine
0 5 0 W Tryptophan
0 12 5 D Aspartic acid
0 10 4 Q Glutamine
12 16 4 G Glycine
0 15 3 P Proline
0 13 10 T Threonine
0 16 8 V Valine
0 16 8 A Alanine
0 8 0 C Cysteine
0 19 3 R Arginine
0 10 2 N Asparagine 

7MKT_1|Chain A|RNA (5'-R(*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*GP*UP*G)-3')|synthetic construct (32630)
>4KAB_1|Chains A, B|Focal adhesion kinase 1|Homo sapiens (9606)
>2NDP_1|Chains A, B|Histone-like DNA-binding superfamily protein|Mycoplasma gallisepticum S6 (1006581)
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 \(w=f(c)\)
7MKT , Knot 3 23 0.13 4 2 2 
GUGUGUGUGUGUGUGUGUGUGUG
4KAB , Knot 126 279 0.84 40 185 266 
GSPSTRDYEIQRERIELGRCIGEGQFGDVHQGIYMSPENPALAVAIKTCKNCTSDSVREKFLQEALTMRQFDHPHIVKLIGVITENPVWIIMELCTLGELRSFLQVRKYSLDLASLILYAYQLSTALAYLESKRFVHRDIAARNVLVSSNDCVKLGDFGLSRYMEDSTYYKASKGKLPIKWMAPESINFRRFTSASDVWMFGVCMWEILMHGVKPFQGVKNNDVIGRIENGERLPMPPNCPPTLYSLMTKCWAYDPSRRPRFTELKAQLSTILEEEKAQ
2NDP , Knot 50 99 0.77 36 76 96 
MAKIKSLSAAEYLKEMADETNIKVQDIRLVVTSLQKVLAKELATTGEVRLFDIGKFKLVTTKPRTGINPKTKQKIQIPAGKKIKLTVSKILTDAVDSHK

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 \(c\).

\(|P_{f(7MKT_1)}(2) \setminus P_{f(4KAB_1)}(2)|=2\), \(|P_{f(4KAB_1)}(2) \setminus P_{f(7MKT_1)}(2)|=185\). 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 1:10101010101010101010101
Pair \(Z_2\) Length of longest common subsequence
7MKT_1,4KAB_1 187 1
7MKT_1,2NDP_1 78 1
4KAB_1,2NDP_1 185 2

Newick tree

 
[
	4KAB_1:10.00,
	[
		7MKT_1:39,2NDP_1:39
	]:66.00
]

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 \((0.85)(0.8)(\frac{302 }{\log_{20} 302}-\frac{23}{\log_{20}23})=92.7\)
Status Protein1 Protein2 d d1/2
Query variables 7MKT_1 4KAB_1 125 63
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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