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Parikh vectors
7TQM_1 6BYH_1 1TAM_1 Letter Amino acid
8 2 3 H Histidine
13 17 13 K Lycine
19 5 1 F Phenylalanine
31 10 3 P Proline
19 4 11 S Serine
9 1 4 Y Tyrosine
43 8 10 A Alanine
11 7 10 Q Glutamine
31 7 10 G Glycine
3 3 2 W Tryptophan
29 11 6 V Valine
29 3 9 R Arginine
12 8 4 N Asparagine
23 19 13 E Glutamic acid
14 12 6 I Isoleucine
41 12 14 L Leucine
5 4 1 M Methionine
22 10 6 T Threonine
25 19 4 D Aspartic acid
6 3 2 C Cysteine 

7TQM_1|Chain A|Cytochrome P450|Rhodopseudomonas palustris HaA2 (316058)
>6BYH_1|Chains A, B, E[auth G]|S-phase kinase-associated protein 1|Homo sapiens (9606)
>1TAM_1|Chain A|HIV-1 MATRIX PROTEIN|HIV-1 M:B_HXB2R (11706)
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 \(w=f(c)\)
7TQM , Knot 166 393 0.84 40 206 372 
TIPHLAIDPFSLDFFDDPYPDQQTLRDAGPVVYLDKWNVYGVARYAEVHAVLNDPTTFCSSRGVGLSDFKKEKPWRPPSLILEADPPAHTRPRAVLSKVLSPATMKTIRDGFAAAADAKVDELLQRGCIDAIADLAEAYPLSVFPDAMGLKQEGREHLLPYAGLVFNAFGPPNELRQTAIERSAPHQAYVNEQCQRPNLAPGGFGACIHAFTDTGEITPDEAPLLVRSLLSAGLNTTVNGIGAAVYCLARFPGELQRLRSDPTLARNAFEEAVRFESPVQTFFRTTTREVELGGAVIGEGEKVLMFLGSANRDPRRWSDPDLYDITRKTSGHVGFGSGVHMCVGQLVARLEGEVMLSALARKVAAIDIDGPVKRRFNNTLRGLESLPVKLTPA
6BYH , Knot 78 165 0.80 40 119 157 
GAMPSIKLQSSDGEIFEVDVEIAKQSVTIKTMLEDLGMDDEGDDDPVPLPNVNAAILKKVIQWCTHHKDDPPPPEDDENKEKRTDDIPVWDQEFLKVDQGTLFELILAANYLDIKGLLDVTCKTVANMIKGKTPEEIRKTFNIKNDFTEEEEAQVRKENQWCEEK
1TAM , Knot 65 132 0.80 40 107 129 
MGARASVLSGGELDRWEKIRLRPGGKKKYKLKHIVWASRELERFAVNPGLLETSEGCRQILGQLQPSLQTGSEELRSLYNTVATLYCVHQRIEIKDTKEALDKIEEEQNKSKKKAQQAAADTGHSSQVSQNY

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 \(c\).

\(|P_{f(7TQM_1)}(2) \setminus P_{f(6BYH_1)}(2)|=130\), \(|P_{f(6BYH_1)}(2) \setminus P_{f(7TQM_1)}(2)|=43\). 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 1:011011101101011001010000100111110100101011100101011100100100001111001000011011011101011100010111001101101001001111110101001100101011101101011011101111000100011101111101111100100011000110010100000010111111110101100010101001111100110111000101111110011011101001000101100110011010011001100000010111111101001111110100010010010100100000101111011010110111010101110111001111010111000100010110011101011
Pair \(Z_2\) Length of longest common subsequence
7TQM_1,6BYH_1 173 3
7TQM_1,1TAM_1 165 4
6BYH_1,1TAM_1 154 3

Newick tree

 
[
	7TQM_1:86.88,
	[
		1TAM_1:77,6BYH_1:77
	]:9.88
]

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 \((0.85)(0.8)(\frac{558 }{\log_{20} 558}-\frac{165}{\log_{20}165})=113.\)
Status Protein1 Protein2 d d1/2
Query variables 7TQM_1 6BYH_1 142 99.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]