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Parikh vectors
5MTG_1 7LZF_1 2RAW_1 Letter Amino acid
0 9 5 I Isoleucine
0 7 3 M Methionine
0 12 11 F Phenylalanine
0 5 5 H Histidine
2 17 6 C Cysteine
0 12 4 Q Glutamine
0 17 11 L Leucine
0 3 3 W Tryptophan
0 14 7 D Aspartic acid
0 15 5 N Asparagine
0 23 19 E Glutamic acid
0 26 16 K Lycine
0 13 2 V Valine
0 22 6 R Arginine
13 21 7 G Glycine
0 10 10 P Proline
0 16 5 S Serine
11 11 7 T Threonine
0 10 0 Y Tyrosine
8 15 13 A Alanine 

5MTG_1|Chain A|UpsB-Q-1 DNA (34-MER)|Plasmodium falciparum (5833)
>7LZF_1|Chain A|Histone-lysine N-methyltransferase SETD2|Homo sapiens (9606)
>2RAW_1|Chain A|Baculoviral IAP repeat-containing protein 5|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 \(w=f(c)\)
5MTG , Knot 11 34 0.38 8 10 16 
CAGGGTTAAGGGTATAACTTTAGGGGTTAGGGTT
7LZF , Knot 126 278 0.85 40 189 269 
GETSVPPGSALVGPSCVMDDFRDPQRWKECAKQGKMPCYFDLIEENVYLTERKKNKSHRDIKRMQCECTPLSKDERAQGEIACGEDCLNRLLMIECSSRCPNGDYCSNRRFQRKQHADVEVILTEKKGWGLRAAKDLPSNTFVLEYCGEVLDHKEFKARVKEYARNKNIHYYFMALKNDEIIDATQKGNCSRFMNHSCEPNCETQKWTVNGQLRVGFFTTKLVPSGSELTFDYQFQRYGKEAQKCFCGSANCRGYLGGENRVSIRAAGGKMKKERSRK
2RAW , Knot 70 145 0.80 38 108 137 
GSHMGAPTLPPAWQPFLKDHRISTFKNWPFLEGCACTPERMAEAGFIHCPTENEPDLAQCFFCFKELEGWEPDDDPIEEHKKHSSGCAFLSVKKQFEELTLGEFLKLDRERAKNKIAKETNNKKKEFEETAKKVRRAIEQLAAMD

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 \(c\).

\(|P_{f(5MTG_1)}(2) \setminus P_{f(7LZF_1)}(2)|=2\), \(|P_{f(7LZF_1)}(2) \setminus P_{f(5MTG_1)}(2)|=181\). 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 1:0111100111110101100001111100111100
Pair \(Z_2\) Length of longest common subsequence
5MTG_1,7LZF_1 183 4
5MTG_1,2RAW_1 106 3
7LZF_1,2RAW_1 167 3

Newick tree

 
[
	7LZF_1:96.40,
	[
		5MTG_1:53,2RAW_1:53
	]:43.40
]

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 \((0.85)(0.8)(\frac{312 }{\log_{20} 312}-\frac{34}{\log_{20}34})=91.0\)
Status Protein1 Protein2 d d1/2
Query variables 5MTG_1 7LZF_1 122 65.5
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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