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Parikh vectors
6XNV_1 2COF_1 1VPI_1 Letter Amino acid
11 4 10 D Aspartic acid
13 8 8 E Glutamic acid
8 10 11 G Glycine
17 14 5 L Leucine
2 3 10 Y Tyrosine
18 7 5 V Valine
4 1 7 T Threonine
5 4 6 Q Glutamine
14 5 2 H Histidine
12 1 5 I Isoleucine
5 1 1 M Methionine
3 5 1 P Proline
10 20 5 S Serine
0 3 1 W Tryptophan
7 3 10 A Alanine
8 5 5 R Arginine
9 4 8 N Asparagine
2 2 14 C Cysteine
6 5 4 K Lycine
9 2 4 F Phenylalanine 

6XNV_1|Chains A, B|CBS domain-containing protein|Listeria monocytogenes (1639)
>2COF_1|Chain A|Protein KIAA1914|Homo sapiens (9606)
>1VPI_1|Chain A|PHOSPHOLIPASE A2 INHIBITOR|Vipera ammodytes (8704)
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 \(w=f(c)\)
6XNV , Knot 75 163 0.78 38 116 154 
MGSSHHHHHHSSGMISNRFGQFIDNELADSMISAEKVAHVQLGNNLEHALLVLTKCGYSVIPVLDFEFKLHGLISAAMITDAILGLERIEFERLEDLKVEDVMQTDFPVIKDFNNNERIVHLLVDHPFVCVVDSDHHFEGIVTRRVVLKQVNRYIHLQVEENR
2COF , Knot 52 107 0.75 40 83 101 
GSSGSSGLETSSYLNVLVNSQWKSRWCSVRDNHLHFYQDRNRSKVAQQPLSLVGCEVVPDPSPDHLYSFRILHKGEELAKLEAKSSEEMGHWLGLLLSESGSGPSSG
1VPI , Knot 65 122 0.85 40 95 119 
NLFQFGDMILQKTGKEAVHSYAIYGCYCGWGGQGRAQDATDRCCFAQDCCYGRVNDCNPKTATYTYSFENGDIVCGDNDLCLRAVCECDRAAAICLGENVNTYDKNYEYYSISHCTEESEQC

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 \(c\).

\(|P_{f(6XNV_1)}(2) \setminus P_{f(2COF_1)}(2)|=88\), \(|P_{f(2COF_1)}(2) \setminus P_{f(6XNV_1)}(2)|=55\). 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 1:1100000000001110001101100011001101001101011001001111100010011111010101011101111001111100101001001010011000111100100000110111001110110000010111000111001000101010000
Pair \(Z_2\) Length of longest common subsequence
6XNV_1,2COF_1 143 3
6XNV_1,1VPI_1 157 2
2COF_1,1VPI_1 142 3

Newick tree

 
[
	6XNV_1:76.39,
	[
		2COF_1:71,1VPI_1:71
	]:5.39
]

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 \((0.85)(0.8)(\frac{270 }{\log_{20} 270}-\frac{107}{\log_{20}107})=51.5\)
Status Protein1 Protein2 d d1/2
Query variables 6XNV_1 2COF_1 63 52
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]