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Parikh vectors
6SMD_1 5CXS_1 3UHK_1 Letter Amino acid
10 14 13 D Aspartic acid
6 17 3 E Glutamic acid
6 15 14 K Lycine
3 8 3 M Methionine
2 14 3 P Proline
1 1 2 W Tryptophan
7 19 18 A Alanine
0 4 1 C Cysteine
8 6 2 H Histidine
6 25 8 I Isoleucine
1 11 5 R Arginine
1 8 6 Q Glutamine
4 26 10 G Glycine
8 34 13 L Leucine
11 13 7 S Serine
8 21 9 N Asparagine
5 8 6 F Phenylalanine
4 8 6 T Threonine
1 8 4 Y Tyrosine
4 27 13 V Valine 

6SMD_1|Chain A|Acyl carrier protein|Photorhabdus luminescens (29488)
>5CXS_1|Chain A|Purine nucleoside phosphorylase|Schistosoma mansoni (6183)
>3UHK_1|Chains A, B, C, D|Globin-1|Scapharca inaequivalvis (2784303)
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 \(w=f(c)\)
6SMD , Knot 49 97 0.77 40 79 91 
GSSHHHHHHSGDPASMNNHPEVKIKTILSLFLNINIDDFNMDANLADAYDMDXTELADLAKEIEKEFGISVTKSQFSHWETGRAVLDFVSSSLNDKN
5CXS , Knot 122 287 0.80 40 165 276 
MTTPVVANYENASMAADYIKRVSNVLPDIGIICGSGLGKLIEEIEERKVIPYINIPNFPKTTVAGHVGNLVLGSVGGRKIVAMQGRLHMYEGYSNQEIALPIRVMKLLGVRVLLITNLAGGINRKLKSGDFVLIKGHINFPGLGLNNVLVGPNQDEFGPRFPDLSNAYDRLLQQLALKIAQENDFQDLVHEGVYAFNGGPTYESPDESNMLLKLGCDVVGMSTVPEVIIACHCGIKVLAVSLIANNSILDAENDVSINHEKVLAVAEKRADLLQMWFKEIITRLPLD
3UHK , Knot 74 146 0.84 40 112 144 
PSVYDAAAQLTADVKKDLRDSWKVIGSDKKGNGVALMTTLFADNQETIGYFKRLGDVSQGMANDKLRGHSITLMYALQNFIDQLDNPDDLVCVVERFAVNHITRKISAAEFGKINGPIKKVLASKNFGDKYANAWAKLVAVVQAAL

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 \(c\).

\(|P_{f(6SMD_1)}(2) \setminus P_{f(5CXS_1)}(2)|=33\), \(|P_{f(5CXS_1)}(2) \setminus P_{f(6SMD_1)}(2)|=119\). 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 1:1000000000101101000101010011011101010010101011010010000110110010001110100001001001011101100010000
Pair \(Z_2\) Length of longest common subsequence
6SMD_1,5CXS_1 152 3
6SMD_1,3UHK_1 125 3
5CXS_1,3UHK_1 141 4

Newick tree

 
[
	5CXS_1:76.56,
	[
		6SMD_1:62.5,3UHK_1:62.5
	]:14.06
]

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 \((0.85)(0.8)(\frac{384 }{\log_{20} 384}-\frac{97}{\log_{20}97})=88.2\)
Status Protein1 Protein2 d d1/2
Query variables 6SMD_1 5CXS_1 106 70
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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