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Parikh vectors
7OPU_1 6SNO_1 1EXY_1 Letter Amino acid
6 5 0 W Tryptophan
36 34 0 V Valine
0 18 0 Q Glutamine
37 55 12 G Glycine
0 34 0 F Phenylalanine
15 25 0 R Arginine
13 9 0 H Histidine
0 6 11 C Cysteine
15 34 0 E Glutamic acid
6 43 0 I Isoleucine
1 13 0 M Methionine
12 26 0 P Proline
18 19 0 Y Tyrosine
24 47 6 A Alanine
24 23 0 N Asparagine
0 37 0 K Lycine
25 42 0 S Serine
12 30 0 T Threonine
12 38 0 D Aspartic acid
30 45 0 L Leucine 

7OPU_1|Chain A|SAKe6BE-3HH|synthetic construct (32630)
>6SNO_1|Chain A|Phosphoglucomutase-1|Homo sapiens (9606)
>1EXY_1|Chain A|RNA APTAMER, 33-MER|null
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 \(w=f(c)\)
7OPU , Knot 34 286 0.22 32 48 55 
GSHMNGLIYAVGGYDGNTHLNSVEAYDPERNEWSLVAPLSTRRSGVGVAVLNGLIYAVGGYDGNTHLNSVEAYDPHHNEWSLVAPLSTRRSGVGVAVLNGLIYAVGGYDGNTHLNSVEAYDPERNEWSLVAPLSTRRSGVGVAVLNGLIYAVGGYDGNTHLNSVEAYDPHHNEWSLVAPLSTRRSGVGVAVLNGLIYAVGGYDGNTHLNSVEAYDPERNEWSLVAPLSTRRSGVGVAVLNGLIYAVGGYDGNTHLNSVEAYDPHHNEWSLVAPLSTRRSGVGVAVL
6SNO , Knot 230 583 0.83 40 260 545 
GAMGSDFEEWISGTYRKMEEGPLPLLTFATAPYHDQKPGTSGLRKKTYYFEEKPCYLENFIQSIFFSIDLKDRQGSSLVVGGDGRYFNKSAIETIVQMAAANGIGRLVIGQNGILSTPAVSCIIRKIKAIGGIILTASHNPGGPNGDFGIKFNISNGGPAPEAITDKIFQISKTIEEYAVCPDLKVDLGVLGKQQFDLENKFKPFTVEIVDSVEAYATMLRSIFDFSALKELLSGPNRLKIRIDAMHGVVGPYVKKILCEELGAPANSAVNCVPLEDFGGHHPDPNLTYAADLVETMKSGEHDFGAAFDGDGDRNMILGKHGFFVNPSDSVAVIAANIFSIPYFQQTGVRGFARSMPTSGALDRVASATKIALYETPTGWKFFGNLMDASKLSLCGEESFGTGSDHIREKDGLWAVLAWLSILATRKQSVEDILKDHWQKYGRNFFTRYDYEEVEAEGANKMMKDLEALMFDRSFVGKQFSANDKVYTVEKADNFEYSDPVDGSISRNQGLRLIFTDGSRIVFRLSGTGSAGATIRLYIDSYEKDVAKINQDPQVMLAPLISIALKVSQLQERTGRTAPTVIT
1EXY , Knot 10 33 0.35 8 13 20 
GGGCGCCGGUACGCAAGUACGACGGUACGCUCC

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 \(c\).

\(|P_{f(7OPU_1)}(2) \setminus P_{f(6SNO_1)}(2)|=12\), \(|P_{f(6SNO_1)}(2) \setminus P_{f(7OPU_1)}(2)|=224\). 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 1:1001011101111001000100101001000010111110000011111110111011110010001001010010000101111100000111111101110111100100010010100100001011111000001111111011101111001000100101001000010111110000011111110111011110010001001010010000101111100000111111101110111100100010010100100001011111000001111111
Pair \(Z_2\) Length of longest common subsequence
7OPU_1,6SNO_1 236 5
7OPU_1,1EXY_1 59 2
6SNO_1,1EXY_1 263 2

Newick tree

 
[
	6SNO_1:14.25,
	[
		7OPU_1:29.5,1EXY_1:29.5
	]:11.75
]

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 \((0.85)(0.8)(\frac{869 }{\log_{20} 869}-\frac{286}{\log_{20}286})=158.\)
Status Protein1 Protein2 d d1/2
Query variables 7OPU_1 6SNO_1 217 119.5
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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