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Parikh vectors
7CIT_1 3MZD_1 6WQU_1 Letter Amino acid
19 34 2 G Glycine
16 4 0 H Histidine
5 12 0 M Methionine
21 23 0 S Serine
20 18 5 T Threonine
22 28 3 A Alanine
16 14 0 P Proline
25 15 0 R Arginine
21 26 0 D Aspartic acid
14 16 0 E Glutamic acid
11 16 0 F Phenylalanine
5 23 0 K Lycine
11 4 0 W Tryptophan
9 10 0 Y Tyrosine
11 22 0 N Asparagine
0 1 5 C Cysteine
5 17 0 Q Glutamine
3 20 0 I Isoleucine
23 33 0 L Leucine
24 27 0 V Valine 

7CIT_1|Chain A|Tyrosinase|Streptomyces castaneoglobisporus (79261)
>3MZD_1|Chain A|D-alanyl-D-alanine carboxypeptidase dacA|Escherichia coli (83333)
>6WQU_1|Chain A|DNA (5'-D(*AP*AP*TP*CP*TP*TP*TP*CP*CP*CP*AP*CP*GP*GP*T)-3')|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 \(w=f(c)\)
7CIT , Knot 124 281 0.83 38 178 266 
MTVRKNQATLTADEKRRFVAAVLELKRSGRYDEFVRTHNEFIMSDTDSGERTGHRSPSFLPWHRRFLLDFEQALQSVDSSVTLPYWDWSADRTVRASLWAPDFLGGTGRSTDGRVMDGPFAASTGNWPINVRVDSRTYLRRSLGGSVAELPTRAEVESVLAISAYDLPPYNSASEGFRNHLEGWRGVNLHNRVHVWVGGQMATGVSPNDPVFWLHHAYVDKLWAEWQRRHPDSAYVPTGGTPDVVDLNETMKPWNTVRPADLLDHTAYYTFDALEHHHHHH
3MZD , Knot 157 363 0.85 40 207 346 
DDLNIKTMIPGVPQIDAESYILIDYNSGKVLAEQNADVRRDPASLTKMMTSYVIGQAMKAGKFKETDLVTIGNDAWATGNPVFKGSSLMFLKPGMQVPVSQLIRGINLQSGNDACVAMADFAAGSQDAFVGLMNSYVNALGLKNTHFQTVHGLDADGQYSSARDMALIGQALIRDVPNEYSIYKEKEFTFNGIRQLNRNGLLWDNSLNVDGIKTGHTDKAGYNLVASATEGQMRLISAVMGGRTFKGREAESKKLLTWGFRFFETVNPLKVGKEFASEPVWFGDSDRASLGVDKDVYLTIPRGRMKDLKASYVLNSSELHAPLQKNQVVGTINFQLDGKTIEQRPLVVLQEIPEGNFGDPVID
6WQU , Knot 8 15 0.48 8 11 13 
AATCTTTCCCACGGT

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 \(c\).

\(|P_{f(7CIT_1)}(2) \setminus P_{f(3MZD_1)}(2)|=67\), \(|P_{f(3MZD_1)}(2) \setminus P_{f(7CIT_1)}(2)|=96\). 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 1:10100001010100000111111010001000011000001110000010001000101111000111010011001000101101010100010101111011110100001011011111001011101010000010001110110110010100111101001110001001100010110110100010111110110110100111110010100111010000100101101101011010001011001011011000100010110000000
Pair \(Z_2\) Length of longest common subsequence
7CIT_1,3MZD_1 163 4
7CIT_1,6WQU_1 181 3
3MZD_1,6WQU_1 208 2

Newick tree

 
[
	6WQU_1:10.25,
	[
		7CIT_1:81.5,3MZD_1:81.5
	]:20.75
]

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 \((0.85)(0.8)(\frac{644 }{\log_{20} 644}-\frac{281}{\log_{20}281})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 7CIT_1 3MZD_1 129 113.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]