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Parikh vectors
7VTF_1 2QBR_1 2DPK_1 Letter Amino acid
15 27 15 E Glutamic acid
29 28 8 L Leucine
6 6 0 W Tryptophan
11 17 5 R Arginine
7 6 3 C Cysteine
11 22 4 K Lycine
27 16 12 V Valine
5 9 9 H Histidine
20 16 11 I Isoleucine
9 14 3 Q Glutamine
7 14 11 F Phenylalanine
9 12 3 P Proline
10 9 2 Y Tyrosine
26 10 6 N Asparagine
18 18 12 D Aspartic acid
8 11 1 M Methionine
26 24 10 S Serine
11 13 14 T Threonine
33 13 9 A Alanine
25 14 14 G Glycine

7VTF_1|Chains A, B, C, D|Pseudouridine kinase|Escherichia coli (562)
>2QBR_1|Chain A|Tyrosine-protein phosphatase non-receptor type 1|Homo sapiens (9606)
>2DPK_1|Chain A|Sodium/calcium exchanger 1|Canis lupus familiaris (9615)
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 \(w=f(c)\)
7VTF , Knot 140 313 0.85 40 191 299
MREKDYVVIIGSANIDVAGYSHESLNYADSNPGKIKFTPGGVGRNIAQNLALLGNKAWLLSAVGSDFYGQSLLTQTNQSGVYVDKCLIVPGENTSSYLSLLDNTGEMLVAINDMNISNAITAEYLAQHREFIQRAKVIVADCNISEEALAWILDNAANVPVFVDPVSAWKCVKVRDRLNQIHTLKPNRLEAETLSGIALSGRDDVAKVAAWFHQHGLNRLVLSMGGDGVYYSDIRGENGWSAPIKTNVINVTGAGDAMMAGLASCWVDGMPFAESVRFAQGCSSMALSCEYTNNPDLSIANVISLVENAECLN
2QBR , Knot 132 299 0.84 40 199 291
MEMEKEFEQIDKSGSWAAIYQDIRHEASDFPCRVAKLPKNKNRNRYRDVSPFDHSRIKLHQEDNDYINASLIKMEEAQRSYILTQGPLPNTCGHFWEMVWEQKSRGVVMLNRVMEKGSLKCAQYWPQKEEKEMIFEDTNLKLTLISEDIKSYYTVRQLELENLTTQETREILHFHYTTWPDFGVPESPASFLNFLFKVRESGSLSPEHGPVVVHCSAGIGRSGTFCLADTCLLLMDKRKDPSSVDIKKVLLEMRKFRMGLIQTADQLRFSYLAVIEGAKFIMGDSSVQDQWKELSHEDL
2DPK , Knot 73 152 0.80 38 105 143
MRGSHHHHHHGIPVSKIFFEQGTYQCLENCGTVALTIIRRGGDLTNTVFVDFRTEDGTANAGSDYEFTEGTVVFKPGETQKEIRVGIIDDDIFEEDENFLVHLSNVKVSSEASEDGILEANHVSALACLGSPSTATVTIFDDDHAGIFTFEE

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 \(c\).

\(|P_{f(7VTF_1)}(2) \setminus P_{f(2QBR_1)}(2)|=85\), \(|P_{f(2QBR_1)}(2) \setminus P_{f(7VTF_1)}(2)|=93\). 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 1:1000001111101010111000001001000110101011111001100111110011110111001010011000000110100011111000000101100010111110010100110100110000110010111100010001111110011011111011011001010001001001010010100101111010001101111100011001110111011000010100110111000110101110111111100110111110010110100011100000001010110110110010010
Pair \(Z_2\) Length of longest common subsequence
7VTF_1,2QBR_1 178 3
7VTF_1,2DPK_1 172 4
2QBR_1,2DPK_1 174 3

Newick tree

 
[
	2QBR_1:88.66,
	[
		7VTF_1:86,2DPK_1:86
	]:2.66
]

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 \((0.85)(0.8)(\frac{612 }{\log_{20} 612}-\frac{299}{\log_{20}299})=87.4\)
Status Protein1 Protein2 d d1/2
Query variables 7VTF_1 2QBR_1 110 108
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]