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Parikh vectors
8TIW_1 4XEB_1 7NGR_1 Letter Amino acid
11 18 0 C Cysteine
0 12 6 Q Glutamine
0 10 15 E Glutamic acid
0 17 10 P Proline
0 45 13 S Serine
0 8 4 W Tryptophan
0 20 4 Y Tyrosine
0 10 18 R Arginine
0 22 21 L Leucine
5 51 19 T Threonine
0 29 13 D Aspartic acid
0 15 9 F Phenylalanine
0 26 13 V Valine
0 16 8 I Isoleucine
0 29 8 N Asparagine
8 51 10 G Glycine
0 7 3 H Histidine
0 9 4 K Lycine
0 7 5 M Methionine
8 34 33 A Alanine 

8TIW_1|Chain A|DNA (5'-D(*CP*CP*CP*GP*GP*AP*CP*CP*TP*GP*TP*GP*AP*CP*AP*AP*AP*TP*TP*GP*CP*CP*CP*TP*CP*AP*GP*AP*CP*GP*GP*A)-3'|Escherichia coli (562)
>4XEB_1|Chain A|Glucanase|Penicillium funiculosum (28572)
>7NGR_1|Chain A|HTH-type transcriptional regulator EthR|Mycobacterium tuberculosis (1773)
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 \(w=f(c)\)
8TIW , Knot 12 32 0.43 8 15 24 
CCCGGACCTGTGACAAATTGCCCTCAGACGGA
4XEB , Knot 176 436 0.81 40 221 410 
QQIGTYTAETHPSLSWSTCKSGGSCTTNSGAITLDANWRWVHGVNTSTNCYTGNTWNSAICDTDASCAQDCALDGADYSGTYGITTSGNSLRLNFVTGSNVGSRTYLMADNTHYQIFDLLNQEFTFTVDVSHLPCGLNGALYFVTMDADGGVSKYPNNKAGAQYGVGYCDSQCPRDLKFIAGQANVEGWTPSANNANTGIGNHGACCAELDIWEANSISEALTPHPCDTPGLSVCTTDACGGTYSSDRYAGTCDPDGCDFNPYRLGVTDFYGSGKTVDTTKPFTVVTQFVTNDGTSTGSLSEIRRYYVQNGVVIPQPSSKISGISGNVINSDYCAAEISTFGGTASFSKHGGLTNMAAGMEAGMVLVMSLWDDYAVNMLWLDSTYPTNATGTPGAARGTCATTSGDPKTVESQSGSSYVTFSDIRVGPFNSTFSGG
7NGR , Knot 97 216 0.80 38 136 207 
MTTSAASQASLPRGRRTARPSGDDRELAILATAENLLEDRPLADISVDDLAKGAGISRPTFYFYFPSKEAVLLTLLDRVVNQADMALQTLAENPADTDRENMWRTGINVFFETFGSHKAVTRAGQAARATSVEVAELWSTFMQKWIAYTAAVIDAERDRGAAPRTLPAHELATALNLMNERTLFASFAGEQPSVPEARVLDTLVHIWVTSIYGENR

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 \(c\).

\(|P_{f(8TIW_1)}(2) \setminus P_{f(4XEB_1)}(2)|=0\), \(|P_{f(4XEB_1)}(2) \setminus P_{f(8TIW_1)}(2)|=206\). 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 1:00011100010110111001000001110111
Pair \(Z_2\) Length of longest common subsequence
8TIW_1,4XEB_1 206 4
8TIW_1,7NGR_1 139 2
4XEB_1,7NGR_1 185 4

Newick tree

 
[
	4XEB_1:10.67,
	[
		8TIW_1:69.5,7NGR_1:69.5
	]:36.17
]

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 \((0.85)(0.8)(\frac{468 }{\log_{20} 468}-\frac{32}{\log_{20}32})=136.\)
Status Protein1 Protein2 d d1/2
Query variables 8TIW_1 4XEB_1 172 90.5
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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