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Parikh vectors
2PWV_1 2IHA_1 3UKZ_1 Letter Amino acid
17 0 8 M Methionine
20 0 15 F Phenylalanine
17 1 25 P Proline
18 0 25 Q Glutamine
10 1 15 H Histidine
27 1 55 L Leucine
32 0 13 R Arginine
22 0 38 I Isoleucine
18 1 36 V Valine
30 0 33 S Serine
8 1 6 Y Tyrosine
24 0 28 D Aspartic acid
33 1 35 G Glycine
14 1 24 K Lycine
23 0 33 E Glutamic acid
18 0 32 T Threonine
4 0 7 W Tryptophan
38 0 49 A Alanine
8 0 27 N Asparagine
5 4 6 C Cysteine 

2PWV_1|Chain A|Queuine tRNA-ribosyltransferase|Zymomonas mobilis (542)
>2IHA_1|Chain A|Lambda-conotoxin CMrVIA|synthetic construct (32630)
>3UKZ_1|Chain A[auth B]|Importin subunit alpha-2|Mus musculus (10090)
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 \(w=f(c)\)
2PWV , Knot 160 386 0.82 40 215 372 
MVEATAQETDRPRFSFSIAAREGKARTGTIEMKRGVIRTPAFMPVGTAATVKALKPETVRATGADIILGNTYHLMLRPGAERIAKLGGLHSFMGWDRPILTDSGGYQVMSLSSLTKQSEEGVTFKSHLDGSRHMLSPERSIEIQHLLGSDIVMAFDECTPYPATPSRAASSMERSMRWAKRSRDAFDSRKEQAENAALFGIQQGSVFENLRQQSADALAEIGFDGYAVGGLAVGQGQDEMFRVLDFSVPMLPDDKPHYLMGVGKPDDIVGAVERGIDMFDCVLPTRSGRNGQAFTWDGPINIRNARFSEDLKPLDSECHCAVCQKWSRAYIHHLIRAGEILGAMLMTEHNIAFYQQLMQKIRDSISEGRFSQFAQDFRARYFARNS
2IHA , Knot 9 12 0.62 18 11 10 
VCCGYKLCHPCX
3UKZ , Knot 206 510 0.84 40 248 467 
MHHHHHHSSGLVPRGSGMLETAAALFERNHMDSPDLGTDDDDLAMADIGSNQGTVNWSVEDIVKGINSNNLESQLQATQAARKLLSREKQPPIDNIIRAGLIPKFVSFLGKTDCSPIQFESAWALTNIASGTSEQTKAVVDGGAIPAFISLLASPHAHISEQAVWALGNIAGDGSAFRDLVIKHGAIDPLLALLAVPDLSTLACGYLRNLTWTLSNLCRNKNPAPPLDAVEQILPTLVRLLHHNDPEVLADSCWAISYLTDGPNERIEMVVKKGVVPQLVKLLGATELPIVTPALRAIGNIVTGTDEQTQKVIDAGALAVFPSLLTNPKTNIQKEATWTMSNITAGRQDQIQQVVNHGLVPFLVGVLSKADFKTQKEAAWAITNYTSGGTVEQIVYLVHCGIIEPLMNLLSAKDTKIIQVILDAISNIFQAAEKLGETEKLSIMIEECGGLDKIEALQRHENESVYKASLNLIEKYFSVEEEEDQNVVPETTSEGFAFQVQDGAPGTFNF

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 \(c\).

\(|P_{f(2PWV_1)}(2) \setminus P_{f(2IHA_1)}(2)|=211\), \(|P_{f(2IHA_1)}(2) \setminus P_{f(2PWV_1)}(2)|=7\). 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 1:11010100000101010111001010010101001110011111110110101101001010110111100001110111001101111001111001110001100110100100000011010001010001101000101001110011111000010110100110010001011000001100000010011111100101100100001011101110101111111101000110110101111100010011111010011111001101100111000100101101011101001010001011000000110001001010011011011111110000111000110010001001010011001010011000
Pair \(Z_2\) Length of longest common subsequence
2PWV_1,2IHA_1 218 2
2PWV_1,3UKZ_1 161 4
2IHA_1,3UKZ_1 249 3

Newick tree

 
[
	2IHA_1:12.86,
	[
		2PWV_1:80.5,3UKZ_1:80.5
	]:46.36
]

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 \((0.85)(0.8)(\frac{398 }{\log_{20} 398}-\frac{12}{\log_{20}12})=125.\)
Status Protein1 Protein2 d d1/2
Query variables 2PWV_1 2IHA_1 156 80.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]