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Parikh vectors
3CKZ_1 6DTA_1 3DDE_1 Letter Amino acid
16 13 5 R Arginine
16 22 24 L Leucine
17 23 15 K Lycine
4 10 8 M Methionine
20 9 7 P Proline
23 15 14 T Threonine
7 12 8 Q Glutamine
26 15 15 V Valine
17 4 2 C Cysteine
40 12 11 G Glycine
6 13 10 H Histidine
24 14 15 I Isoleucine
17 15 8 F Phenylalanine
16 14 23 A Alanine
25 16 8 N Asparagine
19 20 16 D Aspartic acid
18 18 16 E Glutamic acid
47 10 17 S Serine
14 3 4 W Tryptophan
13 11 13 Y Tyrosine 

3CKZ_1|Chain A|Neuraminidase|Influenza A virus (284218)
>6DTA_1|Chain A|RNAP1|Enterobacteria phage N4 (10752)
>3DDE_1|Chains A, B|TENA/THI-4 protein, Domain of Unknown Function with a Heme Oxygenase-like Fold|Shewanella denitrificans OS217 (318161)
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 \(w=f(c)\)
3CKZ , Knot 168 385 0.86 40 221 373 
VKLAGNSSLCPINGWAVYSKDNSIRIGSKGDVFVIREPFISCSHLECRTFFLTQGALLNDKHSNGTVKDRSPHRTLMSCPVGEAPSPYNSRFESVAWSASACHDGTSWLTIGISGPDNGAVAVLKYNGIITDTIKSWRNNILRTQESECACVNGSCFTVMTDGPSNGQASYKIFKMEKGKVVKSVELDAPNYYYEECSCYPNAGEITCVCRDNWHGSNRPWVSFNQNLEYQIGYICSGVFGDNPRPNDGTGSCGPVSSNGAYGVKGFSFKYGNGVWIGRTKSTNSRSGFEMIWDPNGWTETDSSFSVKQDIVAITDWSGYSGSFVQHPELTGLDCIRPCFWVELIRGRPKESTIWTSGSSISFCGVNSDTVGWSWPDGAELPFTI
6DTA , Knot 124 269 0.86 40 187 261 
MSTIEHQMHLEKLYNKNQLLPRMRQEFEENSGIDFKAFFAHIGIDYKFGIDAMVQMALHKRADLPTLVGTLRHHCKSAQEVADNLFKMASEDCFNFDPTIDKFIVIYTISDDVQHELDSFQYPLPMVVRPKLLTKNYGTGYFTCNKSVILKKNHTDDDICLDHLNRMNKIPLSINWDVAHMVKNEWANLDKPKEGETRQEFEKRVRAFQKYDRTAHEVMGLLTQEGNKFYLTHRPDKRGRTYSQGYHVNYQGTSWNKAVLEFAEKEVID
3DDE , Knot 111 239 0.84 40 170 233 
GMSIIDLTKLEQKVATMWDSILTNSPFIHEVLDGKATKALYAIYMTETYHYTKHNAKNQALVGIMGKDLPGKYLSFCFHHAHEEAGHELMALSDIASIGFDREDVLSSKPLPATETLIAYLYWISATGNPVQRLGYSYWAENVYGYIDPVLKAIQSTLDLTPQSMKFFIAHSKIDAKHAEEVNEMLHEVCKTQEDVDSVVAVMENSLVLTARILDDVWKEYQLFQSGASDRYAFLRDNA

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 \(c\).

\(|P_{f(3CKZ_1)}(2) \setminus P_{f(6DTA_1)}(2)|=117\), \(|P_{f(6DTA_1)}(2) \setminus P_{f(3CKZ_1)}(2)|=83\). 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 1:1011100010110111100000010110010111100111000010000111001111000000101000010001100111011010000100111010100010011011101100111111000111000100100011000000010101001011001100101000110100101100101011000000000010110100100001010001110100010001101001111001010010100111000110110110100101111100000000011011101011000000101000111100101001011001010110010101110110101000011001001010110000111011011011101
Pair \(Z_2\) Length of longest common subsequence
3CKZ_1,6DTA_1 200 4
3CKZ_1,3DDE_1 189 3
6DTA_1,3DDE_1 169 3

Newick tree

 
[
	3CKZ_1:10.19,
	[
		3DDE_1:84.5,6DTA_1:84.5
	]:16.69
]

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 \((0.85)(0.8)(\frac{654 }{\log_{20} 654}-\frac{269}{\log_{20}269})=107.\)
Status Protein1 Protein2 d d1/2
Query variables 3CKZ_1 6DTA_1 134 117
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]