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Parikh vectors
3CJK_1 6VRN_1 4FUV_1 Letter Amino acid
5 14 11 S Serine
2 14 14 Y Tyrosine
2 3 21 N Asparagine
8 18 14 L Leucine
2 6 2 M Methionine
5 23 10 T Threonine
6 16 21 V Valine
3 4 0 C Cysteine
2 14 7 H Histidine
2 11 7 P Proline
5 25 7 E Glutamic acid
8 11 11 K Lycine
1 9 8 F Phenylalanine
0 11 7 W Tryptophan
3 25 25 A Alanine
4 19 19 D Aspartic acid
0 18 6 Q Glutamine
1 23 7 R Arginine
6 23 28 G Glycine
3 6 8 I Isoleucine 

3CJK_1|Chain A|Copper transport protein ATOX1|Homo sapiens (9606)
>6VRN_1|Chain A|MHC class I antigen|Homo sapiens (9606)
>4FUV_1|Chain A|porin protein associated with imipenem resistance|Acinetobacter baumannii (980514)
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 \(w=f(c)\)
3CJK , Knot 40 68 0.82 36 60 66 
PKHEFSVDMTCGGCAEAVSRVLNKLGGVKYDIDLPNKKVCIESEHSMDTLLATLKKTGKTVSYLGLEI
6VRN , Knot 129 293 0.83 40 191 281 
MGSHSMRYFFTSVSRPGRGEPRFIAVGYVDDTQFVRFDSDAASQRMEPRAPWIEQEGPEYWDGETRKVKAHSQTHRVDLGTLRGYYNQSEAGSHTVQRMYGCDVGSDWRFLRGYHQYAYDGKDYIALKEDLRSWTAADMAAQTTKHKWEAAHVAEQLRAYLEGTCVEWLRRYLENGKETLQRTDAPKTHMTHHAVSDHEATLRCWALSFYPAEITLTWQRDGEDQTQDTELVETRPAGDGTFQKWAAVVVPSGQEQRYTCHVQHEGLPKPLTLRWEGGGLNDIFEAQKIEWHE
4FUV , Knot 105 233 0.81 38 149 219 
DEAVVHDSYAFDKNQLIPVGARAEVGTTGYGGALLWQANPYVGLALGYNGGDISWSDDVKVNGSTYDLDMDNNNVYLNAEIRPWGASTNRWAQGLYVAAGAAYLDNDYDLTRNVDATRSFRVNNQDFIAGADGVKINGQMSYKNDIAPYLGFGFAPKINKNWGVFGEVGAYYTGNPTVKLVSSGSAVTTGDQSLEEAVNAEARKIANDDKYKWLPVGKVGVNFFWGGHHHHHH

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 \(c\).

\(|P_{f(3CJK_1)}(2) \setminus P_{f(6VRN_1)}(2)|=21\), \(|P_{f(6VRN_1)}(2) \setminus P_{f(3CJK_1)}(2)|=152\). 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 1:10001010100110101100110011110001011000101000001001110100010010011101
Pair \(Z_2\) Length of longest common subsequence
3CJK_1,6VRN_1 173 3
3CJK_1,4FUV_1 143 3
6VRN_1,4FUV_1 172 3

Newick tree

 
[
	6VRN_1:90.63,
	[
		3CJK_1:71.5,4FUV_1:71.5
	]:19.13
]

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 \((0.85)(0.8)(\frac{361 }{\log_{20} 361}-\frac{68}{\log_{20}68})=92.0\)
Status Protein1 Protein2 d d1/2
Query variables 3CJK_1 6VRN_1 116 70
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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