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Parikh vectors
6WXL_1 4FGN_1 6DIZ_1 Letter Amino acid
18 8 25 A Alanine
17 11 10 K Lycine
29 13 27 S Serine
9 7 12 Y Tyrosine
14 1 13 Q Glutamine
21 14 18 L Leucine
14 6 23 P Proline
23 7 26 T Threonine
3 0 4 W Tryptophan
14 4 13 D Aspartic acid
18 7 11 I Isoleucine
20 6 21 V Valine
5 6 4 H Histidine
6 2 10 M Methionine
13 11 13 F Phenylalanine
20 5 16 R Arginine
19 8 14 N Asparagine
9 3 3 C Cysteine
15 9 15 E Glutamic acid
34 4 19 G Glycine 

6WXL_1|Chains A, K[auth C], L[auth G]|Hemagglutinin HA1 chain|Influenza A virus (A/Shanghai/JS01/2013(H7N9)) (1395980)
>4FGN_1|Chains A, B|Large T antigen|Simian virus 40 (1891767)
>6DIZ_1|Chain A|VP1|Enterovirus A71 (39054)
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 \(w=f(c)\)
6WXL , Knot 138 321 0.82 40 205 311 
DKICLGHHAVSNGTKVNTLTERGVEVVNATETVERTNIPRICSKGKRTVDLGQCGLLGTITGPPQCDQFLEFSADLIIERREGSDVCYPGKFVNEEALRQILRESGGIDKEAMGFTYSGIRTNGATSSCRRSGSSFYAEMKWLLSNTDNAAFPQMTKSYKNTRKNPALIVWGIHHSGSTAEQTKLYGSGNKLVTVGSSNYQQSFVPSPGARTQVNGQSGRIDFHWLMLNPNDTVTFSFNGAFIAPDRASFLRGKSMGIQSGVQVDADCEGDCYYSGGTIISNLPFQNIDSRAVGKCPRYVKQRSLLLATGMKNVPEIPKGR
4FGN , Knot 67 132 0.82 38 109 129 
GSKVEDPKDFPSELLSFLSHAVFSNRTLACFAIYTTKEKAALLYKKIMEKYSVTFISRHNSYNHNILFFLTPHRHRVSAINNYAQKLCTFSFLICKGVNKEYLMYSALTRDPFSVIEESLPGGLKEHDFNPE
6DIZ , Knot 130 297 0.83 40 186 285 
GDRVADVIESSIGDSVSRALTQALPAPTGQNTQVSSHRLDTGEVPALQAAEIGASSNTSDESMIETRCVLNSHSTAETTLDSFFSRAGLVGEIDLPLEGTTNPNGYANWDIDITGYAQMRRKVELFTYMRFDAEFTFVACTPTGQVVPQLLQYMFVPPGAPKPESRESLAWQTATNPSVFVKLTDPPAQVSVPFMSPASAYQWFYDGYPTFGEHKQEKDLEYGACPNNMMGTFSVRTVGSSKSKYPLVVRIYMRMKHVRAWIPRPMRNQNYLFKANPNYAGNSIKPTGTSRSAITTL

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 \(c\).

\(|P_{f(6WXL_1)}(2) \setminus P_{f(4FGN_1)}(2)|=144\), \(|P_{f(4FGN_1)}(2) \setminus P_{f(6WXL_1)}(2)|=48\). 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 1:001011001100100100100011011010001000011010001000101100111101011100001101010111000010010011011000110011000111000111100011000110000000100101010111000001111010000000000111111110001001000010101001101100000001110111000101001010101111010001010101111110010110100111001101010001000001101100111001000111001001000011110110011011010
Pair \(Z_2\) Length of longest common subsequence
6WXL_1,4FGN_1 192 4
6WXL_1,6DIZ_1 179 5
4FGN_1,6DIZ_1 177 3

Newick tree

 
[
	6WXL_1:94.19,
	[
		6DIZ_1:88.5,4FGN_1:88.5
	]:5.69
]

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 \((0.85)(0.8)(\frac{453 }{\log_{20} 453}-\frac{132}{\log_{20}132})=95.8\)
Status Protein1 Protein2 d d1/2
Query variables 6WXL_1 4FGN_1 125 87
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]