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Parikh vectors
4CDQ_1 1IPF_1 3EWE_1 Letter Amino acid
3 8 8 C Cysteine
13 18 20 E Glutamic acid
19 23 19 G Glycine
5 4 11 H Histidine
23 6 12 P Proline
12 10 9 Y Tyrosine
27 27 25 A Alanine
25 11 14 T Threonine
21 22 17 V Valine
14 15 13 N Asparagine
11 7 12 Q Glutamine
18 24 35 L Leucine
10 7 5 M Methionine
26 18 43 S Serine
4 3 12 W Tryptophan
16 12 15 R Arginine
11 14 18 I Isoleucine
12 12 22 K Lycine
13 9 9 F Phenylalanine
14 9 30 D Aspartic acid 

4CDQ_1|Chain A|VP1|ENTEROVIRUS A71 (39054)
>1IPF_1|Chains A, B|TROPINONE REDUCTASE-II|Datura stramonium (4076)
>3EWE_1|Chains A, C|Nucleoporin SEH1|Saccharomyces cerevisiae (4932)
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 \(w=f(c)\)
4CDQ , Knot 132 297 0.84 40 189 285 
GDRVADVIESSIGDSVSRALTHALPAPTGQNTQVSSHRLDTGKVPALQAAEIGASSNASDESMIETRCVLNSHSTAETTLDSFFSRAGLVGEIDLPLKGTTNPNGYANWDIDITGYAQMRRKVELFTYMRFDAEFTFVACTPTGEVVPQLLQYMFVPPGAPKPDSRESLAWQTATNPSVFVKLSDPPAQVSVPFMSPASAYQWFYDGYPTFGEHKQEKDLEYGACPNNMMGTFSVRTVGTSKSKYPLVVRIYMRMKHVRAWIPRPMRNQNYLFKANPNYAGNSIKPTGASRTAITTL
1IPF , Knot 116 259 0.83 40 176 249 
AGRWNLEGCTALVTGGSRGIGYGIVEELASLGASVYTCSRNQKELNDCLTQWRSKGFKVEASVCDLSSRSERQELMNTVANHFHGKLNILVNNAGIVIYKEAKDYTVEDYSLIMSINFEAAYHLSVLAHPFLKASERGNVVFISSVSGALAVPYEAVYGATKGAMDQLTRCLAFEWAKDNIRVNGVGPGVIATSLVEMTIQDPEQKENLNKLIDRCALRRMGEPKELAAMVAFLCFPAASYVTGQIIYVDGGLMANCGF
3EWE , Knot 151 349 0.84 40 205 335 
MQPFDSGHDDLVHDVVYDFYGRHVATCSSDQHIKVFKLDKDTSNWELSDSWRAHDSSIVAIDWASPEYGRIIASASYDKTVKLWEEDPDQEECSGRRWNKLCTLNDSKGSLYSVKFAPAHLGLKLACLGNDGILRLYDALEPSDLRSWTLTSEMKVLSIPPANHLQSDFCLSWCPSRFSPEKLAVSALEQAIIYQRGKDGKLHVAAKLPGHKSLIRSISWAPSIGRWYQLIATGCKDGRIRIFKITEKLSPLASEESLTNSNMFDNSADVDMDAQGRSDSNTEEKAELQSNLQVELLSEHDDHNGEVWSVSWNLTGTILSSAGDDGKVRLWKATYSNEFKCMSVITAQQ

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 \(c\).

\(|P_{f(4CDQ_1)}(2) \setminus P_{f(1IPF_1)}(2)|=112\), \(|P_{f(1IPF_1)}(2) \setminus P_{f(4CDQ_1)}(2)|=99\). 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 1:100110110001100100110011111010000100001001011110110111000100001100001100000100010011001111101011101000101010101010101010001011001010101011100101011101100111111110100000111001001011101001110101111011010011001010110000000100110100111010100110000001111010101001011110110000011010100110010101100011001
Pair \(Z_2\) Length of longest common subsequence
4CDQ_1,1IPF_1 211 3
4CDQ_1,3EWE_1 162 3
1IPF_1,3EWE_1 171 3

Newick tree

 
[
	1IPF_1:10.53,
	[
		4CDQ_1:81,3EWE_1:81
	]:19.53
]

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 \((0.85)(0.8)(\frac{556 }{\log_{20} 556}-\frac{259}{\log_{20}259})=84.2\)
Status Protein1 Protein2 d d1/2
Query variables 4CDQ_1 1IPF_1 111 103.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]