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Parikh vectors
5WTE_1 1EQB_1 1GDV_1 Letter Amino acid
2 3 2 C Cysteine
8 14 3 Q Glutamine
5 13 1 H Histidine
23 31 5 L Leucine
11 29 6 K Lycine
8 12 3 M Methionine
27 17 4 S Serine
4 3 1 W Tryptophan
12 14 1 R Arginine
12 29 5 E Glutamic acid
13 21 4 I Isoleucine
11 19 2 Y Tyrosine
13 18 9 N Asparagine
16 21 8 D Aspartic acid
17 36 5 V Valine
17 19 2 P Proline
27 18 3 T Threonine
15 47 12 A Alanine
21 41 7 G Glycine
16 12 2 F Phenylalanine 

5WTE_1|Chain A|VP1|Hepatovirus A (12092)
>1EQB_1|Chains A, B, C, D|SERINE HYDROXYMETHYLTRANSFERASE|Escherichia coli (562)
>1GDV_1|Chain A|CYTOCHROME C6|Porphyra yezoensis (2788)
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 \(w=f(c)\)
5WTE , Knot 122 278 0.82 40 184 267 
VGDDSGGFSTTVSTEQNVPDPQVGITTMRDLKGKANRGKMDVSGVQAPVGAITTIEDPVLAKKVPETFPELKPGESRHTSDHMSIYKFMGRSHFLCTFTFNSNNKEYTFPITLSSTSNPPHGLPSTLRWFFNLFQLYRGPLDLTIIITGATDVDGMAWFTPVGLAVDTPWVEKESALQIDYKTALGAVRFNTRRTGNIQIRLPWYSYLYAVSGALDGLGDKTDSTFGLVSIQIANYNHSDEYLSFSCYLSVTEQSEFYFPRAPLNSNAMLSTESMMSR
1EQB , Knot 177 417 0.85 40 217 399 
MLKREMNIADYDAELWQAMEQEKVRQEEHIELIASENYTSPRVMQAQGSQLTNKYAEGYPGKRYFGGCEYVDIVEQLAIDRAKELFGADYANVQPHSGSQANFAVYTALLEPGDTVLGMNLAHGGHLTHGSPVNFSGKLYNIVPYGIDATGHIDYADLEKQAKEHKPKMIIGGFSAYSGVVDWAKMREIADSIGAYLFVDMAHVAGLVAAGVYPNPVPHAHVVTTTTHKTLAGPRGGLILAKGGSEELYKKLNSAVFPGGQGGPLMHVIAGKAVALKEAMEPEFKTYQQQVAKNAKAMVEVFLERGYKVVSGGTDNHLFLVDLVDKNLTGKEADAALGRANITVNKNSVPNDPKSPFVTSGIRVGTPAITRRGFKEAEAKELAGWMCDVLDSINDEAVIERIKGKVLDICARYPVYA
1GDV , Knot 48 85 0.83 40 72 83 
ADLDNGEKVFSANCAACHAGGNNAIMPDKTLKKDVLEANSMNTIDAITYQVQNGKNAMPAFGGRLVDEDIEDAANYVLSQSEKGW

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 \(c\).

\(|P_{f(5WTE_1)}(2) \setminus P_{f(1EQB_1)}(2)|=70\), \(|P_{f(1EQB_1)}(2) \setminus P_{f(5WTE_1)}(2)|=103\). 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 1:11000111000100000110101110010010101001010101101111110010011110011001101011000000001010011100011001010000000011101000001101110010111011010011101011101100101111101111110011100001101000011111010000010101011100010110111011100000011110101100000000101000101000001011011100011100001100
Pair \(Z_2\) Length of longest common subsequence
5WTE_1,1EQB_1 173 4
5WTE_1,1GDV_1 166 3
1EQB_1,1GDV_1 185 3

Newick tree

 
[
	1EQB_1:91.62,
	[
		5WTE_1:83,1GDV_1:83
	]:8.62
]

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 \((0.85)(0.8)(\frac{695 }{\log_{20} 695}-\frac{278}{\log_{20}278})=115.\)
Status Protein1 Protein2 d d1/2
Query variables 5WTE_1 1EQB_1 147 122.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]