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Parikh vectors
6EVF_1 1XTF_1 2QGO_1 Letter Amino acid
13 11 4 Q Glutamine
34 25 4 E Glutamic acid
39 35 10 K Lycine
7 2 1 W Tryptophan
17 22 5 Y Tyrosine
13 38 10 N Asparagine
33 26 14 G Glycine
38 29 12 I Isoleucine
12 6 6 M Methionine
34 19 3 P Proline
29 22 11 S Serine
32 19 7 A Alanine
14 13 3 R Arginine
31 24 14 D Aspartic acid
11 2 2 C Cysteine
21 12 7 H Histidine
21 32 3 F Phenylalanine
29 30 4 T Threonine
47 34 14 L Leucine
34 26 7 V Valine 

6EVF_1|Chains A, B, C, D|Ferulic acid decarboxylase 1|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>1XTF_1|Chains A, B|neurotoxin BoNT/A|Clostridium botulinum (1491)
>2QGO_1|Chain A|Putative Fe-S biosynthesis protein|Lactobacillus acidophilus (272621)
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 \(w=f(c)\)
6EVF , Knot 212 509 0.86 40 260 479 
MRKLNPALEFRDFIQVLKDEDDLIEITEEIDPNLEVGAIMRKAYESHLPAPLFKNLKGASKDLFSILGCPAGLRSKEKGDHGRIAHHLGLDPKTTIKEIIDYLLECKEKEPLPPITVPVSSAPCKTHILSEEKIHLQSLPTPYLHVSDGGKYLQTYGMWILQTPDKKWTNWSIARGMVVDDKHITGLVIKPQHIRQIADSWAAIGKANEIPFALCFGVPPAAILVSSMPIPEGVSESDYVGAILGESVPVVKCETNDLMVPATSEMVFEGTLSLTDTHLEGPFGDMHGYVFKSQGHPCPLYTVKAMSYRDNAILPVSNPGLCTDETHTLIGSLVATEAKELAIESGLPILDAFMPYEAQALWLILKVDLKGLQALKTTPEEFCKKVGDIYFRTKVGFIVHEIILVADDIDIFNFKEVIWAYVTRHTPVADQMAFDDVTSFPLAPFVSQSSRSKTMKGGKCVTNCIFRQQYERSFDYITCNFEKGYPKGLVDKVNENWKRYGYKHHHHHH
1XTF , Knot 171 427 0.80 40 214 394 
PFVNKQFNYKDPVNGVDIAYIKIPNAGQMQPVKAFKIHNKIWVIPERDTFTNPEEGDLNPPPEAKQVPVSYYDSTYLSTDNEKDNYLKGVTKLFERIYSTDLGRMLLTSIVRGIPFWGGSTIDTELKVIDTNCINVIQPDGSYRSEELNLVIIGPSADIIQFECKSFGHEVLNLTRNGYGSTQYIRFSPDFTFGFEESLEVDTNPLLGAGKFATDPAVTLAHQLIHAGHRLYGIAINPNRVFKVNTNAYYEMSGLEVSFEELRTFGGHDAKFIDSLQENEFRLYYYNKFKDIASTLNKAKSIVGTTASLQYMKNVFKEKYLLSEDTSGKFSVDKLKFDKLYKMLTEIYTEDNFVKFFKVLNRKTFLNFDKAVFKINIVPKVNYTIYDGFNLRNTNLAANFNGQNTEINNMNFTKLKNFTPGHHHHHH
2QGO , Knot 66 141 0.77 40 102 132 
MSLLNIKFTDNAVDYLKRREILDKILILITDDGGGKYSIQGGSCSMGAHFSIIWLDKVDPDYPVKIANEQNVKIYTSDFDKTMLGPNMVMDYNAGSLSLSSDEGLLDGSVDIGNGAALLKANKNVQMGINRQCEGHHHHHH

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 \(c\).

\(|P_{f(6EVF_1)}(2) \setminus P_{f(1XTF_1)}(2)|=98\), \(|P_{f(1XTF_1)}(2) \setminus P_{f(6EVF_1)}(2)|=52\). 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 1:10010111010011011000001101000101010111110010000111111001011000110111011110000010010110011101000100110011000000111110111001100001100001010011010101001100100011111001000100101101111000010111101001001100111110100111110111111111100111101100000111111001111000000111110001110101010000101111010101100010101100101100000111110011100000001110111001001110011111011110010111111010101101100010010001101010001111100111110010110100111101000011100111001001111111000000001011001000110000000100100010010101110010001000100000000
Pair \(Z_2\) Length of longest common subsequence
6EVF_1,1XTF_1 150 6
6EVF_1,2QGO_1 212 6
1XTF_1,2QGO_1 172 7

Newick tree

 
[
	2QGO_1:10.69,
	[
		6EVF_1:75,1XTF_1:75
	]:27.69
]

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 \((0.85)(0.8)(\frac{936 }{\log_{20} 936}-\frac{427}{\log_{20}427})=135.\)
Status Protein1 Protein2 d d1/2
Query variables 6EVF_1 1XTF_1 174 156.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]