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Parikh vectors
6HOX_1 6YEG_1 7VYE_1 Letter Amino acid
8 2 3 M Methionine
8 9 11 P Proline
11 1 2 W Tryptophan
29 9 5 Y Tyrosine
41 7 10 L Leucine
2 0 1 C Cysteine
22 15 12 E Glutamic acid
24 22 4 G Glycine
44 11 4 I Isoleucine
35 10 4 K Lycine
39 11 4 S Serine
15 9 2 T Threonine
21 5 7 R Arginine
20 12 7 V Valine
33 13 11 D Aspartic acid
47 6 6 N Asparagine
13 12 3 Q Glutamine
9 6 1 H Histidine
20 7 6 F Phenylalanine
5 13 4 A Alanine 

6HOX_1|Chain A|Binding domain (Hc) of Paraclostridial Mosquitocidal Protein 1|Paraclostridium bifermentans (1490)
>6YEG_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|Tail tube protein gp17.1*|Bacillus phage SPP1 (10724)
>7VYE_13|Chain M[auth e]|NADH dehydrogenase [ubiquinone] 1 beta subcomplex subunit 11, mitochondrial|Sus scrofa (9823)
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 \(w=f(c)\)
6HOX , Knot 177 446 0.80 40 211 402 
HHHHHHSQDPNALIDRLGIQLKDNLVFSLGVESDKIKDLSGNNTNLEVKTGVQIVDGRDSKTIRLNSNENSSIIVQKNESINFSYFSDFTISFWIRVPRLNKNDFIDLGIEYDLVNNMDNQGWKISLKDGNLVWRMKDRFGKIIDIITSLTFSNSFIDKYISSNIWRHITITVNQLKDCTLYINGDKIDSKSINELRGIDNNSPIIFKLEGNRNKNQFIRLDQFNIYQRALNESEVEMLFNSYFNSNILRDFWGEPLEYNKSYYMINQAILGGPLRSTYKSWYGEYYPYISRMRTFNVSSFILIPYLYHKGSDVEKVKIINKNNVDKYVRKNDVADVKFENYGNLILTLPMYSKIKERYMVLNEGRNGDLKLIQLQSNDKYYCQIRIFEMYRNGLLSIADDENWLYSSGWYLYSSGWYLDNYKTLDLKKHTKTNWYFVSEDEGWKE
6YEG , Knot 86 180 0.82 38 127 171 
MPIMGQDVKYLFQSIDAATGSAPLFPAYQTDGSVSGERELFDEQTKNGRILGPGSVADSGEVTYYGKRGDAGQKAIEDAYQNGKQIKFWRVDTVKNENDKYDAQFGFAYIESREYSDGVEGAVEISISLQVIGELKNGEIDTLPEEIVNVSKGGYDFQQPGQTTGEAPGTVPAPHHHHHH
7VYE , Knot 53 107 0.77 40 84 102 
PPEPTIRLQEDPDPEDENLYEKNPDSHGYDKDPIVDLWNMRVVFFFGFSIVLVLGSTFVAYLPDYRMQEWARREAERLVKYREANGLPLMESNCFDPNKIQLPEDED

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 \(c\).

\(|P_{f(6HOX_1)}(2) \setminus P_{f(6YEG_1)}(2)|=129\), \(|P_{f(6YEG_1)}(2) \setminus P_{f(6HOX_1)}(2)|=45\). 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 1:00000000010111001110100011101110000100101000010100110110100000101000000011100000101001001010111011010000110111000110010001101010010111010001101101100101000110001000110010101001000010101001000010010110000111101010000001101001010001100001011100010001100111011000000011001111111000000101000101001001010011111010001001001011000010001000011010100010111011100010000111001001010110100000000010110100011101100001100011010001101000001010000000101100001100
Pair \(Z_2\) Length of longest common subsequence
6HOX_1,6YEG_1 174 6
6HOX_1,7VYE_1 189 4
6YEG_1,7VYE_1 147 3

Newick tree

 
[
	6HOX_1:95.91,
	[
		6YEG_1:73.5,7VYE_1:73.5
	]:22.41
]

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 \((0.85)(0.8)(\frac{626 }{\log_{20} 626}-\frac{180}{\log_{20}180})=127.\)
Status Protein1 Protein2 d d1/2
Query variables 6HOX_1 6YEG_1 153 108
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]