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Parikh vectors
9CTE_1 8QOV_1 5IQK_1 Letter Amino acid
12 8 12 Q Glutamine
7 11 22 S Serine
1 6 8 Y Tyrosine
4 14 16 V Valine
10 21 33 A Alanine
15 5 11 E Glutamic acid
1 7 20 P Proline
1 0 4 W Tryptophan
8 5 13 R Arginine
0 1 6 C Cysteine
7 1 9 H Histidine
5 9 9 I Isoleucine
1 2 3 M Methionine
7 4 8 F Phenylalanine
7 4 9 N Asparagine
9 12 24 G Glycine
14 11 28 L Leucine
8 6 8 K Lycine
5 7 11 T Threonine
10 6 17 D Aspartic acid 

9CTE_1|Chain A|De novo protein|synthetic construct (32630)
>8QOV_1|Chains A, B|2-iminobutanoate/2-iminopropanoate deaminase|Capra hircus (9925)
>5IQK_1|Chains A, B|beta-lactamase Rm3|uncultured bacterium (77133)
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 \(w=f(c)\)
9CTE , Knot 61 132 0.75 38 89 114 
MGSSHHHHHHGSGENLYFQSGGTTNDEEIARKLKQTADEAIQLFQRLREIFDKGDDDSFEQVLEELEEALQKHRQLANNARKNGAPTTDLANLGNRFVQLFQRFREAWDKGDKDSLEQILEELEQVAQKVIS
8QOV , Knot 65 140 0.76 38 103 136 
GSHMSSLVRRIISTAKAPAAIGPYSQAVLVDRTIYISGQLGMDPASGQLVPGGVVEEAKQALTNIGEILKAAGCDFTNVVKATVLLADINDFSAVNDVYKQYFQSSFPARAAYQVAALPKGGRVEIEAYAVQGPLTTASL
5IQK , Knot 121 271 0.83 40 174 257 
TPGCEVCATWNADQAPFRLFGNTYYVGMKGLSSVLVTSPQGHVLIDGGLPESAPKIIANIGALGFRIEDVKLILNSHGHIDHAGGLAELQRRSNALVAASPSAALDLASGEVGPDDPQYHALPKYPPVKDMRLARDGGQFNVGPVYLTAHATPGHTPGGLSWTWQSCDGPRCLNMVYADSINAVSRPGFKFSASSEYPNALADLRHSFETLEKLPCDVLISAHPEASQLWQRLEASATGGSDAFVDPQACRAYVAAARTLLDSRLDQEKQQ

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 \(c\).

\(|P_{f(9CTE_1)}(2) \setminus P_{f(8QOV_1)}(2)|=54\), \(|P_{f(8QOV_1)}(2) \setminus P_{f(9CTE_1)}(2)|=68\). 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 1:110000000010100101001100000011001000100110110010011001000010011001001100000110010001110001101100110110010011001000010011001001100110
Pair \(Z_2\) Length of longest common subsequence
9CTE_1,8QOV_1 122 4
9CTE_1,5IQK_1 175 3
8QOV_1,5IQK_1 153 4

Newick tree

 
[
	5IQK_1:88.12,
	[
		9CTE_1:61,8QOV_1:61
	]:27.12
]

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 \((0.85)(0.8)(\frac{272 }{\log_{20} 272}-\frac{132}{\log_{20}132})=43.7\)
Status Protein1 Protein2 d d1/2
Query variables 9CTE_1 8QOV_1 56 51
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]