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Parikh vectors
9ONQ_1 5UGD_1 4JKW_1 Letter Amino acid
11 21 12 L Leucine
7 13 6 K Lycine
3 2 3 M Methionine
3 19 5 P Proline
7 16 11 S Serine
21 14 11 A Alanine
5 9 4 Q Glutamine
15 17 8 E Glutamic acid
10 13 5 T Threonine
3 24 10 V Valine
7 7 8 D Aspartic acid
6 10 4 F Phenylalanine
13 25 9 G Glycine
5 7 8 H Histidine
7 13 6 R Arginine
6 8 2 N Asparagine
0 12 2 C Cysteine
3 10 4 I Isoleucine
1 6 1 W Tryptophan
7 5 5 Y Tyrosine 

9ONQ_1|Chains A, B, C, D, E, F|Rubrerythrin|Burkholderia pseudomallei (28450)
>5UGD_1|Chain A|Plasminogen|Homo sapiens (9606)
>4JKW_1|Chain A|Butyrophilin subfamily 3 member A1|Homo sapiens (9606)
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 \(w=f(c)\)
9ONQ , Knot 67 140 0.78 38 102 135 
MAQLKGSKTEENLKYAFAGESQANRRYLYFASKADVEGQNDIAALFRSTAEGETGHAHGHLEYLEAVGDPATGLPFGTSRQNLQSAIAGETHEYTDMYPGMAKTARDEGFEEIANWFETLAKAERSHANRYTKALDGLVD
5UGD , Knot 114 251 0.83 40 171 243 
EFAPSFDCGKPQVEPKKCPGRVVGGCVAHPHSWPWQVSLRTRFGMHFCGGTLISPEWVLTAAHCLEKSPRPSSYKVILGAHQEVNLEPHVQEIEVSRLFLEPTRKDIALLKLSSPAVITDKVIPACLPSPNYVVADRTECFITGWGETQGTFGAGLLKEAQLPVIENKVCNRYEFLNGRVQSTELCAGHLAGGTDSCQGDSGGPLVCFEKDKYILQGVTSWGLGCARPNKPGVYVRVSRFVTWIEGVMRNN
4JKW , Knot 63 124 0.81 40 95 118 
SAQFSVLGPSGPILAMVGEDADLPCHLFPTMSAETMELKWVSSSLRQVVNVYADGKEVEDRQSAPYRGRTSILRDGITAGKAALRIHNVTASDSGKYLCYFQDGDFYEKALVELKVLEHHHHHH

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 \(c\).

\(|P_{f(9ONQ_1)}(2) \setminus P_{f(5UGD_1)}(2)|=52\), \(|P_{f(5UGD_1)}(2) \setminus P_{f(9ONQ_1)}(2)|=121\). 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 1:11010100000010011110001000010110010101000111110001010010101010010111011011111000001001111000000010111100100011001101100110100001000001101110
Pair \(Z_2\) Length of longest common subsequence
9ONQ_1,5UGD_1 173 3
9ONQ_1,4JKW_1 135 3
5UGD_1,4JKW_1 162 3

Newick tree

 
[
	5UGD_1:88.56,
	[
		9ONQ_1:67.5,4JKW_1:67.5
	]:21.06
]

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 \((0.85)(0.8)(\frac{391 }{\log_{20} 391}-\frac{140}{\log_{20}140})=75.7\)
Status Protein1 Protein2 d d1/2
Query variables 9ONQ_1 5UGD_1 96 74.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]