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Parikh vectors
3BQZ_1 2KIR_1 1IUF_1 Letter Amino acid
13 1 5 Y Tyrosine
9 1 8 A Alanine
2 2 11 R Arginine
23 2 5 N Asparagine
7 2 11 Q Glutamine
9 1 7 F Phenylalanine
10 2 9 S Serine
3 0 5 W Tryptophan
17 2 10 I Isoleucine
11 0 4 T Threonine
0 6 0 C Cysteine
19 0 10 E Glutamic acid
17 1 12 L Leucine
23 6 12 K Lycine
1 2 8 P Proline
7 1 5 V Valine
3 1 7 D Aspartic acid
8 2 8 G Glycine
9 0 6 H Histidine
3 2 1 M Methionine 

3BQZ_1|Chains A, B|HTH-type transcriptional regulator qacR|Staphylococcus aureus (1280)
>2KIR_1|Chain A|Designer toxin|synthetic (32630)
>1IUF_1|Chain A|centromere abp1 protein|Schizosaccharomyces pombe (4896)
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 \(w=f(c)\)
3BQZ , Knot 86 194 0.77 38 120 182 
MNLKDKILGVAKELFIKNGYNATTTGEIVKLSESSKGNLYYHFKTKENLFLEILNIEESKWQEQWKKEQIKAKTNREKFYLYNELSLTTQYYYPLQNAIIEFYTEYYKTNSINEKMNKLENKYIDAYHVIFKEGNLNGEWSINDVNAVSKIAANAVNGIVTFTHEQNINERIKLMNKFSQIFLNGLSKHHHHHH
2KIR , Knot 24 34 0.83 32 31 32 
INVKCSLPQQCIKPCKDAGMRFGKCMNKKCRCYS
1IUF , Knot 70 144 0.80 38 114 140 
GIHMGKIKRRAITEHEKRALRHYFFQLQNRSGQQDLIEWFREKFGKDISQPSVSQILSSKYSYLDNTVEKPWDVKRNRPPKYPLLEAALFEWQVQQGDDATLSGETIKRAAAILWHKIPEYQDQPVPNFSNGWLEGFRKRHILH

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 \(c\).

\(|P_{f(3BQZ_1)}(2) \setminus P_{f(2KIR_1)}(2)|=111\), \(|P_{f(2KIR_1)}(2) \setminus P_{f(3BQZ_1)}(2)|=22\). 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 1:10100011111001110010010001011010000010100010000011101101000010001000010100000010100010100000011001110100000000010001001000010100111001010101010010110011101101110100000100010110010011101100000000
Pair \(Z_2\) Length of longest common subsequence
3BQZ_1,2KIR_1 133 3
3BQZ_1,1IUF_1 156 4
2KIR_1,1IUF_1 127 3

Newick tree

 
[
	3BQZ_1:75.23,
	[
		2KIR_1:63.5,1IUF_1:63.5
	]:11.73
]

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 \((0.85)(0.8)(\frac{228 }{\log_{20} 228}-\frac{34}{\log_{20}34})=65.9\)
Status Protein1 Protein2 d d1/2
Query variables 3BQZ_1 2KIR_1 78 46.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]