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Parikh vectors
6RBU_1 6FAP_1 5KXT_1 Letter Amino acid
19 3 2 E Glutamic acid
15 2 3 F Phenylalanine
10 2 2 P Proline
20 1 10 S Serine
19 6 6 V Valine
13 3 11 R Arginine
18 5 7 D Aspartic acid
17 3 1 H Histidine
2 1 6 W Tryptophan
12 1 3 Y Tyrosine
20 4 12 G Glycine
22 5 8 L Leucine
8 2 2 M Methionine
6 2 3 Q Glutamine
19 1 6 I Isoleucine
17 3 6 K Lycine
12 2 7 T Threonine
15 2 12 A Alanine
7 2 14 N Asparagine
1 8 8 C Cysteine 

6RBU_1|Chain A|NAD kinase 1|Listeria monocytogenes EGD-e (169963)
>6FAP_1|Chains A, B, C, D|Bromodomain adjacent to zinc finger domain protein 2A|Homo sapiens (9606)
>5KXT_1|Chain A|Lysozyme C|Gallus gallus (9031)
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 \(w=f(c)\)
6RBU , Knot 123 272 0.84 40 185 261 
MKYMITSKGDEKSDLLRLNMIAGFGEYDMEYDDVEPEIVISIGGDGTFLSAFHQYEERLDEIAFIGIHTGHLGFYADWRPAEADKLVKLLAKGEYQKVSYPLLKTTVKYGIGKKEATYLALNESTVKSSGGPFVVDVVINDIHFERFRGDGLCMSTPSGTTAYNKSLGGALMHPSIEAMQLTEMASINNRVYRTIGSPLVFPKHHVVSLQPVNDKDFQISVDHLSILHRDVQEIRYEVSAKKIHFARFRSFPFWRRVHDSFIEDLEHHHHHH
6FAP , Knot 35 58 0.81 40 50 56 
HMSVNKVTCLVCRKGDNDEFLLLCDGCDRGCHIYCHRPKMEAVPEGDWFCTVCLAQQV
5KXT , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL

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 \(c\).

\(|P_{f(6RBU_1)}(2) \setminus P_{f(6FAP_1)}(2)|=161\), \(|P_{f(6FAP_1)}(2) \setminus P_{f(6RBU_1)}(2)|=26\). 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 1:10011000100000110101111110001000010101110111010110110000001001111110010111010101101001101110100001001110001001110001001110000100011111101110010100101011010010100100001111110101011010011010001000110111110001101011000010101001011000100100010100101101001111001000110010000000
Pair \(Z_2\) Length of longest common subsequence
6RBU_1,6FAP_1 187 3
6RBU_1,5KXT_1 183 4
6FAP_1,5KXT_1 126 3

Newick tree

 
[
	6RBU_1:10.43,
	[
		5KXT_1:63,6FAP_1:63
	]:37.43
]

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 \((0.85)(0.8)(\frac{330 }{\log_{20} 330}-\frac{58}{\log_{20}58})=86.8\)
Status Protein1 Protein2 d d1/2
Query variables 6RBU_1 6FAP_1 114 68
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]