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Parikh vectors
5AWS_1 8IHN_1 1RBJ_1 Letter Amino acid
12 0 0 F Phenylalanine
20 1 0 S Serine
4 0 0 W Tryptophan
9 3 0 R Arginine
12 0 0 D Aspartic acid
16 5 0 K Lycine
6 0 0 M Methionine
21 0 0 V Valine
25 5 4 A Alanine
3 0 0 H Histidine
12 0 0 I Isoleucine
19 4 0 T Threonine
28 1 0 L Leucine
8 0 0 Y Tyrosine
19 0 0 N Asparagine
5 0 0 C Cysteine
15 2 0 Q Glutamine
11 0 0 E Glutamic acid
18 2 0 G Glycine
19 1 0 P Proline 

5AWS_1|Chains A, B|SH3-containing GRB2-like protein 3-interacting protein 1|Homo sapiens (9606)
>8IHN_1|Chain A|Histone H3|Xenopus laevis (8355)
>1RBJ_1|Chain A[auth B]|DNA (5'-D(*AP*AP*AP*A)-3')|
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 \(w=f(c)\)
5AWS , Knot 125 282 0.83 40 187 273 
GPLGSLTMGAQDTLPVAAAFTETVNAYFKGADPSKCIVKITGEMVLSFPAGITRHFANNPSPAALTFRVINFSRLEHVLPNPQLLCCDNTQNDANTKEFWVNMPNLMTHLKKVSEQKPQATYYNVDMLKYQVSAQGIQSTPLNLAVNWRCEPSSTDLRIDYKYNTDAMTTAVALNNVQFLVPIDGGVTKLQAVLPPAVWNAEQQRILWKIPDISQKSENGGVGSLLARFQLSEGPSKPSPLVVQFTSEGSTLSGCDIELVGAGYRFSLIKKRFAAGKYLADN
8IHN , Knot 15 24 0.66 18 18 22 
ARTKQTARKSTGGKAPRKQLATKA
1RBJ , Knot 2 4 0.23 2 1 1 
AAAA

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 \(c\).

\(|P_{f(5AWS_1)}(2) \setminus P_{f(8IHN_1)}(2)|=176\), \(|P_{f(8IHN_1)}(2) \setminus P_{f(5AWS_1)}(2)|=7\). 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 1:111101011100011111110001010101101000110101011101111100011001011110101101001001110101100000000100001110110110010010000101000010110001010110001101110100010000101000000011001111001011111011100101111111101000011101101000000111101110101001100101111010001001010010111110010110001111001100
Pair \(Z_2\) Length of longest common subsequence
5AWS_1,8IHN_1 183 2
5AWS_1,1RBJ_1 186 3
8IHN_1,1RBJ_1 19 1

Newick tree

 
[
	5AWS_1:10.38,
	[
		8IHN_1:9.5,1RBJ_1:9.5
	]:96.88
]

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 \((0.85)(0.8)(\frac{306 }{\log_{20} 306}-\frac{24}{\log_{20}24})=93.5\)
Status Protein1 Protein2 d d1/2
Query variables 5AWS_1 8IHN_1 122 65.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]