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Parikh vectors
6ZSS_1 1NFK_1 8XCE_1 Letter Amino acid
3 0 7 K Lycine
3 0 14 P Proline
11 0 19 S Serine
5 0 11 E Glutamic acid
12 3 10 C Cysteine
3 3 14 G Glycine
4 0 14 L Leucine
3 0 5 F Phenylalanine
0 0 1 W Tryptophan
3 0 8 Y Tyrosine
5 0 15 V Valine
1 0 18 R Arginine
7 0 7 Q Glutamine
0 0 7 H Histidine
5 0 6 I Isoleucine
4 0 6 M Methionine
7 0 9 N Asparagine
2 0 8 D Aspartic acid
2 3 14 T Threonine
6 2 7 A Alanine 

6ZSS_1|Chain A|Ly6/PLAUR domain-containing protein 1|Homo sapiens (9606)
>1NFK_1|Chains A[auth C], B[auth D]|DNA (5'-D(*TP*GP*GP*GP*AP*AP*TP*TP*CP*CP*C)-3')|
>8XCE_1|Chains A, B, C, D|Cellular tumor antigen p53|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 \(w=f(c)\)
6ZSS , Knot 44 86 0.76 36 70 83 
MIQCYQCEEFQLNNDCSSPEFIVNCTVNVQDMCQKEVMEQSAGIMYRKSCASSAACLIASAGYQSFCSPGKLNSVCISCCNTPLCN
1NFK , Knot 6 11 0.43 8 8 9 
TGGGAATTCCC
8XCE , Knot 94 200 0.83 40 143 195 
SSSVPSQKTYQGSYGFRLGFLHSGTAKSVTCTYSPALNKMFCQLAKTCPVQLWVDSTPPPGTRVRAMAIYKQSQHMTEVVRRCPHHERCSDSDGLAPPQHLIRVEGNLRVEYLDDRNTFRHSVVVPYEPPEVGSDCTTIHYNYMCNSSCMGGMNRRPILTIITLEDSSGNLLGRNSFEVRVCACPGRDRRTEEENLRKKG

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 \(c\).

\(|P_{f(6ZSS_1)}(2) \setminus P_{f(1NFK_1)}(2)|=68\), \(|P_{f(1NFK_1)}(2) \setminus P_{f(6ZSS_1)}(2)|=6\). 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 1:11000000010100000010111000101001000011000111100000100110111011000100110100101000001100
Pair \(Z_2\) Length of longest common subsequence
6ZSS_1,1NFK_1 74 2
6ZSS_1,8XCE_1 151 2
1NFK_1,8XCE_1 145 2

Newick tree

 
[
	8XCE_1:82.75,
	[
		6ZSS_1:37,1NFK_1:37
	]:45.75
]

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 \((0.85)(0.8)(\frac{97 }{\log_{20} 97}-\frac{11}{\log_{20}11})=33.8\)
Status Protein1 Protein2 d d1/2
Query variables 6ZSS_1 1NFK_1 41 22.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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