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Parikh vectors
6UIS_1 6WBV_1 8QWN_1 Letter Amino acid
18 1 19 R Arginine
19 0 9 N Asparagine
14 2 9 H Histidine
49 0 17 L Leucine
41 0 14 V Valine
25 1 9 D Aspartic acid
2 8 11 C Cysteine
36 0 7 Q Glutamine
13 2 5 F Phenylalanine
37 1 18 P Proline
19 0 1 W Tryptophan
22 0 8 Y Tyrosine
58 2 8 K Lycine
6 1 5 M Methionine
24 1 20 S Serine
26 0 9 A Alanine
47 0 13 E Glutamic acid
35 2 15 G Glycine
41 2 6 I Isoleucine
40 2 16 T Threonine 

6UIS_1|Chain A|p66 Reverse transcriptase/RNaseH|Human immunodeficiency virus type 1 group M subtype B (isolate HXB2) (11706)
>6WBV_1|Chain A[auth B]|Hepcidin|Homo sapiens (9606)
>8QWN_1|Chain A|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 \(w=f(c)\)
6UIS , Knot 226 572 0.83 40 257 525 
MGSSHHHHHHSSPISPIETVPVKLKPGMDGPKVKQWPLTEEKIKALVEICTEMEKEGKISKIGPENPYNTPVFAIKKKDSTKWRKLVDFRELNKRTQDFWEVQLGIPHPAGLKKKKSVTVLDVGDAYFSVPLDEDFRKYTAFTIPSINNETPGIRYQYNVLPQGWKGSPAIFQSSMTKILEPFRKQNPDIVIYQYVDDLYVGSDLEIGQHRTKIEELRQHLLRWGLTTPDKKHQKEPPFLWMGYELHPDKWTVQPIVLPEKDSWTVNDICKLVGKLNWASQIYPGIKVRQLSKLLRGTKALTEVIPLTEEAELELAENREILKEPVHGVYYDPSKDLIAEIQKQGQGQWTYQIYQEPFKNLKTGKYARMRGAHTNDVKQLTEAVQKITTESIVIWGKTPKFKLPIQKETWETWWTEYWQATWIPEWEFVNTPPLVKLWYQLEKEPIVGAETFYVDGAANRETKLGKAGYVTNRGRQKVVTLTDTTNQKTELQAIYLALQDSGLEVNIVTDSQYALGIIQAQPDQSESELVNQIIEQLIKKEKVYLAWVPAHKGIGGNEQVDKLVSAGIRKVL
6WBV , Knot 17 25 0.73 24 21 23 
DTHFPICIFCCGCCHRSKCGMCCKT
8QWN , Knot 102 219 0.83 40 150 211 
SSSVPSQKTYQGSYGFRLGFLHSGTAKSVTCTYSPALNKLFCQLAKTCPVQLWVDSTPPPGTRVRAMAIYKQSQHMTEVVRRCPHHERCSDSDGLAPPQHLIRVEGNLRAEYLDDRNTFRHSVVVPCEPPEVGSDCTTIHYNYMCYSSCMGGMNRRPILTIITLEDSSGNLLGRDSFEVRVCACPGRDRRTEEENLRKKGEPHHELPPGSTKRALPNNT

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 \(c\).

\(|P_{f(6UIS_1)}(2) \setminus P_{f(6WBV_1)}(2)|=248\), \(|P_{f(6WBV_1)}(2) \setminus P_{f(6UIS_1)}(2)|=12\). 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 1:11000000000011011001110101110110100111000010111010001000101001110010001111100000001001101001000000110101111011110000010110110101011100010000110110100001110000011101101011110001001101100001011100010010110010110000010010001101110010000000111111100101001010111110000101001001110101100101110100100110100110011110001010110000110011011000100011101000101010001000110010010010101100001001001100100001111100101011100001001100010101110101100111101100100011111001010111000001101101000100011010000000001011011100011010110000011111010100000011001100110000101111110011110001001101110011
Pair \(Z_2\) Length of longest common subsequence
6UIS_1,6WBV_1 260 2
6UIS_1,8QWN_1 203 4
6WBV_1,8QWN_1 161 2

Newick tree

 
[
	6UIS_1:12.39,
	[
		8QWN_1:80.5,6WBV_1:80.5
	]:45.89
]

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 \((0.85)(0.8)(\frac{597 }{\log_{20} 597}-\frac{25}{\log_{20}25})=174.\)
Status Protein1 Protein2 d d1/2
Query variables 6UIS_1 6WBV_1 220 114.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]