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Parikh vectors
7LRM_1 7JKU_1 3MEW_1 Letter Amino acid
34 17 8 G Glycine
48 0 13 L Leucine
6 0 0 M Methionine
13 0 3 F Phenylalanine
38 0 17 P Proline
39 9 7 T Threonine
22 0 9 Y Tyrosine
15 0 9 R Arginine
39 0 13 V Valine
47 0 10 E Glutamic acid
40 0 6 I Isoleucine
1 0 3 C Cysteine
36 0 8 Q Glutamine
19 0 3 W Tryptophan
21 0 3 N Asparagine
23 0 13 D Aspartic acid
8 0 3 H Histidine
60 0 8 K Lycine
20 0 7 S Serine
26 0 16 A Alanine 

7LRM_1|Chains A, C|Reverse transcriptase p66|Human immunodeficiency virus type 1 (11676)
>7JKU_1|Chain A|26-mer DNA|Tetrahymena thermophila (5911)
>3MEW_1|Chain A|SAGA-associated factor 29 homolog|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 \(w=f(c)\)
7LRM , Knot 219 555 0.83 40 251 509 
PISPIETVPVKLKPGMDGPKVKQWPLTEEKIKALVEICTEMEKEGKISKIGPENPYNTPVFAIKKKDSTKWRKLVDFRELNKRTQDFWEVQLGIPHPAGLKKKKSVTVLDVGDAYFSVPLDEDFRKYTAFTIPSINNETPGIRYQYNVLPQGWKGSPAIFQSSMTKILEPFKKQNPDIVIYQYMDDLYVGSDLEIGQHRTKIEELRQHLLRWGLTTPDKKHQKEPPFLWMGYELHPDKWTVQPIVLPEKDSWTVNDIQKLVGKLNWASQIYPGIKVRQLSKLLRGTKALTEVIPLTEEAELELAENREILKEPVHGVYYDPSKDLIAEIQKQGQGQWTYQIYQEPFKNLKTGKYARMRGAHTNDVKQLTEAVQKITTESIVIWGKTPKFKLPIQKETWETWWTEYWQATWIPEWEFVNTPPLVKLWYQLEKEPIVGAETFYVDGAANRETKLGKAGYVTNKGRQKVVPLTNTTNQKTELQAIYLALQDSGLEVNIVTNSQYALGIIQAQPDKSESELVNQIIEQLIKKEKVYLAWVPAHKGIGGNEQVDKLVSAG
7JKU , Knot 5 26 0.20 4 4 5 
GTTGGGGTTGGGGTTGGGGTTGGGGT
3MEW , Knot 71 159 0.75 38 108 154 
TLPLWIGKPGDKPPPLCGAIPASGDYVARPGDKVAARVKAVDGDEQWILAEVVSYSHATNKYEVDDIDEEGKERHTLSRRRVIPLPQWKANPETDPEALFQKEQLVLALYPQTTCFYRALIHAPPQRPQDDYSVLFEDTSYADGYSPPLNVAQRYVVAC

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 \(c\).

\(|P_{f(7LRM_1)}(2) \setminus P_{f(7JKU_1)}(2)|=247\), \(|P_{f(7JKU_1)}(2) \setminus P_{f(7LRM_1)}(2)|=0\). 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 1:110110011101011101101001110000101110100010001010011100100011111000000010011010010000001101011110111100000101101101010111000100001101101000011100000111011010111100010011011000010111000100101100101100000100100011011100100000001111111001010010101111100001010010011101011001011101001001101001100111100010101100001100110110001000111010001010100010001100100100101011000010010011001000011111001010111000010011000101011101011001111011001000111110010101110000011011010001000111100000000010110111000110101100000111110101000000110011001100001011111100111100010011011
Pair \(Z_2\) Length of longest common subsequence
7LRM_1,7JKU_1 247 2
7LRM_1,3MEW_1 205 4
7JKU_1,3MEW_1 110 2

Newick tree

 
[
	7LRM_1:12.13,
	[
		3MEW_1:55,7JKU_1:55
	]:72.13
]

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 \((0.85)(0.8)(\frac{581 }{\log_{20} 581}-\frac{26}{\log_{20}26})=169.\)
Status Protein1 Protein2 d d1/2
Query variables 7LRM_1 7JKU_1 216 109.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]