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Parikh vectors
6BEW_1 1TDV_1 2QNU_1 Letter Amino acid
0 6 29 A Alanine
1 1 8 Q Glutamine
0 13 1 K Lycine
0 4 10 F Phenylalanine
0 1 7 W Tryptophan
0 6 4 N Asparagine
1 7 9 D Aspartic acid
0 11 29 G Glycine
0 5 7 I Isoleucine
0 9 28 L Leucine
0 5 13 R Arginine
0 14 3 C Cysteine
1 1 2 H Histidine
0 2 4 M Methionine
2 5 19 P Proline
1 7 14 S Serine
0 5 7 T Threonine
0 3 14 V Valine
1 7 14 E Glutamic acid
0 9 4 Y Tyrosine 

6BEW_1|Chain A|(DHI)P(DAS)(DGN)(DSN)(DGL)P|Homo sapiens (9606)
>1TDV_1|Chain A|Phospholipase A2 VRV-PL-VIIIa|Daboia russellii pulchella (97228)
>2QNU_1|Chains A, B|Uncharacterized protein PA0076|Pseudomonas aeruginosa PAO1 (208964)
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 \(w=f(c)\)
6BEW , Knot 7 7 0.64 12 6 5 
HPDQSEP
1TDV , Knot 60 121 0.79 40 95 118 
SLLEFGKMILEETGKLAIPSYSSYGCYCGWGGKGTPKDATDRCCFVHDCCYGNLPDCNPKSDRYKYKRVNGAIVCEKGTSCENRICECDKAAAICFRQNLNTYSKKYMLYPDFLCKGELKC
2QNU , Knot 100 226 0.80 40 145 215 
MNSVGFYGKLAGRGDFVSRGLPNTFVEPWDAWLASGMRASQDELGAAWLDAYLTSPLWRFAIAPGLLGGEAVTGVVMPSIDRVGRYFPLTVACLLPANADLGGLVGGDDGWFEQVESLLLSTLEPEAEVEAFEQAVAQLPAPPCGPRIEQSLISGNLLRSEAVTPAQRLAALAQHACDGASHWWGRGSARISAGLMRYQGLPPAPAFGRFLTGEGEVIPLFPGIPG

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 \(c\).

\(|P_{f(6BEW_1)}(2) \setminus P_{f(1TDV_1)}(2)|=5\), \(|P_{f(1TDV_1)}(2) \setminus P_{f(6BEW_1)}(2)|=94\). 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 1:0100001
Pair \(Z_2\) Length of longest common subsequence
6BEW_1,1TDV_1 99 2
6BEW_1,2QNU_1 145 2
1TDV_1,2QNU_1 170 4

Newick tree

 
[
	2QNU_1:86.62,
	[
		6BEW_1:49.5,1TDV_1:49.5
	]:37.12
]

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 \((0.85)(0.8)(\frac{128 }{\log_{20} 128}-\frac{7}{\log_{20}7})=46.4\)
Status Protein1 Protein2 d d1/2
Query variables 6BEW_1 1TDV_1 58 30.5
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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