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Parikh vectors
2RLP_1 3ANS_1 2GEE_1 Letter Amino acid
1 17 3 M Methionine
9 23 18 P Proline
3 25 23 S Serine
7 12 8 Y Tyrosine
15 20 15 G Glycine
8 12 7 N Asparagine
6 12 12 D Aspartic acid
8 8 0 C Cysteine
1 15 8 H Histidine
6 12 12 I Isoleucine
5 19 3 K Lycine
6 20 6 A Alanine
8 28 14 L Leucine
3 10 2 W Tryptophan
11 26 11 E Glutamic acid
4 13 5 Q Glutamine
3 15 5 F Phenylalanine
11 9 22 T Threonine
6 25 21 V Valine
8 15 8 R Arginine 

2RLP_1|Chain A|Complement factor H|Homo sapiens (9606)
>3ANS_1|Chains A, B|Epoxide hydrolase 2|Homo sapiens (9606)
>2GEE_1|Chain A|hypothetical protein|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 \(w=f(c)\)
2RLP , Knot 67 129 0.84 40 107 124 
EAEAAGDCNELPPRRNTEILTGSWSDQTYPEGTQAIYKCRPGYRSLGNVIMVCRKGEWVALNPLRKCQKRPCGHPGDTPFGTFTLTGGNVFEYGVKAVYTCNEGYQLLGEINYRECDTDGWTNDIPICE
3ANS , Knot 145 336 0.83 40 202 321 
MKKGHHHHHHTSCNPSDMSHGYVTVKPRVRLHFVELGSGPAVCLCHGFPESWYSWRYQIPALAQAGYRVLAMDMKGYGESSAPPEIEEYCMEVLCKEMVTFLDKLGLSQAVFIGHDWGGMLVWYMALFYPERVRAVASLNTPFIPANPNMSPLESIKANPVFDYQLYFQEPGVAEAELEQNLSRTFKSLFRASDESVLSMHKVCEAGGLFVNSPEEPSLSRMVTEEEIQFYVQQFKKSGFRGPLNWYRNMERNWKWACKSLGRKILIPALMVTAEKDFVLVPQMSQHMEDWIPHLKRGHIEDCGHWTQMDKPTEVNQILIKWLDSDARNPPVVSKM
2GEE , Knot 88 203 0.76 38 130 185 
MGSSHHHHHHSSGLVPRGSHMEVPQPTDLSFVDITDSSIGLRWTPLNSSTIIGYRITVVAAGEGIPIFEDFVDSSVGYYTVTGLEPGIDYDISVYTVKNGGESTPTTLTQQTAVPPPTDLRFTNIGPDTMRVTWAPPPSIDLTNFLVRYSPVKNEEDVAELSISPSDNAVVLTNLLPGTEYVVSVSSVYEQHESTPLRGRQKT

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 \(c\).

\(|P_{f(2RLP_1)}(2) \setminus P_{f(3ANS_1)}(2)|=53\), \(|P_{f(3ANS_1)}(2) \setminus P_{f(2RLP_1)}(2)|=148\). 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 1:010111000011100000110101000001010011000011000110111100010111101100000010101100111010101101100110110000010011101000000001100011100
Pair \(Z_2\) Length of longest common subsequence
2RLP_1,3ANS_1 201 3
2RLP_1,2GEE_1 149 3
3ANS_1,2GEE_1 186 6

Newick tree

 
[
	3ANS_1:10.19,
	[
		2RLP_1:74.5,2GEE_1:74.5
	]:28.69
]

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 \((0.85)(0.8)(\frac{465 }{\log_{20} 465}-\frac{129}{\log_{20}129})=100.\)
Status Protein1 Protein2 d d1/2
Query variables 2RLP_1 3ANS_1 129 88.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]