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Parikh vectors
3WBG_1 5YUP_1 3FIV_1 Letter Amino acid
2 11 4 Y Tyrosine
14 9 7 K Lycine
4 3 3 M Methionine
2 14 3 P Proline
3 6 14 N Asparagine
1 5 2 C Cysteine
3 5 4 Q Glutamine
10 2 1 H Histidine
11 30 2 S Serine
19 21 8 T Threonine
2 5 0 W Tryptophan
11 10 5 D Aspartic acid
13 18 11 G Glycine
15 15 11 L Leucine
6 7 5 F Phenylalanine
11 20 8 V Valine
6 15 1 A Alanine
5 9 8 R Arginine
8 8 6 E Glutamic acid
7 6 13 I Isoleucine 

3WBG_1|Chains A, B, C, D|Fatty acid-binding protein, heart|Homo sapiens (9606)
>5YUP_1|Chain A[auth H]|the heavy chain of the Fab fragment of FVIIa antibody mAb4F5|Mus musculus (10090)
>3FIV_1|Chains A, B|FELINE IMMUNODEFICIENCY VIRUS PROTEASE|Feline immunodeficiency virus (11673)
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 \(w=f(c)\)
3WBG , Knot 73 153 0.80 40 110 142 
MGSSHHHHHHSSGLVPRGSHMVDAFLGTWKLVDSKNFDDYMKSLGVGFATRQVASMTKPTTIIEKNGDILTLKTHSTFKNTEISFKLGVEFDETTADDRKVKSIVTLDGGKLVHLQKWDGQETTLVRELIDGKLILTLTHGTAVCTRTYEKEA
5YUP , Knot 101 219 0.82 40 152 210 
EVKLVESGGGLVQPGGSRKLSCAASGFTFSDYGMAWVRQAPGKGPEWIAFISNLSRIYYADTVTGRFTISRENDKNTLFLEMSSLRSEDSAIYYCTRDDGYYRVDYWGQGATLTVSSAKTTPPSVYPLAPGSAAQTNSMVTLGCLVKGYFPEPVTVTWNSGSLSSGVHTFPAVLQSDLYTLSSSVTVPSSTWPSETVTCNVAHPASSTKVDKKIVPRDC
3FIV , Knot 58 116 0.79 38 87 111 
YNKVGTTTTLEKRPEILIFVNGYPIKFLLNTGADITILNRRDFQVKNSIENGRQNMIGVGGGKRGTNYINVHLEIRDENYKTQCIFGNVCVLEDNSLIQPLLGRDNMIKFNIRLVM

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 \(c\).

\(|P_{f(3WBG_1)}(2) \setminus P_{f(5YUP_1)}(2)|=55\), \(|P_{f(5YUP_1)}(2) \setminus P_{f(3WBG_1)}(2)|=97\). 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 1:110000000000111101001101111010110000100010011111100011010010011000101101000001000010101110100001000010011010110110100101000011001101011101001011000000001
Pair \(Z_2\) Length of longest common subsequence
3WBG_1,5YUP_1 152 3
3WBG_1,3FIV_1 131 3
5YUP_1,3FIV_1 171 3

Newick tree

 
[
	5YUP_1:85.40,
	[
		3WBG_1:65.5,3FIV_1:65.5
	]:19.90
]

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 \((0.85)(0.8)(\frac{372 }{\log_{20} 372}-\frac{153}{\log_{20}153})=66.0\)
Status Protein1 Protein2 d d1/2
Query variables 3WBG_1 5YUP_1 83 69
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]