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Parikh vectors
5KEN_1 8SSS_1 7BTL_1 Letter Amino acid
16 7 6 F Phenylalanine
15 8 2 P Proline
5 15 1 C Cysteine
7 6 2 Q Glutamine
4 21 3 H Histidine
20 15 9 S Serine
5 0 1 W Tryptophan
22 7 20 G Glycine
23 13 9 L Leucine
0 6 2 M Methionine
11 8 7 Y Tyrosine
15 20 2 R Arginine
20 10 8 E Glutamic acid
16 18 12 K Lycine
12 5 16 I Isoleucine
24 17 13 T Threonine
19 8 6 V Valine
16 7 5 A Alanine
14 4 7 N Asparagine
12 8 9 D Aspartic acid 

5KEN_1|Chains A, E, K|Ebola surface glycoprotein, GP1|Zaire ebolavirus (128952)
>8SSS_1|Chains A, D|Transcriptional repressor CTCF|Homo sapiens (9606)
>7BTL_1|Chains A, B, C, D, E, F, G|lectin|Methanococcus voltae (strain ATCC BAA-1334 / A3) (456320)
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 \(w=f(c)\)
5KEN , Knot 122 276 0.82 38 178 266 
IPLGVIHNSTLQVSDVDKLVCRDKLSSTNQLRSVGLNLEGNGVATDVPSATKRWGFRSGVPPKVVNYEAGEWAENCYNLEIKKPDGSECLPAAPDGIRGFPRCRYVHKVSGTGPCAGDFAFHKEGAFFLYDRLASTVIYRGTTFAEGVVAFLILPQAKKDFFSSHPLREPVNATEDPSSGYYSTTIRYQATGFGTNETEYLFEVDNLTYVQLESRFTPQFLLQLNETIYTSGKRSNTTGKLIWKVNPEIDTTIGEWAFWETKKNLTRKIRSEELSF
8SSS , Knot 91 203 0.79 38 134 184 
KKTFQCELCSYTCPRRSNLDRHMKSHTDERPHKCHLCGRAFRTVTLLRNHLNTHTGTRPHKCPDCDMAFVTSGELVRHRRYKHTHEKPFKCSMCDYASVEVSKLKRHIRSHTGERPFQCSLCSYASRDTYKLKRHMRTHSGEKPYECYICHARFTQSGTMKMHILQKHTENVAKFHCPHCDTVIARKSDLGVHLRKQHSYIEQ
7BTL , Knot 68 140 0.80 40 102 136 
DNYIYSTEVGGVGGTPFTFMQESGTITSIKFNWSDQYKLLHHIEVKFINNANIYATGDPKGNHEVILEIDDDETIIGSVIGYKKGNDGRCTGVKLTTSKGKSIMAGYFEESLITTYTGKLAGIKGGAGSDIDRLGLIFLK

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 \(c\).

\(|P_{f(5KEN_1)}(2) \setminus P_{f(8SSS_1)}(2)|=119\), \(|P_{f(8SSS_1)}(2) \setminus P_{f(5KEN_1)}(2)|=75\). 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 1:111111000010100100110000100000100111010101110011010001110011110110001101100000101001010001111101101110000100101011011011100011111000110011001001101111111110100011000110011010001001000001000101110000001101001001010001010111010001000100000010111010101000110111100000100010000101
Pair \(Z_2\) Length of longest common subsequence
5KEN_1,8SSS_1 194 3
5KEN_1,7BTL_1 164 4
8SSS_1,7BTL_1 164 3

Newick tree

 
[
	8SSS_1:92.27,
	[
		5KEN_1:82,7BTL_1:82
	]:10.27
]

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 \((0.85)(0.8)(\frac{479 }{\log_{20} 479}-\frac{203}{\log_{20}203})=80.2\)
Status Protein1 Protein2 d d1/2
Query variables 5KEN_1 8SSS_1 103 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]