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Parikh vectors
8ZKW_1 2LBU_1 7JPB_1 Letter Amino acid
17 6 0 R Arginine
15 0 6 C Cysteine
32 1 0 M Methionine
34 1 0 F Phenylalanine
26 4 0 S Serine
35 5 2 T Threonine
21 1 0 Y Tyrosine
23 5 0 N Asparagine
23 5 0 E Glutamic acid
40 10 6 G Glycine
51 6 0 I Isoleucine
26 4 0 K Lycine
19 2 0 Q Glutamine
9 7 0 H Histidine
10 1 0 W Tryptophan
46 8 0 V Valine
47 6 7 A Alanine
11 4 0 D Aspartic acid
66 3 0 L Leucine
39 0 0 P Proline 

8ZKW_1|Chains A, B|Protein I'm not dead yet|Drosophila melanogaster (7227)
>2LBU_1|Chains A, B, C, D, E|Small s protein|Podospora anserina (2587412)
>7JPB_1|Chain A|DNA (5'-D(*GP*AP*GP*CP*AP*GP*AP*CP*CP*TP*GP*AP*CP*GP*AP*GP*AP*CP*TP*CP*A)-3')|synthetic construct (32630)
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 \(w=f(c)\)
8ZKW , Knot 232 590 0.83 40 269 544 
MATETTKMIYTPPPLDIKMEIEIGEQPQPPVKCSNFFANHWKGLVVFLVPLLCLPVMLLNEGAEFRCMYLLLVMAIFWVTEALPLYVTSMIPIVAFPIMGIMSSDQTCRLYFKDTLVMFMGGIMVALAVEYCNLHKRLALRVIQIVGCSPRRLHFGLIMVTMFLSMWISNAACTAMMCPIIQAVLEELQAQGVCKINHEPQYQIVGGNKKNNEDEPPYPTKITLCYYLGIAYASSLGGCGTIIGTATNLTFKGIYEARFKNSTEQMDFPTFMFYSVPSMLVYTLLTFVFLQWHFMGLWRPKSKEAQEVQRGREGADVAKKVIDQRYKDLGPMSIHEIQVMILFIFMVVMYFTRKPGIFLGWADLLNSKDIRNSMPTIFVVVMCFMLPANYAFLRYCTRRGGPVPTGPTPSLITWKFIQTKVPWGLVFLLGGGFALAEGSKQSGMAKLIGNALIGLKVLPNSVLLLVVILVAVFLTAFSSNVAIANIIIPVLAEMSLAIEIHPLYLILPAGLACSMAFHLPVSTPPNALVAGYANIRTKDMAIAGIGPTIITIITLFVFCQTWGLVVYPNLNSFPEWAQIYAAAALGNKTH
2LBU , Knot 43 79 0.79 36 64 73 
MKIDAIVGRNSAKDIRTEERARVQLGNVVTAAALHGGIRISDQTTNSVETVVGKGESRVLIGNEYGGKGFWDNHHHHHH
7JPB , Knot 9 21 0.43 8 10 15 
GAGCAGACCTGACGAGACTCA

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 \(c\).

\(|P_{f(8ZKW_1)}(2) \setminus P_{f(2LBU_1)}(2)|=221\), \(|P_{f(2LBU_1)}(2) \setminus P_{f(8ZKW_1)}(2)|=16\). 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 1:11000001100111101010101100101110000111001011111111110111111001101001011111111110011110100111111111111100000001010001111111111111100001000111011011100100101111110111011100110011101110111001010110010001000111100000000110100101000111101001110101110100101011001010000001011011100110111001101111010111110100001001001001101100110000001111010010111111111110100011111111011000010001101111110111110011100000011111011010110101100011111111111111110100001110111011111011100111111111111101100011110111111101011101011011111111001110111001101111101010000111111110110110111100011111010100110110101111110000
Pair \(Z_2\) Length of longest common subsequence
8ZKW_1,2LBU_1 237 4
8ZKW_1,7JPB_1 263 3
2LBU_1,7JPB_1 74 1

Newick tree

 
[
	8ZKW_1:14.94,
	[
		2LBU_1:37,7JPB_1:37
	]:10.94
]

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 \((0.85)(0.8)(\frac{669 }{\log_{20} 669}-\frac{79}{\log_{20}79})=172.\)
Status Protein1 Protein2 d d1/2
Query variables 8ZKW_1 2LBU_1 214 119.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]