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Parikh vectors
6UNJ_1 3OCS_1 4RIP_1 Letter Amino acid
18 11 3 A Alanine
30 24 0 E Glutamic acid
34 8 0 P Proline
26 10 1 T Threonine
26 16 3 G Glycine
29 13 0 I Isoleucine
16 15 0 Y Tyrosine
37 18 0 V Valine
25 14 0 D Aspartic acid
7 6 2 C Cysteine
51 27 0 L Leucine
18 14 0 M Methionine
30 20 0 S Serine
3 6 0 W Tryptophan
22 13 0 R Arginine
18 8 0 N Asparagine
15 11 0 Q Glutamine
12 6 0 H Histidine
38 19 0 K Lycine
32 12 0 F Phenylalanine 

6UNJ_1|Chains A, B|Cytochrome P450 3A4|Homo sapiens (9606)
>3OCS_1|Chain A|Tyrosine-protein kinase BTK|Homo sapiens (9606)
>4RIP_1|Chain A|DNA (5'-D(*AP*CP*(BRU)P*CP*GP*GP*AP*(BRU)P*GP*AP*T)-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 \(w=f(c)\)
6UNJ , Knot 203 487 0.86 40 248 467 
MAYLYGTHSHGLFKKLGIPGPTPLPFLGNILSYHKGFCMFDMECHKKYGKVWGFYDGQQPVLAITDPDMIKTVLVKECYSVFTNRRPFGPVGFMKSAISIAEDEEWKRLRSLLSPTFTSGKLKEMVPIIAQYGDVLVRNLRREAETGKPVTLKDVFGAYSMDVITSTSFGVNIDSLNNPQDPFVENTKKLLRFDFLDPFFLSITVFPFLIPILEVLNICVFPREVTNFLRKSVKRMKESRLEDTQKHRVDFLQLMIDSQNSKETESHKALSDLELVAQSIIFIFAGYETTSSVLSFIMYELATHPDVQQKLQEEIDAVLPNKAPPTYDTVLQMEYLDMVVNETLRLFPIAMRLERVCKKDVEINGMFIPKGVVVMIPSYALHRDPKYWTEPEKFLPERFSKKNKDNIDPYIYTPFGSGPRNCIGMRFALMNMKLALIRVLQNFSFKPCKETQIPLKLSLGGLLQPEKPVVLKVESRDGTVSGAHHHH
3OCS , Knot 126 271 0.86 40 189 260 
MGSWEIDPKDLTFLKELGTGQFGVVKYGKWRGQYDVAIKMIKEGSMSEDEFIEEAKVMMNLSHEKLVQLYGVCTKQRPIFIITEYMANGCLLNYLREMRHRFQTQQLLEMCKDVCEAMEYLESKQFLHRDLAARNCLVNDQGVVKVSDFGLSRYVLDDEYTSSVGSKFPVRWSPPEVLMYSKFSSKSDIWAFGVLMWEIYSLGKMPYERFTNSETAEHIAQGLRLYRPHLASEKVYTIMYSCWHEKADERPTFKILLSNILDVMDENLYGQ
4RIP , Knot 7 11 0.50 10 9 9 
ACUCGGAUGAT

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 \(c\).

\(|P_{f(6UNJ_1)}(2) \setminus P_{f(3OCS_1)}(2)|=120\), \(|P_{f(3OCS_1)}(2) \setminus P_{f(6UNJ_1)}(2)|=61\). 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 1:1101010000111001111110111111011000011011010000001011110010011111001011001110000011000011111111001101100001001001101010010100111111001011100100010010110100111100101100001110100100100111000001101011011110101111111110110101110010011000100100001000000010110111000000000000110010111001111111000000110111001100101000100010111100111000011010010111000101111110100100001010111110111111100110001001001001110010000000101010011101100011101111010111101100101010000011101011111010011110100001010110000
Pair \(Z_2\) Length of longest common subsequence
6UNJ_1,3OCS_1 181 4
6UNJ_1,4RIP_1 251 2
3OCS_1,4RIP_1 198 1

Newick tree

 
[
	4RIP_1:11.59,
	[
		6UNJ_1:90.5,3OCS_1:90.5
	]:29.09
]

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 \((0.85)(0.8)(\frac{758 }{\log_{20} 758}-\frac{271}{\log_{20}271})=134.\)
Status Protein1 Protein2 d d1/2
Query variables 6UNJ_1 3OCS_1 168 130
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]