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Parikh vectors
9COV_1 6GWJ_1 1KJH_1 Letter Amino acid
7 2 2 C Cysteine
16 0 1 Y Tyrosine
18 1 5 N Asparagine
15 3 5 Q Glutamine
51 10 11 L Leucine
34 13 7 P Proline
22 15 4 R Arginine
29 5 12 I Isoleucine
18 3 2 M Methionine
32 4 2 F Phenylalanine
26 19 13 G Glycine
25 11 3 D Aspartic acid
30 4 4 E Glutamic acid
12 5 1 H Histidine
38 2 7 K Lycine
30 9 0 S Serine
26 5 8 T Threonine
3 1 2 W Tryptophan
18 20 3 A Alanine
37 11 7 V Valine 

9COV_1|Chain A|Cytochrome P450 3A4|Homo sapiens (9606)
>6GWJ_1|Chain A[auth B]|EKC/KEOPS complex subunit LAGE3|Homo sapiens (9606)
>1KJH_1|Chains A, B|POL POLYPROTEIN|Human immunodeficiency virus 1 (11676)
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 \(w=f(c)\)
9COV , Knot 203 487 0.86 40 248 467 
MAYLYGTHSHGLFKKLGIPGPTPLPFLGNILSYHKGFCMFDMECHKKYGKVWGFYDGQQPVLAITDPDMIKTVLVKECYSVFTNRRPFGPVGFMKSAISIAEDEEWKRLRSLLSPTFTSGKLKEMVPIIAQYGDVLVRNLRREAETGKPVTLKDVFGAYSMDVITSTSFGVNIDSLNNPQDPFVENTKKLLRFDFLDPFFLSITVFPFLIPILEVLNICVFPREVTNFLRKSVKRMKESRLEDTQKHRVDFLQLMIDSQNSKETESHKALSDLELVAQSIIFIFAGYETTSSVLSFIMYELATHPDVQQKLQEEIDAVLPNKAPPTYDTVLQMEYLDMVVNETLRLFPIAMRLERVCKKDVEINGMFIPKGVVVMIPSYALHRDPKYWTEPEKFLPERFSKKNKDNIDPYIYTPFGSGPRNCIGMRFALMNMKLALIRVLQNFSFKPCKETQIPLKLSLGGLLQPEKPVVLKVESRDGTVSGAHHHH
6GWJ , Knot 67 143 0.77 38 95 133 
MRDADADAGGGADGGDGRGGHSCRGGVDTAAAPAGGAPPAHAPGPGRDAASAARGSRMRPHIFTLSVPFPTPLEAEIAHGSLAPDAEPHQRVVGKDLTVSGRILVVRWKAEDCRLLRISVINFLDQLSLVVRTMQRFGPPVSR
1KJH , Knot 53 99 0.82 38 80 94 
PQITLWKRPLVTIRIGGQLKEALLNTGADDTVLEEMNLPGKWKPKMIGGIGGFIKVRQYDQIPVEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNF

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 \(c\).

\(|P_{f(9COV_1)}(2) \setminus P_{f(6GWJ_1)}(2)|=177\), \(|P_{f(6GWJ_1)}(2) \setminus P_{f(9COV_1)}(2)|=24\). 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
9COV_1,6GWJ_1 201 4
9COV_1,1KJH_1 198 4
6GWJ_1,1KJH_1 115 3

Newick tree

 
[
	9COV_1:11.29,
	[
		1KJH_1:57.5,6GWJ_1:57.5
	]:52.79
]

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 \((0.85)(0.8)(\frac{630 }{\log_{20} 630}-\frac{143}{\log_{20}143})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 9COV_1 6GWJ_1 183 114.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]