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Parikh vectors
2NOQ_1 2AOJ_1 7NDO_1 Letter Amino acid
37 13 9 G Glycine
0 2 15 M Methionine
0 6 8 P Proline
0 1 7 Y Tyrosine
0 10 44 L Leucine
0 2 7 F Phenylalanine
0 4 12 R Arginine
0 3 7 N Asparagine
33 0 1 C Cysteine
0 1 10 H Histidine
56 5 15 A Alanine
0 5 9 Q Glutamine
0 15 14 I Isoleucine
0 6 11 V Valine
0 8 6 T Threonine
0 2 4 W Tryptophan
0 4 13 D Aspartic acid
0 4 18 E Glutamic acid
0 7 14 K Lycine
0 1 23 S Serine 

2NOQ_1|Chain A|CrPV IRES|null
>2AOJ_1|Chains A, B|POL POLYPROTEIN|Human immunodeficiency virus type 1 (BH5 ISOLATE) (11682)
>7NDO_1|Chains A, B|Estrogen receptor|Homo sapiens (9606)
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 \(w=f(c)\)
2NOQ , Knot 48 190 0.44 8 16 58 
AAAAAUGUGAUCUUGCUUGUAAAUACAAUUUUGAGAGGUUAAUAAAUUACAAGUAGUGCUAUUUUUGUAUUUAGGUUAGCUAUUUAGCUUUACGUUCCAGGAUGCCUAGUGGCAGCCCCACAAUAUCCAGGAAGCCCUCUCUGCGGUUUUUCAGAUUAGGUAGUCGAAAAACCUAAGAAAUUUACCUGCU
2AOJ , Knot 53 99 0.82 38 77 95 
PQITLWKRPLVTIKIGGQLKEALLDTGADDTVIEEMSLPGRWKPKMIGGIGGFIKVRQYDQIIIEIAGHKAIGTVLVGPTPVNIIGRNLLTQIGATLNF
7NDO , Knot 108 247 0.80 40 157 236 
SMNSLALSLTADQIISALLEAEPPILYSEYDPSRPFSEAYMMGLLTNLADRELVHMINWAKKVPGFVDLSRHDQVHLLESAWLEILMIGLVWRSMDHPGKLLFAPDLLLDREQGKSVEGMVEIFDMLLATSERFREMKLQREEFVCLKAIILLNSGVYTFLSSTLKSLENKEKIHRMLDKITDALIWYMAKSGLSLQQQHQRLAQLLLILSHIRHMSNKGMEHLYSMKSKNVVPSYDLLLEMLDAHR

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 \(c\).

\(|P_{f(2NOQ_1)}(2) \setminus P_{f(2AOJ_1)}(2)|=13\), \(|P_{f(2AOJ_1)}(2) \setminus P_{f(2NOQ_1)}(2)|=74\). 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 1:1111101011000010001011101011000011111100110111001011101101001000001010001110011001000110000101000011110100011011011000010110100011111100000000101100000011100111011001111110001111110001000100
Pair \(Z_2\) Length of longest common subsequence
2NOQ_1,2AOJ_1 87 2
2NOQ_1,7NDO_1 173 1
2AOJ_1,7NDO_1 168 4

Newick tree

 
[
	7NDO_1:95.19,
	[
		2NOQ_1:43.5,2AOJ_1:43.5
	]:51.69
]

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 \((0.85)(0.8)(\frac{289 }{\log_{20} 289}-\frac{99}{\log_{20}99})=60.0\)
Status Protein1 Protein2 d d1/2
Query variables 2NOQ_1 2AOJ_1 49 48
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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