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Parikh vectors
4XOQ_1 4YSY_1 2LOD_1 Letter Amino acid
18 44 0 R Arginine
0 22 0 N Asparagine
6 16 0 Q Glutamine
3 37 0 K Lycine
4 17 0 M Methionine
4 21 0 F Phenylalanine
16 26 0 P Proline
33 56 5 A Alanine
13 62 13 G Glycine
4 22 0 H Histidine
9 39 0 I Isoleucine
11 45 1 T Threonine
18 36 0 D Aspartic acid
25 51 0 L Leucine
8 31 0 S Serine
4 6 0 W Tryptophan
3 22 0 Y Tyrosine
1 13 3 C Cysteine
10 42 0 E Glutamic acid
17 37 0 V Valine 

4XOQ_1|Chains A, B, C, D|Coenzyme F420:L-glutamate ligase|Mycobacterium tuberculosis (strain ATCC 25618 / H37Rv) (83332)
>4YSY_1|Chains A, E|Succinate dehydrogenase flavoprotein|Ascaris suum (6253)
>2LOD_1|Chain A|DNA (5'-D(*GP*GP*GP*AP*TP*GP*GP*GP*AP*CP*AP*CP*AP*GP*GP*GP*GP*AP*CP*GP*GP*G)-3')|
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 \(w=f(c)\)
4XOQ , Knot 90 207 0.77 38 124 197 
GAMTAEALELGRQQAQLLRRSVRRFSTDPVPGDLVEAAVAEALTAPAPHHTRPTRFVWLQTPAIRARLLDRMKDKWRSDLTSDGLPADAIERRVARGQILYDAPEVVIPMLVPDGAHSYPDAARTDAEHTMFTVAVGAAVQALLVALAVRGLGSCWIGSTIFAADLVRDELDLPVDWEPLGAIAIGYADEPSGLRDPVPAADLLILK
4YSY , Knot 253 645 0.84 40 282 603 
MLRAVRALICRIGARRTLSVSSSRLDVSTSNIAQYKVIDHAYDVVIIGAGGAGLRAAMGLGEAGFKTAVVTKMFPTRSHTTAAQGGINAALGSMNPDDWKWHFYDTVKGSDWLGDQNAMHYLTRNAVEAVTELENFGMPFSRTPEGKIYQRSFGGQSNNYGKGGVAKRTCCVADRTGHSMLHTLYGNSLRCHCTFFIEYFALDLLMDKGRCVGVIALCLEDGTIHRFRSKRTIVATGGYGRAYFSCTTAHMNTGDGTALATRAGIALEDLEFIQFHPTGIYGVGCLITEGSRGEGGFLVNSEGERFMERYAPKAKDLASRDVVSRAETIEIMEGRGVGPEKDHIYLQLHHLPAEQLHQRLPGISETAKIFAGVDVTKEPIPVIPTVHYNMGGIPTNYKAQVIKYTKEGGDKIVPGLYACGECACHSVHGANRLGANSLLDAVVFGRACSINIKEELKPDEKIPELPEGAGEESIANLDAVRYANGDVPTAELRLTMQKTMQKHAGVFRRGDILAEGVKKMMDLFKELKRLKTTDRSLIWNSDLTESLELQNLMLNATQTIVAAENRKESRGAHARDDFPKREDEYDYSKPIEGQTKRPFEKHWRKHTLTKQDPRTGHITLDYRPVIDKTLDPAEVDWIPPIIRSY
2LOD , Knot 7 22 0.32 8 8 12 
GGGATGGGACACAGGGGACGGG

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 \(c\).

\(|P_{f(4XOQ_1)}(2) \setminus P_{f(4YSY_1)}(2)|=22\), \(|P_{f(4YSY_1)}(2) \setminus P_{f(4XOQ_1)}(2)|=180\). 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 1:111010110110001011000100100011110110111101101111000010011110011101011001000100010001111011000110101100110111111110110001011000100011011111110111111110111001110011110110001011101011111111010010110011111011110
Pair \(Z_2\) Length of longest common subsequence
4XOQ_1,4YSY_1 202 4
4XOQ_1,2LOD_1 130 2
4YSY_1,2LOD_1 274 4

Newick tree

 
[
	4YSY_1:13.80,
	[
		4XOQ_1:65,2LOD_1:65
	]:68.80
]

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 \((0.85)(0.8)(\frac{852 }{\log_{20} 852}-\frac{207}{\log_{20}207})=178.\)
Status Protein1 Protein2 d d1/2
Query variables 4XOQ_1 4YSY_1 229 148
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]