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Parikh vectors
2LYE_1 7VFL_1 6VAX_1 Letter Amino acid
0 21 54 A Alanine
0 27 23 Q Glutamine
0 32 40 E Glutamic acid
2 19 66 G Glycine
0 30 20 F Phenylalanine
6 23 39 R Arginine
0 30 33 D Aspartic acid
0 20 27 H Histidine
0 49 51 L Leucine
0 17 25 P Proline
0 4 5 W Tryptophan
0 36 37 S Serine
4 32 44 V Valine
0 30 19 N Asparagine
6 4 18 C Cysteine
0 34 28 I Isoleucine
0 34 27 K Lycine
0 7 15 M Methionine
0 19 36 T Threonine
0 37 25 Y Tyrosine 

2LYE_1|Chain A|BTD-2|null
>7VFL_1|Chains A, B[auth C]|Glycosyl transferase, group 1 family protein|Staphylococcus aureus (strain USA300) (367830)
>6VAX_1|Chains A, C|Succinate dehydrogenase [ubiquinone] flavoprotein subunit, mitochondrial|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 \(w=f(c)\)
2LYE , Knot 7 18 0.37 8 7 8 
GVCRCVCRRGVCRCVCRR
7VFL , Knot 207 505 0.85 40 246 466 
AMNYFVGNSLGVNLTGIEKAIINRLNLFKEMGRPAQCVFLSWNRYLYRNAQNYITSSDYINMYDFFQEATYLERNEPFDWLSYWTDECHYTLKHVENSHDFRIYDQERFLMYAHFQDPKYRILDYVNHFDSQRRKVKRDFYDVRGFLSCSRILVDKQQTLCEFFYNPEGDTKLEKYFSYKDGKPEVQKIIVYYANKQYFFNNETELGAFFIKQLYQHGDLFFSDRNVYTAPIFNLTPESIPVVAVLHSTHIKNIDALDSSPFKNVYKAMFENLSRYRAIIVSTEQQKLDVEKRINHTIPVVNIPVGYSETIDTPVQTLDQRSVKLISVARYSPEKQLHQQIELIKRLVSYVPKIELHMYGFGSESKKLNELIQKYGLENHVYLRGFLSNLDQEYSDAYLSLITSNMEGFSLALLESLAHGVPVISYDIKYGPNELITSDFNGYLITKNDEDALFDKVKYVIDHPEVQQRLSKGSLAKAQQYSKASLIKQWDQFVRLILEHHHHHH
6VAX , Knot 249 632 0.84 40 274 590 
MRGSHHHHHHGSAKVSDSISAQYPVVDHEFDAVVVGAGGAGLRAAFGLSEAGFNTACVTKLFPTRSHTVAAQGGINAALGNMEEDNWRWHFYDTVKGSDWLGDQDAIHYMTEQAPAAVVELENYGMPFSRTEDGKIYQRAFGGQSLKFGKGGQAHRCCCVADRTGHSLLHTLYGRSLRYDTSYFVEYFALDLLMENGECRGVIALCIEDGSIHRIRAKNTVVATGGYGRTYFSCTSAHTSTGDGTAMITRAGLPCQDLEFVQFHPTGIYGAGCLITEGCRGEGGILINSQGERFMERYAPVAKDLASRDVVSRSMTLEIREGRGCGPEKDHVYLQLHHLPPEQLATRLPGISETAMIFAGVDVTKEPIPVLPTVHYNMGGIPTNYKGQVLRHVNGQDQIVPGLYACGEAACASVHGANRLGANSLLDLVVFGRACALSIEESCRPGDKVPPIKPNAGEESVMNLDKLRFADGSIRTSELRLSMQKSMQNHAAVFRVGSVLQEGCGKISKLYGDLKHLKTFDRGMVWNTDLVETLELQNLMLCALQTIYGAEARKESRGAHAREDYKVRIDEYDYSKPIQGQQKKPFEEHWRKHTLSYVDVGTGKVTLEYRPVIDKTLNEADCATVPPAIRSY

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 \(c\).

\(|P_{f(2LYE_1)}(2) \setminus P_{f(7VFL_1)}(2)|=3\), \(|P_{f(7VFL_1)}(2) \setminus P_{f(2LYE_1)}(2)|=242\). 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 1:110001000110001000
Pair \(Z_2\) Length of longest common subsequence
2LYE_1,7VFL_1 245 2
2LYE_1,6VAX_1 271 3
7VFL_1,6VAX_1 128 6

Newick tree

 
[
	2LYE_1:14.49,
	[
		7VFL_1:64,6VAX_1:64
	]:80.49
]

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 \((0.85)(0.8)(\frac{523 }{\log_{20} 523}-\frac{18}{\log_{20}18})=157.\)
Status Protein1 Protein2 d d1/2
Query variables 2LYE_1 7VFL_1 202 103
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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