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Parikh vectors
5NEF_1 5QRQ_1 7FLT_1 Letter Amino acid
0 8 11 R Arginine
0 9 23 I Isoleucine
0 12 19 K Lycine
0 12 10 P Proline
0 7 21 T Threonine
0 4 5 W Tryptophan
0 12 14 N Asparagine
7 2 1 C Cysteine
0 5 9 Q Glutamine
0 12 15 E Glutamic acid
7 13 7 G Glycine
0 14 29 L Leucine
0 6 8 M Methionine
0 8 10 F Phenylalanine
0 9 18 S Serine
0 14 14 V Valine
3 9 18 A Alanine
0 4 14 D Aspartic acid
0 6 5 H Histidine
0 6 7 Y Tyrosine 

5NEF_1|Chain A|RNA (5'-R(*GP*GP*UP*GP*GP*GP*GP*AP*CP*GP*AP*CP*CP*CP*CP*AP*(CBV)P*C)-3')|Gloeobacter violaceus (33072)
>5QRQ_1|Chain A|T-box transcription factor T|Homo sapiens (9606)
>7FLT_1|Chain A|Pre-mRNA-splicing factor 8|Saccharomyces cerevisiae S288C (559292)
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 \(w=f(c)\)
5NEF , Knot 8 18 0.42 8 8 12 
GGUGGGGACGACCCCACC
5QRQ , Knot 81 172 0.80 40 131 168 
GELRVGLEESELWLRFKELTNEMIVTKNGRRMFPVLKVNVSGLDPNAMYSFLLDFVAADNHRWKYVNGEWVPGGKPEPQAPSCVYIHPDSPNFGAHWMKAPVSFSKVKLTNKLNGGGQIMLNSLHKYEPRIHIVRVGGPQRMITSHCFPETQFIAVTAYQNEEITALKIKYN
7FLT , Knot 117 258 0.84 40 175 251 
GAMNSSNYAELFNNDIKLFVDDTNVYRVTVHKTFEGNVATKAINGCIFTLNPKTGHLFLKIIHTSVWAGQKRLSQLAKWKTAEEVSALVRSLPKEEQPKQIIVTRKAMLDPLEVHMLDFPNIAIRPTELRLPFSAAMSIDKLSDVVMKATEPQMVLFNIYDDWLDRISSYTAFSRLTLLLRALKTNEESAKMILLSDPTITIKSYHLWPSFTDEQWITIESQMRDLILTEYGRKYNVNISALTQTEIKDIILGQNIKA

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 \(c\).

\(|P_{f(5NEF_1)}(2) \setminus P_{f(5QRQ_1)}(2)|=6\), \(|P_{f(5QRQ_1)}(2) \setminus P_{f(5NEF_1)}(2)|=129\). 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 1:110111110110000100
Pair \(Z_2\) Length of longest common subsequence
5NEF_1,5QRQ_1 135 3
5NEF_1,7FLT_1 181 2
5QRQ_1,7FLT_1 172 3

Newick tree

 
[
	7FLT_1:94.19,
	[
		5NEF_1:67.5,5QRQ_1:67.5
	]:26.69
]

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 \((0.85)(0.8)(\frac{190 }{\log_{20} 190}-\frac{18}{\log_{20}18})=61.0\)
Status Protein1 Protein2 d d1/2
Query variables 5NEF_1 5QRQ_1 78 42
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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