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Parikh vectors
2NRB_1 7EDT_1 8YSP_1 Letter Amino acid
37 0 22 E Glutamic acid
43 0 53 L Leucine
3 0 4 W Tryptophan
39 1 30 A Alanine
20 0 17 R Arginine
7 0 10 H Histidine
17 0 15 F Phenylalanine
13 0 12 M Methionine
26 0 34 S Serine
12 0 10 Y Tyrosine
13 0 13 Q Glutamine
49 4 28 G Glycine
32 0 25 I Isoleucine
37 0 12 K Lycine
28 0 19 T Threonine
40 0 25 V Valine
22 0 19 N Asparagine
21 0 21 D Aspartic acid
4 5 2 C Cysteine
18 0 23 P Proline 

2NRB_1|Chains A, B, C, D|Succinyl-CoA:3-ketoacid-coenzyme A transferase 1|Sus scrofa (9823)
>7EDT_1|Chains A, B|RNA (5'-R(*GP*GP*AP*CP*UP*CP*CP*GP*GP*(5BU)P*CP*C)-3')|synthetic construct (32630)
>8YSP_1|Chains A, B|CylI|Cylindrospermum licheniforme UTEX B 2014 (379530)
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 \(w=f(c)\)
2NRB , Knot 195 481 0.83 40 227 449 
TKFYTDAVEAVKDIPNGATVLVGGFGLSGIPENLIGALLKTGVKELTAVSNNAGVDNFGLGLLLQSKQIKRMISSYVGENAEFERQYLAGELEVELTPQGTLAERIRAGGAGVPAFYTSTGYGTLVQEGGSPIKYNKDGSIAIASKPREVREFNGQHFILEEAIRGDFALVKAWKADQAGNVTFRKSARNFNLPMCKAAETTVVEVEEIVDIGSFAPEDIHIPKIYVHRLVKGEKYEKRIERLSVRKEEDVKTRSGKLGDNVRERIIKRAALEFEDGMYANLGIGIPLLASNFISPNMTVHLQSENGILGLGPYPLQNEVDADLINAGKETVTVLPGASYFSSDESFAMIRGGHVNLTMLGAMQVSKYGDLANWMIPGKLVKGMGGAMDLVSSAKTKVVVTMEHSAKGNAHKIMEKCTLPLTGKQCVNRIITEKAVFDVDRKKGLTLIELWEGLTVDDIKKSTGCDFAVSPKLIPMQQVTT
7EDT , Knot 7 12 0.48 8 8 9 
GGACUCCGGUCC
8YSP , Knot 166 394 0.84 40 209 365 
MGSSHHHHHHSSGENLYFQGHMTYIVSTSTAFPENYYPQTVLAAALRRFFTVMELDFDLEQIDRFFTNVKIDGRYFALPLDSLLDPPTWGVSISRGLENSLNLAETAITKLLEKTNVQPQDISLLASVSMTPAIPSLDGRLMNRIPFSSTLKRLPMNGVGCMGGAFGISRVADYLKAHPKEAAILFAVEISSALWQGSLQANLTSLIRRLPENPSLYSEIIMDIITAALFADGCGAVLMVGKEHPLAKSGLPQVIDNRSFLVPNTVELMGLDVVDNGFRNILRPEVSDALKQGLRPLINGLLADNNIESENLYRWIVHPGGPKVIDTVEAEFGLDSQTLQLSRDTLAEVGNISSATVLYMLDKVLSEEQSPPDSYGLIVAMGPGLAQEAILLKW

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 \(c\).

\(|P_{f(2NRB_1)}(2) \setminus P_{f(7EDT_1)}(2)|=225\), \(|P_{f(7EDT_1)}(2) \setminus P_{f(2NRB_1)}(2)|=6\). 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 1:0010001101100110110111111110111001111110011001011000111001111111000010011000110010100001110101010101011001011111111100001010110011011000001011110010010010100111001101011110110100110101000100101110011000110100110110111001011010100110100000010010100000100001011001000110011101001101011111111100110101010100001111111011000101011011000101111100100000111101101010111110100010110111110110111111011001000111010001010100110000111010001001100011101000011011011011010010000100111010111100100
Pair \(Z_2\) Length of longest common subsequence
2NRB_1,7EDT_1 231 3
2NRB_1,8YSP_1 154 4
7EDT_1,8YSP_1 211 3

Newick tree

 
[
	7EDT_1:11.73,
	[
		2NRB_1:77,8YSP_1:77
	]:42.73
]

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 \((0.85)(0.8)(\frac{493 }{\log_{20} 493}-\frac{12}{\log_{20}12})=152.\)
Status Protein1 Protein2 d d1/2
Query variables 2NRB_1 7EDT_1 192 98.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]