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Parikh vectors
3TVW_1 1QBM_1 1YDT_1 Letter Amino acid
33 12 16 N Asparagine
2 5 2 C Cysteine
29 12 14 Q Glutamine
50 9 21 I Isoleucine
67 13 32 L Leucine
54 11 24 A Alanine
45 10 19 D Aspartic acid
63 9 27 E Glutamic acid
33 8 25 F Phenylalanine
32 10 13 P Proline
42 20 14 T Threonine
53 10 20 V Valine
50 6 15 R Arginine
44 13 34 K Lycine
25 10 14 Y Tyrosine
57 15 22 G Glycine
15 4 9 H Histidine
18 2 7 M Methionine
43 30 16 S Serine
14 5 6 W Tryptophan 

3TVW_1|Chains A, B, C|Acetyl-CoA carboxylase|Saccharomyces cerevisiae S288c (559292)
>1QBM_1|Chain A[auth L]|E8B ANTIBODY|Mus musculus (10090)
>1YDT_1|Chain A[auth E]|C-AMP-DEPENDENT PROTEIN KINASE|Bos taurus (9913)
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 \(w=f(c)\)
3TVW , Knot 300 769 0.86 40 290 698 
MASGSMHLRPIATPYPVKEWLQPKRYKAHLMGTTYVYDFPELFRQASSSQWKNFSADVKLTDDFFISNELIEDENGELTEVEREPGANAIGMVAFKITVKTPEYPRGRQFVVVANDITFKIGSFGPQEDEFFNKVTEYARKRGIPRIYLAANSGARIGMAEEIVPLFQVAWNDAANPDKGFQYLYLTSEGMETLKKFDKENSVLTERTVINGEERFVIKTIIGSEDGLGVECLRGSGLIAGATSRAYHDIFTITLVTCRSVGIGAYLVRLGQRAIQVEGQPIILTGASALNKVLGREVYTSNLQLGGTQIMYNNGVSHLTAVDDLAGVEKIVEWMSYVPAKRNMPVPILETKDTWDRPVDFTPTNDETYDVRWMIEGRETESGFEYGLFDKGSFFETLSGWAKGVVVGRARLGGIPLGVIGVETRTVENLIPADPANPNSAETLIQQAGQVWFPNSAFKTAQAINDFNNGEQLPMMILANWRGFSGGQRDMFNEVLKYGSFIVDALVDYKQPIIIYIPPTGELRGGSWVVVDPTINADQMEMYADVNARAGVLEPEGTVEIKFRREKLLDTMNRLDDKYRELRSQLSNKSLAPEVHQQISKQLADRERELLPIYGQISLQFADLHDRSSRMVAKGVISKELEWTEARRFFFWRLRRRLNEEYLIKRLSHQVGEASRLEKIARIRSWYPASVDHEDDRQVATWIEENYKTLDDKLKGLKLESFAQDLAKKIRSDHDNAIDGLSEVIKMLSTDDKEKLLKTLKLEHHHHHH
1QBM , Knot 99 214 0.82 40 155 208 
DIQMTQSPASLSASVGETVTITCRASGNIHNYLAWYQQKQGKSPQLLVYNAKTLADGVPSRFSGSGSGTQYSLKINSLQPEDFGSYYCQHFWSTPWTFGGGTKLEIKRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNEC
1YDT , Knot 150 350 0.83 40 209 334 
GNAAAAKKGSEQESVKEFLAKAKEDFLKKWENPAQNTAHLDQFERIKTLGTGSFGRVMLVKHMETGNHYAMKILDKQKVVKLKQIEHTLNEKRILQAVNFPFLVKLEFSFKDNSNLYMVMEYVAGGEMFSHLRRIGRFSEPHARFYAAQIVLTFEYLHSLDLIYRDLKPENLLIDQQGYIQVTDFGFAKRVKGRTWTLCGTPEYLAPEIILSKGYNKAVDWWALGVLIYEMAAGYPPFFADQPIQIYEKIVSGKVRFPSHFSSDLKDLLRNLLQVDLTKRFGNLKDGVNDIKNHKWFATTDWIAIYQRKVEAPFIPKFKGPGDTSNFDDYEEEEIRVSINEKCGKEFSEF

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 \(c\).

\(|P_{f(3TVW_1)}(2) \setminus P_{f(1QBM_1)}(2)|=169\), \(|P_{f(1QBM_1)}(2) \setminus P_{f(3TVW_1)}(2)|=34\). 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 1:1101010101110101100110100001011100010011011001000010010101010001110001100001010010001110111111101010010010100111110010101101110000110010001000111010111001101111001111101110011010011001010001100100100000110000110100011100111000111100101011111100010001101011000011111011011001101010111101101100111001000010111001100011001011001111001101100111000111111000001001101010000000101110100000110011100101100101110111110101111111111100001001111011010010011001101111001100101100100100111111101011011000110011001011101110000111101110101011011110101010010101010101111010101010100001100100100000010001000011101000100011000001111010101011010000001110111000101001001111010001000011001000110100100110100101101000000011011000000100010110100110011001000000110110011011000000011001010000000
Pair \(Z_2\) Length of longest common subsequence
3TVW_1,1QBM_1 203 3
3TVW_1,1YDT_1 157 4
1QBM_1,1YDT_1 178 3

Newick tree

 
[
	1QBM_1:10.47,
	[
		3TVW_1:78.5,1YDT_1:78.5
	]:21.97
]

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 \((0.85)(0.8)(\frac{983 }{\log_{20} 983}-\frac{214}{\log_{20}214})=209.\)
Status Protein1 Protein2 d d1/2
Query variables 3TVW_1 1QBM_1 268 169
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]