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Parikh vectors
6ZQG_1 5FHK_1 2PXV_1 Letter Amino acid
22 9 0 T Threonine
18 13 0 P Proline
24 10 0 R Arginine
42 14 0 D Aspartic acid
2 1 12 C Cysteine
43 20 0 L Leucine
19 4 0 Q Glutamine
20 12 17 G Glycine
38 11 0 K Lycine
34 13 0 S Serine
27 17 0 I Isoleucine
7 10 0 M Methionine
23 5 0 F Phenylalanine
4 3 0 W Tryptophan
39 13 12 A Alanine
21 12 0 N Asparagine
49 10 0 E Glutamic acid
9 8 0 H Histidine
17 8 0 Y Tyrosine
25 14 0 V Valine 

6ZQG_10|Chain K[auth JH]|Essential nuclear protein 1|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>5FHK_1|Chains A, B, C, D, E, F|LysR family transcriptional regulator|Vibrio vulnificus (672)
>2PXV_1|Chain A[auth B]|4.5 S RNA|Escherichia coli (562)
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 \(w=f(c)\)
6ZQG , Knot 193 483 0.82 40 249 449 
MARASSTKARKQRHDPLLKDLDAAQGTLKKINKKKLAQNDAANHDAANEEDGYIDSKASRKILQLAKEQQDEIEGEELAESERNKQFEARFTTMSYDDEDEDEDEDEEAFGEDISDFEPEGDYKEEEEIVEIDEEDAAMFEQYFKKSDDFNSLSGSYNLADKIMASIREKESQVEDMQDDEPLANEQNTSRGNISSGLKSGEGVALPEKVIKAYTTVGSILKTWTHGKLPKLFKVIPSLRNWQDVIYVTNPEEWSPHVVYEATKLFVSNLTAKESQKFINLILLERFRDNIETSEDHSLNYHIYRAVKKSLYKPSAFFKGFLFPLVETGCNVREATIAGSVLAKVSVPALHSSAALSYLLRLPFSPPTTVFIKILLDKKYALPYQTVDDCVYYFMRFRILDDGSNGEDATRVLPVIWHKAFLTFAQRYKNDITQDQRDFLLETVRQRGHKDIGPEIRRELLAGASREFVDPQEANDDLMIDVN
5FHK , Knot 100 207 0.85 40 154 204 
GAMGASGKIKISTPYNLTKRMMMPMLNGFMSQYPEINIELTTESNADQLDPTEWDVIFRVGPQRDSSLIARKIGSVKDILVASPEYVNAHPMPTHAEDLHDHFLLKGHPLLKWTLINSKGETVVNVDRGRFQANALNVVRSACSEGLGITLMPDVMIKEYIADGSLVRILPDWSANPRDIYMLYNHKDHLPEKVRLFIDYVIAYNIH
2PXV , Knot 16 49 0.42 8 15 30 
GGUGGUGUUUACCAGGUCAGGUCCGAAAGGAAGCAGCCAAGGCACUGCC

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 \(c\).

\(|P_{f(6ZQG_1)}(2) \setminus P_{f(5FHK_1)}(2)|=130\), \(|P_{f(5FHK_1)}(2) \setminus P_{f(6ZQG_1)}(2)|=35\). 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 1:110100001000000111001011010100100001100011000110000101000100011011000000101001100000001010100100000000000000111001001010100000001101000011110001000001001010001100111010000001001000011100000001010011001011111001101000110110010010110110111010010011010010010101100100111001010000011011110010001000000010001001100010010111011111110010010010111011101011110001110011011101100111011100001110001000100110101100100100100111111001110110000001000000111001000100011101000111110001101001000111010
Pair \(Z_2\) Length of longest common subsequence
6ZQG_1,5FHK_1 165 5
6ZQG_1,2PXV_1 256 2
5FHK_1,2PXV_1 165 2

Newick tree

 
[
	2PXV_1:11.85,
	[
		6ZQG_1:82.5,5FHK_1:82.5
	]:32.35
]

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 \((0.85)(0.8)(\frac{690 }{\log_{20} 690}-\frac{207}{\log_{20}207})=135.\)
Status Protein1 Protein2 d d1/2
Query variables 6ZQG_1 5FHK_1 168 119
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]