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Parikh vectors
7XAU_1 6ZBB_1 5ICX_1 Letter Amino acid
29 1 9 D Aspartic acid
11 0 4 C Cysteine
37 9 16 T Threonine
10 3 3 W Tryptophan
54 1 14 V Valine
18 2 11 E Glutamic acid
35 0 13 G Glycine
52 13 16 L Leucine
22 6 10 P Proline
22 2 8 Y Tyrosine
29 0 12 A Alanine
19 0 8 R Arginine
25 3 11 N Asparagine
17 4 0 M Methionine
41 3 34 S Serine
15 3 12 Q Glutamine
16 2 3 H Histidine
52 4 10 I Isoleucine
28 6 11 K Lycine
31 4 8 F Phenylalanine 

7XAU_1|Chain A|Somatostatin receptor type 2,LargeBit|Homo sapiens (9606)
>6ZBB_1|Chain A[auth 8]|ATP synthase protein 8|Bos taurus (9913)
>5ICX_1|Chains A, C|Cetuximab Fab light chain|MUS MUSCULUS (10090)
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 \(w=f(c)\)
7XAU , Knot 227 563 0.85 40 262 512 
MKTIIALSYIFCLVFADYKDDDDKGSGSHHHHHHHHHHLEVLFQGPMDMADEPLNGSHTWLSIPFDLNGSVVSTNTSNQTEPYYDLTSNAVLTFIYFVVCIIGLCGNTLVIYVILRYAKMKTITNIYILNLAIADELFMLGLPFLAMQVALVHWPFGKAICRVVMTVDGINQFTSIFCLTVMSIDRYLAVVHPIKSAKWRRPRTAKMITMAVWGVSLLVILPIMIYAGLRSNQWGRSSCTINWPGESGAWYTGFIIYTFILGFLVPLTIICLCYLFIIIKVKSSGIRVGSSKRKKSEKKVTRMVSIVVAVFIFCWLPFYIFNVSSVSMAISPTPALKGMFDFVVVLTYANSCANPILYAFLSDNFKKSFQNVLCLVKVSGTDDGERSDSKQDKSRLNETTETQRTVFTLEDFVGDWEQTAAYNLDQVLEQGGVSSLLQNLAVSVTPIQRIVRSGENALKIDIHVIIPYEGLSADQMAQIEEVFKVVYPVDDHHFKVILPYGTLVIDGVTPNMLNYFGRPYEGIAVFDGKKITVTGTLWNGNKIIDERLITPDGSMLFRVTINS
6ZBB , Knot 36 66 0.76 32 54 63 
MPQLDTSTWLTMILSMFLTLFIIFQLKVSKHNFYHNPELTPTKMLKQNTPWETKWTKIYLPLLLPL
5ICX , Knot 96 213 0.80 38 145 204 
DILLTQSPVILSVSPGERVSFSCRASQSIGTNIHWYQQRTNGSPRLLIKYASESISGIPSRFSGSGSGTDFTLSINSVESEDIADYYCQQNNNWPTTFGAGTKLELKRTVAAPSVFIFPPSDEQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGA

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 \(c\).

\(|P_{f(7XAU_1)}(2) \setminus P_{f(6ZBB_1)}(2)|=219\), \(|P_{f(6ZBB_1)}(2) \setminus P_{f(7XAU_1)}(2)|=11\). 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 1:10011110011011110000000010100000000000101110111011001101000110111010101100000000010001000111011011101111010011101110010100100101101111001111111111101111011110110011101011001001101011010001111011001010010010110111111011111111101110000110000010111001110011110011111111101101001111101000110110000000000100110111111110111101101001011101011101110111110010001011101110001000100110110101000100000000000100000000011010011101000110010011001110011001110101100110010011010101111001101001101001101101100001011110101110110101100110100111110100101010110100110001101010111010100
Pair \(Z_2\) Length of longest common subsequence
7XAU_1,6ZBB_1 230 4
7XAU_1,5ICX_1 185 4
6ZBB_1,5ICX_1 159 3

Newick tree

 
[
	7XAU_1:11.41,
	[
		5ICX_1:79.5,6ZBB_1:79.5
	]:31.91
]

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 \((0.85)(0.8)(\frac{629 }{\log_{20} 629}-\frac{66}{\log_{20}66})=166.\)
Status Protein1 Protein2 d d1/2
Query variables 7XAU_1 6ZBB_1 208 116
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]