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Parikh vectors
7VTZ_1 5EES_1 2GFC_1 Letter Amino acid
14 9 15 R Arginine
42 17 18 D Aspartic acid
29 9 25 F Phenylalanine
33 2 14 Y Tyrosine
22 11 17 N Asparagine
18 15 27 E Glutamic acid
38 27 22 G Glycine
25 7 34 K Lycine
13 8 14 P Proline
14 30 20 V Valine
47 29 23 A Alanine
0 1 2 C Cysteine
17 14 21 I Isoleucine
9 5 7 M Methionine
16 11 14 Q Glutamine
13 7 9 H Histidine
23 20 32 L Leucine
28 12 16 S Serine
26 12 14 T Threonine
15 1 6 W Tryptophan 

7VTZ_1|Chain A|Chitoporin|Escherichia coli K-12 (83333)
>5EES_1|Chain A|4-hydroxy-tetrahydrodipicolinate reductase|Corynebacterium glutamicum (strain ATCC 13032 / DSM 20300 / JCM 1318 / LMG 3730 / NCIMB 10025) (196627)
>2GFC_1|Chain A|cAMP-dependent protein kinase, alpha-catalytic subunit|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 \(w=f(c)\)
7VTZ , Knot 183 442 0.84 38 230 424 
EGFIDDSTLTGGIYYWQRERDRKDVTDGDKYKTNLSHSTWNANLDFQSGYAADMFGLDIAAFTAIEMAENGDSSHPNEIAFSKSNKAYDEDWSGDKSGISLYKAAAKFKYGPVWARAGYIQPTGQTLLAPHWSFMPGTYQGAEAGANFDYGDAGALSFSYMWTNEYKAPWHLEMDEFYQNDKTTKVDYLHSFGAKYDFKNNFVLEAAFGQAEGYIDQYFAKASYKFDIAGSPLTTSYQFYGTRDKVDDRSVNDLYDGTAWLQALTFGYRAADVVDLRLEGTWVKADGQQGYFLQRMTPTYASSNGRLDIWWDNRSDFNANGEKAVFFGAMYDLKNWNLPGFAIGASYVYAWDAKPATWQSNPDAYYDKNRTIEESAYSLDAVYTIQDGRAKGTMFKLHFTEYDNHSDIPSWGGGYGNIFQDERDVKFMVIAPFTIFHHHHHH
5EES , Knot 107 247 0.79 40 149 232 
GIKVGVLGAKGRVGQTIVAAVNESDDLELVAEIGVDDDLSLLVDNGAEVVVDFTTPNAVMGNLEFCINNGISAVVGTTGFDDARLEQVRDWLEGKDNVGVLIAPNFAISAVLTMVFSKQAARFFESAEVIELHHPNKLDAPSGTAIHTAQGIAAARKEAGMDAQPDATEQALEGSRGASVDGIPVHAVRMSGMVAHEQVIFGTQGQTLTIKQDSYDRNSFAPGVLVGVRNIAQHPGLVVGLEHYLGL
2GFC , Knot 150 350 0.83 40 209 335 
GNAAAAKKGSEQESVKEFLAKAKEDFLKKWENPAQNTAHLDQFERIKTLGTGSFGRVMLVKHMETGNHYAMKILDKQKVVKLKQIEHTLNEKRILQAVNFPFLVKLEFSFKDNSNLYMVMEYVPGGEMFSHLRRIGRFSEPHARFYAAQIVLTFEYLHSLDLIYRDLKPENLLIDQQGYIQVTDFGFAKRVKGRTWTLCGTPEYLAPEIILSKGYNKAVDWWALGVLIYEMAAGYPPFFADQPIQIYEKIVSGKVRFPSHFSSDLKDLLRNLLQVDLTKRFGNLKNGVNDIKNHKWFATTDWIAIYQRKVEAPFIPKFKGPGDTSNFDDYEEEEIRVSINEKCGKEFSEF

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 \(c\).

\(|P_{f(7VTZ_1)}(2) \setminus P_{f(5EES_1)}(2)|=123\), \(|P_{f(5EES_1)}(2) \setminus P_{f(7VTZ_1)}(2)|=42\). 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 1:0111000010111001000000001001000000100001010101001011011110111101101100100001001110000010000101000110100111010011111011010101001111010111100011011101001011110100110000011101010010000000010010011100010001110111101010100011010001011101100000101000010000100100101110110110011011010101011010100101100101001000101011100000101010011111110010010111111110010110101101000101000000010001001011001001010101101010000000011011110101100000101111111011000000
Pair \(Z_2\) Length of longest common subsequence
7VTZ_1,5EES_1 165 4
7VTZ_1,2GFC_1 155 4
5EES_1,2GFC_1 164 4

Newick tree

 
[
	5EES_1:83.77,
	[
		7VTZ_1:77.5,2GFC_1:77.5
	]:6.27
]

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 \((0.85)(0.8)(\frac{689 }{\log_{20} 689}-\frac{247}{\log_{20}247})=123.\)
Status Protein1 Protein2 d d1/2
Query variables 7VTZ_1 5EES_1 153 117.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]