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Parikh vectors
7PZZ_1 2WVC_1 3FDZ_1 Letter Amino acid
20 8 12 Q Glutamine
35 13 16 E Glutamic acid
15 4 4 M Methionine
19 2 14 P Proline
3 1 6 W Tryptophan
33 8 19 V Valine
44 5 30 A Alanine
23 12 15 D Aspartic acid
3 2 1 C Cysteine
41 15 27 L Leucine
18 4 2 F Phenylalanine
19 11 9 N Asparagine
25 14 11 I Isoleucine
39 7 13 K Lycine
31 11 10 S Serine
21 9 16 R Arginine
10 5 12 H Histidine
24 6 11 T Threonine
22 3 13 Y Tyrosine
35 8 16 G Glycine 

7PZZ_1|Chains A, B, C, D|Serine hydroxymethyltransferase 2, mitochondrial|Arabidopsis thaliana (3702)
>2WVC_1|Chains A, B|PUTATIVE NICKEL-RESPONSIVE REGULATOR|HELICOBACTER PYLORI (85962)
>3FDZ_1|Chain A|2,3-bisphosphoglycerate-dependent phosphoglycerate mutase|Burkholderia pseudomallei 1710b (320372)
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 \(w=f(c)\)
7PZZ , Knot 194 480 0.83 40 237 455 
SNAEKSRSSWIKQLNASLDEIDPEVADIIELEKARQWKGFELIPSENFTSLSVMQAVGSVMTNKYSEGYPGARYYGGNEYIDMAETLCQKRALEAFQLDPSKWGVNVQSLSGSPANFQVYTALLKPHERIMALDLPHGGHLSHGYQTDTKKISAVSIFFETMPYRLDENTGYIDYDQLEKSAVLFRPKLIVAGASAYARLYDYARIRKVCNKQKAVMLADMAHISGLVAAGVIPSPFEYADVVTTTTHKSLRGPRGAMIFFRKGLKEINKQGKEVMYDYEDRINQAVFPGLQGGPHNHTITGLAVALKQARTPEYKAYQDQVLRNCSKFAETLLAKGYDLVSGGTDNHLVLVNLKNKGIDGSRVEKVLELVHIAANKNTVPGDVSAMVPGGIRMGTPALTSRGFIEEDFAKVAEYFDLAVKIALKIKAESQGTKLKDFVATMQSNEKLQSEMSKLREMVEEYAKQFPTIGFEKETMRYKE
2WVC , Knot 74 148 0.83 40 115 144 
MDTPNKDDSIIRFSVSLQQNLLDELDNRIIKNGYSSRSELVRDMIREKLVEDNWAEDNPNDESKIAVLVVIYDGGQRELNQRMIDIQHASGTHVLCTTHIHMDEHNCLETIILQGNSFEIQRLQLEIGGLRGVKFAKLTKASSFEYNE
3FDZ , Knot 115 257 0.82 40 159 244 
MAHHHHHHMYKLVLIRHGESTWNKENRFTGWVDVDLTEQGNREARQAGQLLKEAGYTFDIAYTSVLKRAIRTLWHVQDQMDLMYVPVVHSWRLNERHYGALSGLNKAETAAKYGDEQVLVWRRSYDTPPPALEPGDERAPYADPRYAKVPREQLPLTECLKDTVARVLPLWNESIAPAVKAGKQVLIAAHGNSLRALIKYLDGISDADIVGLNIPNGVPLVYELDESLTPIRHYYLGDQEAIAKAQAAVAQQGKSAA

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 \(c\).

\(|P_{f(7PZZ_1)}(2) \setminus P_{f(2WVC_1)}(2)|=154\), \(|P_{f(2WVC_1)}(2) \setminus P_{f(7PZZ_1)}(2)|=32\). 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 1:001000000110010101001010110110100100101101110001001011011101100000010111000110001011001000011011010100111010010101101010011101000111101101101001000000010110111001100100001010000100011110101111110101010001010010000011111011010111111111011001011000000010110111111001100100010011000000100111111011100001011111100100100010000110000011001110100110110000111101000110100100110110111000011101011111110110111000111000110110010111011101010001001001110100000100010010011000100110111000010000
Pair \(Z_2\) Length of longest common subsequence
7PZZ_1,2WVC_1 186 3
7PZZ_1,3FDZ_1 176 3
2WVC_1,3FDZ_1 166 3

Newick tree

 
[
	7PZZ_1:92.91,
	[
		3FDZ_1:83,2WVC_1:83
	]:9.91
]

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 \((0.85)(0.8)(\frac{628 }{\log_{20} 628}-\frac{148}{\log_{20}148})=138.\)
Status Protein1 Protein2 d d1/2
Query variables 7PZZ_1 2WVC_1 177 115
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]