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Parikh vectors
2UWR_1 7VJA_1 9OFG_1 Letter Amino acid
4 34 34 A Alanine
10 19 20 N Asparagine
6 35 22 K Lycine
1 11 14 M Methionine
3 27 33 V Valine
2 25 40 R Arginine
5 45 43 E Glutamic acid
1 17 8 H Histidine
7 45 37 L Leucine
1 12 3 W Tryptophan
4 19 12 Y Tyrosine
4 23 28 F Phenylalanine
2 26 14 P Proline
2 39 43 S Serine
6 13 32 T Threonine
5 23 27 D Aspartic acid
11 5 3 C Cysteine
3 9 17 Q Glutamine
1 32 42 G Glycine
1 23 47 I Isoleucine 

2UWR_1|Chain A|CD59 GLYCOPROTEIN|HOMO SAPIENS (9606)
>7VJA_1|Chain A|DNA photolyase|Methanosarcina mazei Go1 (192952)
>9OFG_1|Chains A, B, C, D, E, F|Circadian clock protein kinase KaiC|Synechococcus elongatus (32046)
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 \(w=f(c)\)
2UWR , Knot 42 79 0.77 40 67 75 
MLQCYNCPNPTADCKTAVNCSSDFDACLITKAGLQVYNKCWKFEHCNFNDVTTRLRENELTYYCCKKDLCNFNEQLENC
7VJA , Knot 196 482 0.83 40 243 441 
MGSSHHHHHHSSGLVPRGSHMNPKRIRALKSGKQGDGPVVYWMSRDQRAEDNWALLFSRAIAKEANVPVVVVFCLTDEFLEAGIRQYEFMLKGLQELEVSLSRKKIPSFFLRGDPGEKISRFVKDYNAGTLVTDFSPLRIKNQWIEKVISGISIPFFEVDAHNVVPCWEASQKHEYAAHTFRPKLYALLPEFLEEFPELEPNSVTPELSAGAGMVETLSDVLETGVKALLPERALLKNKDPLFEPWHFEPGEKAAKKVMESFIADRLDSYGALRNDPTKNMLSNLSPYLHFGQISSQRVVLEVEKAESNPGSKKAFLDEILIWKEISDNFCYYNPGYDGFESFPSWAKESLNAHRNDVRSHIYTLEEFEAGKTHDPLWNASQMELLSTGKMHGYTRMYWAKKILEWSESPEKALEIAICLNDRYELDGRDPNGYAGIAWSIGGVHDRAWGEREVTGKIRYMSYEGCKRKFDVKLYIEKYSAL
9OFG , Knot 205 519 0.82 40 236 480 
MTSAEMTSPNNNSEHQAIAKMRTMIEGFDDISHGGLPIGRSTLVSGTSGTGKTLFSIQFLYNGIIEFDEPGVFVTFEETPQDIIKNARSFGWDLAKLVDEGKLFILDASPDPEGQEVVGGFDLSALIERINYAIQKYRARRVSIDSVTSVFQQYDASSVVRRELFRLVARLKQIGATTVMTTERIEEYGPIARYGVEEFVSDNVVILRNVLEGERRRRTLEILKLRGTSHMKGEYPFTITDHGINIFPLGAMRLTQRSSNVRVSSGVVRLDEMCGGGFFKDSIILATGATGTGKTLLVSRFVENACANKERAILFAYEESRAQLLRNAYSWGMDFEEMERQNLLKIVCAYPESAGLEDHLQIIKSEINDFKPARIAIDSLSALARGVSNNAFRQFVIGVTGYAKQEEITGLFTNTSDQFMGAHSITDSHIAEITDTIILLQYVEIRGEMSRAINVFKMRGSWHDKAIREFMISDKGPDIKDSFRNFERIISGSPTRITVDEKSELSRIVRGVQEKGPES

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 \(c\).

\(|P_{f(2UWR_1)}(2) \setminus P_{f(7VJA_1)}(2)|=26\), \(|P_{f(7VJA_1)}(2) \setminus P_{f(2UWR_1)}(2)|=202\). 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 1:1100000101010000110000010101100111010000101000010010001000010000000010010001000
Pair \(Z_2\) Length of longest common subsequence
2UWR_1,7VJA_1 228 3
2UWR_1,9OFG_1 235 3
7VJA_1,9OFG_1 151 4

Newick tree

 
[
	2UWR_1:12.36,
	[
		7VJA_1:75.5,9OFG_1:75.5
	]:50.86
]

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 \((0.85)(0.8)(\frac{561 }{\log_{20} 561}-\frac{79}{\log_{20}79})=143.\)
Status Protein1 Protein2 d d1/2
Query variables 2UWR_1 7VJA_1 182 105
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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