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Parikh vectors
3WBZ_1 5EPQ_1 7NIE_1 Letter Amino acid
10 4 19 Q Glutamine
22 8 33 E Glutamic acid
8 12 18 P Proline
12 12 38 V Valine
3 4 14 C Cysteine
12 8 30 I Isoleucine
26 13 46 L Leucine
18 10 33 S Serine
10 9 30 T Threonine
20 15 11 Y Tyrosine
13 5 16 R Arginine
8 8 38 G Glycine
6 6 7 H Histidine
27 11 33 K Lycine
10 1 12 M Methionine
15 6 17 F Phenylalanine
11 11 41 A Alanine
17 9 21 N Asparagine
17 11 18 D Aspartic acid
6 1 12 W Tryptophan 

3WBZ_1|Chains A, B, C, D, E, F, G, H|Likely histidyl tRNA-specific guanylyltransferase|Candida albicans (237561)
>5EPQ_1|Chain A|Milk protein|Diploptera punctata (6984)
>7NIE_1|Chains A, B, O, P|Glycerol kinase|Sus scrofa (9823)
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 \(w=f(c)\)
3WBZ , Knot 121 271 0.83 40 179 261 
GGSMANSKYEYVKLFEKENYLLPDTYIIIRVDGKGFHKFSQFYEFEKPNDLKALQVMNSAAEKLMSKYSDVMLAYGDSDEYSFLLRKNCQLYERREMKLTTLFSSLMSTYYMYFWSQYFPDKPLHIDHLPNFDARAVLYPDFKHIRNYFSWRQVDCHINNLYNTTFWNLVLKLKMTPQQAEQRLMGTVASDKNEILFKECGVNYNNESEMYKKGTIIVREFENYETEDEAELSKRQVQRLEKKRKKAELKIYHVDIINDDSWWKSRPWLKD
5EPQ , Knot 81 164 0.84 40 123 160 
IAAILVANAKEPCPPENLQLPPRALVGKWYLRTTSPDIFKQVSNITEFYSAHGNDYYGTVTDYSPEYGLEAHRVNLTVSGSTLKFYMNDTHDYDSEYQILAVDKDYFIFYGHPPAAPSGLALIHYRQSCPKEDVIKRVKKNLKNVCLDYKYFGNDTSVPCHYVE
7NIE , Knot 197 487 0.83 40 243 447 
MAASKKAVLGPLVGAVDQGTSSTRFLVFNSKTAELLSHHQVEIEQKFPKEGWVEQDPKEILQSVYECIEKTCEKLGQLNIDISNIKAIGVSNQRETTVVWDKLTGEPLYNAVVWLDLRTQSTVANLSKIIPVNNNFVKTKTGLPLSTYFSAVKLRWLLDNVRKIQKAVEEDRALFGTIDSWLIWSLTGGARGGVHCTDVTNASRTMLFNIHSLEWDKELCEFFEVPMKILPNVRSSSEIYGLMKAGALEGVPISGCLGDQSAALVGQMCFQDGQAKNTYGTGCFLLCNTGHKCSVAIAGAVVRWLRDNLGIIKTSEEIEKLAKEVGTSYGCYFVPAFSGLYAPYWEPSARGIICGLTQFTNKCHIAFAALEAVCFQTREILDAMNRDCGIPLSHLQVDGGMTNNKILMQLQADILYIPVVKPSMPETTALGAAMAAGAAEGVGVWSLKPEDLSAVTMERFEPQINAKESEIRYSTWKKAVKKSMGWV

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 \(c\).

\(|P_{f(3WBZ_1)}(2) \setminus P_{f(5EPQ_1)}(2)|=115\), \(|P_{f(5EPQ_1)}(2) \setminus P_{f(3WBZ_1)}(2)|=59\). 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 1:1101100000010110000011100011101010110010010010010010110110011001100000111101000000111000001000001010011001100001011000110011010011010101110101001000101001000100100001101110101010010001110110000011100011000000010001011100100000000101000010010000001010100101100001100011100
Pair \(Z_2\) Length of longest common subsequence
3WBZ_1,5EPQ_1 174 3
3WBZ_1,7NIE_1 188 3
5EPQ_1,7NIE_1 212 4

Newick tree

 
[
	7NIE_1:10.20,
	[
		3WBZ_1:87,5EPQ_1:87
	]:17.20
]

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 \((0.85)(0.8)(\frac{435 }{\log_{20} 435}-\frac{164}{\log_{20}164})=80.3\)
Status Protein1 Protein2 d d1/2
Query variables 3WBZ_1 5EPQ_1 103 82.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]