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Parikh vectors
2PYC_1 3RAZ_1 5IUC_1 Letter Amino acid
3 11 16 V Valine
6 11 9 A Alanine
5 6 7 R Arginine
14 4 0 C Cysteine
7 6 6 E Glutamic acid
5 5 6 I Isoleucine
13 13 4 K Lycine
9 5 6 Y Tyrosine
7 6 7 D Aspartic acid
1 5 6 Q Glutamine
9 10 5 L Leucine
5 8 5 P Proline
4 3 5 F Phenylalanine
7 11 7 S Serine
6 8 10 N Asparagine
11 11 11 G Glycine
1 7 0 H Histidine
2 5 1 M Methionine
5 11 14 T Threonine
1 5 2 W Tryptophan 

2PYC_1|Chain A|Phospholipase A2 VRV-PL-VIIIa|Daboia russellii pulchella (97228)
>3RAZ_1|Chain A|Thioredoxin-related protein|Neisseria meningitidis serogroup B (491)
>5IUC_1|Chains A, B|Platelet binding protein GspB|Streptococcus gordonii (1302)
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 \(w=f(c)\)
2PYC , Knot 60 121 0.79 40 95 118 
SLLEFGKMILEETGKLAIPSYSSYGCYCGWGGKGTPKDATDRCCFVHDCCYGNLPDCNPKSDRYKYKRVNGAIVCEKGTSCENRICECDKAAAICFRQNLNTYSKKYMLYPDFLCKGELKC
3RAZ , Knot 76 151 0.84 40 122 145 
MSLSADELAGWKDNTPQSLQSLKAPVRIVNLWATWCGPCRKEMPAMSKWYKAQKKGSVDMVGIALDTSDNIGNFLKQTPVSYPIWRYTGANSRNFMKTYGNTVGVLPFTVVEAPKCGYRQTITGEVNEKSLTDAVKLAHSKCREGHHHHHH
5IUC , Knot 61 127 0.77 36 94 123 
GPGSDTERPVVNVPSEITVYRGESFEYFATVTDNSNAFDLAKTVVRWLYSNQPGRGTEWLQYSVTQVGNQLKVRIFGNVPIDTTIGDYTRYVVATDAAGNVNATQTEMGNAAVDKTSVNGQFKLIIR

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 \(c\).

\(|P_{f(2PYC_1)}(2) \setminus P_{f(3RAZ_1)}(2)|=55\), \(|P_{f(3RAZ_1)}(2) \setminus P_{f(2PYC_1)}(2)|=82\). 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 1:0110110111000101111000001000111101010010000011000001011000100000000010111100010000001000001111010001000000011010110010100
Pair \(Z_2\) Length of longest common subsequence
2PYC_1,3RAZ_1 137 3
2PYC_1,5IUC_1 147 3
3RAZ_1,5IUC_1 142 3

Newick tree

 
[
	5IUC_1:73.47,
	[
		2PYC_1:68.5,3RAZ_1:68.5
	]:4.97
]

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 \((0.85)(0.8)(\frac{272 }{\log_{20} 272}-\frac{121}{\log_{20}121})=47.4\)
Status Protein1 Protein2 d d1/2
Query variables 2PYC_1 3RAZ_1 58 52.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]