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Parikh vectors
7YKM_1 8UHA_1 1DUB_1 Letter Amino acid
2 39 10 D Aspartic acid
0 2 5 C Cysteine
2 8 19 I Isoleucine
4 23 6 P Proline
7 39 11 S Serine
6 15 14 T Threonine
1 2 1 W Tryptophan
9 24 32 A Alanine
7 17 13 V Valine
5 3 3 H Histidine
14 24 21 L Leucine
1 7 5 Y Tyrosine
13 50 9 R Arginine
5 16 11 Q Glutamine
5 30 22 E Glutamic acid
3 12 12 F Phenylalanine
1 10 13 N Asparagine
3 28 22 K Lycine
5 6 8 M Methionine
12 25 24 G Glycine 

7YKM_1|Chain A|DciA DUF721 domain|Deinococcus radiodurans (1299)
>8UHA_1|Chain A[auth X]|Negative elongation factor E|Homo sapiens (9606)
>1DUB_1|Chains A, B, C, D, E, F|2-ENOYL-COA HYDRATASE|Rattus norvegicus (10116)
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 \(w=f(c)\)
7YKM , Knot 52 105 0.76 38 81 102 
MTRSRRSGPLDMSTLMGATLGKGKLGYGVQRARALLLWPQAVGPEIARMTRPRSVQGGTLFVEVRDSAAAHHLTMQRHHFLKRLNELLGAGQEVSELRFSVGHIR
8UHA , Knot 144 380 0.75 40 188 316 
MLVIPPGLSEEEEALQKKFNKLKKKKKALLALKKQSSSSTTSQGGVKRSLSEQPVMDTATATEQAKQLVKSGAISAIKAETKNSGFKRSRTLEGKLKDPEKGPVPTFQPFQRSISADDDLQESSRRPQRKSLYESFVSSSDRLRELGPDGEEAEGPGAGDGPPRSFDWGYEERSGAHSSASPPRSRSRDRSHERNRDRDRDRERDRDRDRDRDRERDRDRDRDRDRDRERDRDRERDRDRDREGPFRRSDSFPERRAPRKGNTLYVYGEDMTPTLLRGAFSPFGNIIDLSMDPPRNCAFVTYEKMESADQAVAELNGTQVESVQLKVNIARKQPMLDAATGKSVWGSLAVQNSPKGCHRDKRTQIVYSDDVYKENLVDGF
1DUB , Knot 115 261 0.81 40 159 249 
GANFQYIITEKKGKNSSVGLIQLNRPKALNALCNGLIEELNQALETFEEDPAVGAIVLTGGEKAFAAGADIKEMQNRTFQDCYSGKFLSHWDHITRIKKPVIAAVNGYALGGGCELAMMCDIIYAGEKAQFGQPEILLGTIPGAGGTQRLTRAVGKSLAMEMVLTGDRISAQDAKQAGLVSKIFPVETLVEEAIQCAEKIANNSKIIVAMAKESVNAAFEMTLTEGNKLEKKLFYSTFATDDRREGMSAFVEKRKANFKDH

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 \(c\).

\(|P_{f(7YKM_1)}(2) \setminus P_{f(8UHA_1)}(2)|=27\), \(|P_{f(8UHA_1)}(2) \setminus P_{f(7YKM_1)}(2)|=134\). 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 1:100000011101001111011010110110010111111011110110100100101101110100011100101000011001001111100100101011010
Pair \(Z_2\) Length of longest common subsequence
7YKM_1,8UHA_1 161 3
7YKM_1,1DUB_1 152 3
8UHA_1,1DUB_1 143 4

Newick tree

 
[
	7YKM_1:80.41,
	[
		1DUB_1:71.5,8UHA_1:71.5
	]:8.91
]

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 \((0.85)(0.8)(\frac{485 }{\log_{20} 485}-\frac{105}{\log_{20}105})=113.\)
Status Protein1 Protein2 d d1/2
Query variables 7YKM_1 8UHA_1 127 82
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]