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Parikh vectors
2RVB_1 5KBL_1 1TTD_1 Letter Amino acid
0 6 0 Y Tyrosine
3 3 0 R Arginine
0 10 0 I Isoleucine
3 9 0 L Leucine
2 12 1 T Threonine
1 0 0 W Tryptophan
3 6 0 D Aspartic acid
1 10 0 K Lycine
1 9 0 P Proline
7 16 0 S Serine
3 9 0 V Valine
2 3 0 M Methionine
3 13 5 A Alanine
0 2 2 C Cysteine
13 8 0 E Glutamic acid
3 15 3 G Glycine
3 7 0 H Histidine
3 16 0 N Asparagine
0 1 0 Q Glutamine
1 4 0 F Phenylalanine 

2RVB_1|Chain A|DNA repair protein complementing XP-C cells|Homo sapiens (9606)
>5KBL_1|Chain A|Cell surface Cu-only superoxide dismutase 5|Candida albicans (strain SC5314 / ATCC MYA-2876) (237561)
>1TTD_1|Chain A|DNA (5'-D(*GP*CP*AP*CP*GP*AP*AP*(TTD)P*AP*AP*G)-3')|
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 \(w=f(c)\)
2RVB , Knot 29 52 0.73 32 43 48 
GSHMAHHLKRGATMNEDSNEEEEESENDWEEVEELSEPVLGDVRESTAFSRS
5KBL , Knot 73 159 0.77 38 116 148 
GAMVSPSLIAKFEKTSKSNIEGTIKFTPANNGTVSVSVDLKGLPSDIGPFPYHVHEKPVPASKNCSATENHFNPYNGTVRAATPAAHQVGDLAGKHGNIMGESYKTEYDDSYISLNEKSRSYIGGLSIVIHANNGTRLNCANITLLDEGHGNANTTMSN
1TTD , Knot 7 11 0.50 8 9 9 
GCACGAATAAG

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 \(c\).

\(|P_{f(2RVB_1)}(2) \setminus P_{f(5KBL_1)}(2)|=27\), \(|P_{f(5KBL_1)}(2) \setminus P_{f(2RVB_1)}(2)|=100\). 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 1:1001100100110100000000000000100100100111101000011000
Pair \(Z_2\) Length of longest common subsequence
2RVB_1,5KBL_1 127 3
2RVB_1,1TTD_1 46 2
5KBL_1,1TTD_1 115 3

Newick tree

 
[
	5KBL_1:68.67,
	[
		2RVB_1:23,1TTD_1:23
	]:45.67
]

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 \((0.85)(0.8)(\frac{211 }{\log_{20} 211}-\frac{52}{\log_{20}52})=53.5\)
Status Protein1 Protein2 d d1/2
Query variables 2RVB_1 5KBL_1 67 43.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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