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Parikh vectors
8EYV_1 3TFF_1 8GZG_1 Letter Amino acid
0 6 7 M Methionine
0 5 17 R Arginine
0 13 18 D Aspartic acid
24 16 18 G Glycine
0 9 15 K Lycine
0 6 14 P Proline
0 3 1 W Tryptophan
6 14 26 A Alanine
0 4 15 N Asparagine
9 2 2 C Cysteine
0 7 19 Q Glutamine
0 13 23 S Serine
0 10 14 T Threonine
0 10 23 V Valine
0 19 32 E Glutamic acid
0 8 9 H Histidine
0 7 24 I Isoleucine
0 19 34 L Leucine
0 9 9 F Phenylalanine
0 9 8 Y Tyrosine 

8EYV_1|Chains A, B|RNA (45-MER)|synthetic construct (32630)
>3TFF_1|Chains A, B|Alr2278 protein|Nostoc sp. (103690)
>8GZG_1|Chains A, B|DNA-directed RNA polymerase subunit alpha|Synechocystis sp. PCC 6803 (1148)
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 \(w=f(c)\)
8EYV , Knot 17 49 0.45 8 14 28 
GCGCCGGUUAGGCAGAGGUGGGUGGUGUGGAGGAGUAUCUGUCCGGCGC
3TFF , Knot 91 189 0.84 40 137 183 
MYGLVNKAIQDMISKHHGEDTWEAIKQKAGLEDIDFFVGMEAYSDDVTYHLVGAASEVLGKPAEELWIAFGEYWVTYTSEEGYGELLASAGDSLPEFMENLDNLHARVGLSFPQLRPPAFECQHTSSKSMELHYQSTRCGLAPMVLGLLHGLGKRFQTKVEVTQTAFRETGEDHDIFSIKYEDSNLYDD
8GZG , Knot 140 328 0.82 40 195 312 
MGSSHHHHHHSQDPMAQFQIECVESSTRKNQQQYSKFSLEPLDRGQGTTVGNALRRVLLSNLPGAAVTAIRIAGVNHEFATILGVREDVLEIMLNMKELVLKSYTDQPQIGRLTAIGPGTVTAAQFEVPSEVEVIDPNQYIATLAEGAKLEMEFRVERGVGYRVIERGKDENSSLDFLQIDSVFMPVTKVNYTVEDIRADGMSPKDRLILDIWTNGSIQPREALSEASDIIANLFIPLKDLNELEAAHSDYQDEVNPESQIPIEELQLSVRAYNCLKRAQINSVADLLEYSQEDLLEIKNFGLKSAEEVIEALQKRLGITLPHEKAKA

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 \(c\).

\(|P_{f(8EYV_1)}(2) \setminus P_{f(3TFF_1)}(2)|=11\), \(|P_{f(3TFF_1)}(2) \setminus P_{f(8EYV_1)}(2)|=134\). 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 1:1010011001110111110111011010111111101000100011010
Pair \(Z_2\) Length of longest common subsequence
8EYV_1,3TFF_1 145 2
8EYV_1,8GZG_1 205 2
3TFF_1,8GZG_1 174 3

Newick tree

 
[
	8GZG_1:10.47,
	[
		8EYV_1:72.5,3TFF_1:72.5
	]:28.97
]

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 \((0.85)(0.8)(\frac{238 }{\log_{20} 238}-\frac{49}{\log_{20}49})=62.9\)
Status Protein1 Protein2 d d1/2
Query variables 8EYV_1 3TFF_1 87 51
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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