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Parikh vectors
6VAR_1 1DYM_1 8JKG_1 Letter Amino acid
0 11 6 M Methionine
0 15 13 F Phenylalanine
0 17 7 R Arginine
0 30 16 E Glutamic acid
0 10 10 H Histidine
0 26 20 L Leucine
19 47 23 G Glycine
0 24 10 P Proline
0 17 7 S Serine
0 28 18 T Threonine
8 21 8 A Alanine
0 22 12 N Asparagine
0 18 19 D Aspartic acid
0 12 7 Q Glutamine
0 7 1 W Tryptophan
16 18 2 C Cysteine
0 19 11 Y Tyrosine
0 23 16 V Valine
0 14 12 I Isoleucine
0 23 20 K Lycine 

6VAR_1|Chain A|RNA (61-MER)|Hepatitis B virus (10407)
>1DYM_1|Chain A|ENDOGLUCANASE I|HUMICOLA INSOLENS (85995)
>8JKG_1|Chains A, B, C, D|Green fluorescent protein|Aequorea victoria (6100)
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 \(w=f(c)\)
6VAR , Knot 20 61 0.44 8 15 33 
GGUUCAUGUCCUACUGUUCAAGCCUCCAAGCUGUGCCUUGGGUGGCUUUGGGGCAUGGACC
1DYM , Knot 174 402 0.86 40 239 386 
QKPGETKEVHPQLTTFRCTKRGGCKPATNFIVLDSLSHPIHRAEGLGPGGCGDWGNPPPKDVCPDVESCAKNCIMEGIPDYSQYGVTTNGTSLRLQHILPDGRVPSPRVYLLDKTKRRYEMLHLTGFEFTFDVDATKLPCGMNSALYLSEMHPTGAKSKYNPGGAYYGTGYCDAQCFVTPFINGLGNIEGKGSCCNAMDIWEANSRASHVAPHTCNKKGLYLCEGEECAFEGVCDKNGCGWNNYRVNVTDYYGRGEEFKVNTLKPFTVVTQFLANRRGKLEKIHRFYVQDGKVIESFYTNKEGVPYTNMIDDEFCEATGSRKYMELGATQGMGEALTRGMVLAMSIWWDQGGNMEWLDHGEAGPCAKGEGAPSNIVQVEPFPEVTYTNLRWGEIGSTYQELQ
8JKG , Knot 108 238 0.82 40 158 223 
MSKGEELFTGVVPILVELDGDVNGHKFSVSGEGEGDATYGKLTLKFICTTGKLPVPWPTLVTTLTYGVQCFSRYPDHMKRHDFFKSAMPEGYVQERTIFFKDDGNYKTRAEVKFEGDTLVNRIELKGIDFKEDGNILGHKLEYNYNDHQVYIMADKQKNGIKANFKIRHNIEDGGVQLADHYQQNTPIGDGPVLLPDNHYLFTTSTLSKDPNEKRDHMVLLEFVTAAGITHGMDELYK

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 \(c\).

\(|P_{f(6VAR_1)}(2) \setminus P_{f(1DYM_1)}(2)|=9\), \(|P_{f(1DYM_1)}(2) \setminus P_{f(6VAR_1)}(2)|=233\). 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 1:1100010100001001000111000001110010100001110110000111101011100
Pair \(Z_2\) Length of longest common subsequence
6VAR_1,1DYM_1 242 3
6VAR_1,8JKG_1 167 3
1DYM_1,8JKG_1 189 3

Newick tree

 
[
	1DYM_1:11.71,
	[
		6VAR_1:83.5,8JKG_1:83.5
	]:32.21
]

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 \((0.85)(0.8)(\frac{463 }{\log_{20} 463}-\frac{61}{\log_{20}61})=123.\)
Status Protein1 Protein2 d d1/2
Query variables 6VAR_1 1DYM_1 171 95
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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