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Parikh vectors
2EFV_1 3IQP_1 8SGF_1 Letter Amino acid
1 21 9 C Cysteine
1 0 20 P Proline
4 0 23 D Aspartic acid
1 0 16 H Histidine
12 0 21 E Glutamic acid
6 0 14 I Isoleucine
14 0 27 L Leucine
2 0 6 M Methionine
4 0 19 T Threonine
4 0 14 Y Tyrosine
5 28 19 A Alanine
1 0 8 Q Glutamine
5 0 21 V Valine
4 31 33 G Glycine
11 0 14 K Lycine
2 0 19 F Phenylalanine
2 0 27 S Serine
0 0 14 W Tryptophan
8 0 20 R Arginine
5 0 18 N Asparagine 

2EFV_1|Chain A|Hypothetical protein MJ0366|Methanocaldococcus jannaschii DSM 2661 (243232)
>3IQP_1|Chain A|SAM-I riboswitch|
>8SGF_1|Chains A, B|Kelch domain-containing protein 2|Homo sapiens (9606)
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 \(w=f(c)\)
2EFV , Knot 49 92 0.80 38 72 87 
MPLVGFMKEKKRATFYLYKNIDGRKLRYLLHKLENVENVDIDTLRRAIEAEKKYKRSITLTEEEEVIIQRLGKSANLLLNCELVKLDEGERA
3IQP , Knot 29 94 0.46 8 16 47 
GGCUUAUCAAGAGAGGUGGAGGGACUGGCCCGAUGAAACCCGGCAACCAGAAAUGGUGCCAAUUCCUGCAGCGGAAACGUUGAAAGAUGAGCCG
8SGF , Knot 155 362 0.84 40 228 343 
GADGNEDLRADDLPGPAFESYESMELACPAERSGHVAVSDGRHMFVWGGYKSNQVRGLYDFYLPREELWIYNMETGRWKKINTEGDVPPSMSGSCAVCVDRVLYLFGGHHSRGNTNKFYMLDSRSTDRVLQWERIDCQGIPPSSKDKLGVWVYKNKLIFFGGYGYLPEDKVLGTFEFDETSFWNSSHPRGWNDHVHILDTETFTWSQPITTGKAPSPRAAHACATVGNRGFVFGGRYRDARMNDLHYLNLDTWEWNELIPQGICPVGRSWHSLTPVSSDHLFLFGGFTTDKQPLSDAWTYCISKNEWIQFNHPYTEKPRLWHTACASDEGEVIVFGGCANNLLVHHRAAHSNEILIFSVQPK

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 \(c\).

\(|P_{f(2EFV_1)}(2) \setminus P_{f(3IQP_1)}(2)|=72\), \(|P_{f(3IQP_1)}(2) \setminus P_{f(2EFV_1)}(2)|=16\). 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 1:11111110000010101000101001001100100100101001001101000000010100000111001100101110001101001001
Pair \(Z_2\) Length of longest common subsequence
2EFV_1,3IQP_1 88 1
2EFV_1,8SGF_1 208 4
3IQP_1,8SGF_1 232 4

Newick tree

 
[
	8SGF_1:12.64,
	[
		2EFV_1:44,3IQP_1:44
	]:80.64
]

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 \((0.85)(0.8)(\frac{186 }{\log_{20} 186}-\frac{92}{\log_{20}92})=31.0\)
Status Protein1 Protein2 d d1/2
Query variables 2EFV_1 3IQP_1 45 36.5
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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