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Parikh vectors
7EVL_1 2BPY_1 1MQV_1 Letter Amino acid
31 13 7 I Isoleucine
26 2 5 F Phenylalanine
22 8 6 T Threonine
18 3 26 A Alanine
4 2 2 C Cysteine
9 1 1 H Histidine
24 6 18 K Lycine
12 2 2 M Methionine
19 6 4 P Proline
3 2 1 W Tryptophan
11 1 0 Y Tyrosine
25 3 2 N Asparagine
29 13 8 G Glycine
46 12 10 L Leucine
33 6 4 V Valine
30 4 4 E Glutamic acid
34 1 6 S Serine
16 4 2 R Arginine
24 4 12 D Aspartic acid
9 6 5 Q Glutamine 

7EVL_1|Chain A[auth B]|Tubulin-like protein|Odinarchaeota archaeon (strain LCB_4) (1841599)
>2BPY_1|Chains A, B|HIV-1 PROTEASE|Human immunodeficiency virus 1 (11676)
>1MQV_1|Chains A, B|CYTOCHROME C'|Rhodopseudomonas palustris (1076)
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 \(w=f(c)\)
7EVL , Knot 175 425 0.83 40 219 399 
MPGREILVLHVGQGGNQIGYNFWKTICEEHNIDIRSNQRKSVEEDKVDYKSVFLVEAPDGFHPRALFIDLEPLAVEFLVKEMKLGSFFSEDLMVLSYSGAHNVWSIGYQTGKKLIPVILEKIRDTMPETLQGFLIIHTLGGGTGSGFGSLLTETLKKEFPGKGVLNFSVLPSEVNDVTLAPYNTVLSLNHLSRFSDLVVLFDNTALIRIVKDQLNYPVIKQFSDLNFLIGRVMASITASLRFPGPLNMDLMEMAHNLVALPETKFIIPSVAPLTKEESEMSTELDLVERCFDPTHYMVNCSGQGKTISSVLMFRGNIAIENAFSIMTDIKSNVAFAPGVHPDLGLKYGICESAPVDFDKEVTLLSNNTIISEVFNRVLERFDSLFNRDWYTSDYVNAGTSKSNLKEARDNFDRIIKIYKEIEGSQ
2BPY , Knot 52 99 0.80 40 81 94 
PQITLWQRPLVTIKIGGQLKEALLDTGADDTVLEEMSLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNF
1MQV , Knot 62 125 0.79 38 85 118 
ATDVIAQRKAILKQMGEATKPIAAMLKGEAKWDQAVVQKSLAAIADDSKKLPALFPADSKTGGDTAALPKIFEDKAKFDDLFAKLAAAATAAQGTIKDEASLKANIGGVLGNCKSCHDDFRAKKS

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 \(c\).

\(|P_{f(7EVL_1)}(2) \setminus P_{f(2BPY_1)}(2)|=162\), \(|P_{f(2BPY_1)}(2) \setminus P_{f(7EVL_1)}(2)|=24\). 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 1:11100111101101100110011001000001010000000100001000011110110110101111010111101110010110110001111000110011011000100111111001000110010111110011110101110110001000111011101011100100101110001101001001001111100011101100010011100100101111011101010101111101011011001111100011110111100000010001011000101000110001010010011110101110011011001000111111101011100110001110100010110000110011001100100110001000001011000001001000100110100010100
Pair \(Z_2\) Length of longest common subsequence
7EVL_1,2BPY_1 186 4
7EVL_1,1MQV_1 194 3
2BPY_1,1MQV_1 118 3

Newick tree

 
[
	7EVL_1:10.29,
	[
		2BPY_1:59,1MQV_1:59
	]:45.29
]

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 \((0.85)(0.8)(\frac{524 }{\log_{20} 524}-\frac{99}{\log_{20}99})=126.\)
Status Protein1 Protein2 d d1/2
Query variables 7EVL_1 2BPY_1 154 94.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]