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Parikh vectors
7EVD_1 3LRK_1 7BGW_1 Letter Amino acid
22 24 10 T Threonine
33 21 12 V Valine
18 34 27 A Alanine
25 35 8 N Asparagine
30 17 33 E Glutamic acid
46 38 24 L Leucine
12 13 9 M Methionine
26 21 5 F Phenylalanine
16 17 13 R Arginine
9 14 9 Q Glutamine
9 7 3 H Histidine
31 22 10 I Isoleucine
24 21 17 K Lycine
4 10 2 C Cysteine
29 46 17 G Glycine
34 43 20 S Serine
3 12 2 W Tryptophan
11 26 10 Y Tyrosine
24 42 15 D Aspartic acid
19 16 7 P Proline 

7EVD_1|Chain A[auth B]|Tubulin-like protein|Odinarchaeota archaeon (strain LCB_4) (1841599)
>3LRK_1|Chain A|Alpha-galactosidase 1|Saccharomyces cerevisiae (4932)
>7BGW_1|Chain A|14-3-3 protein sigma|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 \(w=f(c)\)
7EVD , Knot 175 425 0.83 40 219 399 
MPGREILVLHVGQGGNQIGYNFWKTICEEHNIDIRSNQRKSVEEDKVDYKSVFLVEAPDGFHPRALFIDLEPLAVEFLVKEMKLGSFFSEDLMVLSYSGAHNVWSIGYQTGKKLIPVILEKIRDTMPETLQGFLIIHTLGGGTGSGFGSLLTETLKKEFPGKGVLNFSVLPSEVNDVTLAPYNTVLSLNHLSRFSDLVVLFDNTALIRIVKDQLNYPVIKQFSDLNFLIGRVMASITASLRFPGPLNMDLMEMAHNLVALPETKFIIPSVAPLTKEESEMSTELDLVERCFDPTHYMVNCSGQGKTISSVLMFRGNIAIENAFSIMTDIKSNVAFAPGVHPDLGLKYGICESAPVDFDKEVTLLSNNTIISEVFNRVLERFDSLFNRDWYTSDYVNAGTSKSNLKEARDNFDRIIKIYKEIEGSQ
3LRK , Knot 195 479 0.83 40 239 457 
MFAFYFLTACISLKGVFGVSPSYNGLGLTPQMGWDNWNTFACDVSEQLLLDTADRISDLGLKDMGYKYIILDDCWSSGRDSDGFLVADEQKFPNGMGHVADHLHNNSFLFGMYSSAGEYTCAGYPGSLGREEEDAQFFANNRVDYLKYDNCYNKGQFGTPEISYHRYKAMSDALNKTGRPVFYSLCNWGQDLTFYWGSGIANSWRMSGDVTAEFTRPDSRCPCDGDEYDCKYAGFHCSIMNILNKAAPMGQNAGVGGWNDLDNLEVGVGNLTDDEEKAHFSMWAMVKSPLIIGANVNNLKASSYSIYSQASVIAINQDSNGIPATRVWRYYVSDTDEYGQGEIQMWSGPLDNGDQVVALLNGGSVSRPMNTTLEEIFFDSNLGSKKLTSTWDIYDLWANRVDNSTASAILGRNKTATGILYNATEQSYKDGLSKNDTRLFGQKIGSLSPNAILNTTVPAHGIAFYRLRPSSDYKDDDDK
7BGW , Knot 114 253 0.83 40 170 244 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWTADNAGEEGGEAPQEPQS

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 \(c\).

\(|P_{f(7EVD_1)}(2) \setminus P_{f(3LRK_1)}(2)|=73\), \(|P_{f(3LRK_1)}(2) \setminus P_{f(7EVD_1)}(2)|=93\). 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
7EVD_1,3LRK_1 166 5
7EVD_1,7BGW_1 161 5
3LRK_1,7BGW_1 175 4

Newick tree

 
[
	3LRK_1:86.81,
	[
		7EVD_1:80.5,7BGW_1:80.5
	]:6.31
]

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 \((0.85)(0.8)(\frac{904 }{\log_{20} 904}-\frac{425}{\log_{20}425})=127.\)
Status Protein1 Protein2 d d1/2
Query variables 7EVD_1 3LRK_1 165 154.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]