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Parikh vectors
2FEL_1 4IDS_1 7YWL_1 Letter Amino acid
9 31 0 P Proline
18 33 16 T Threonine
55 76 10 A Alanine
20 28 0 I Isoleucine
43 46 0 L Leucine
4 9 0 W Tryptophan
17 17 0 Q Glutamine
0 2 13 C Cysteine
33 47 11 G Glycine
15 22 0 H Histidine
14 22 0 F Phenylalanine
22 31 0 S Serine
1 18 0 Y Tyrosine
17 43 0 V Valine
7 15 0 N Asparagine
21 41 0 D Aspartic acid
23 23 0 E Glutamic acid
9 13 0 K Lycine
11 9 0 M Methionine
20 37 0 R Arginine 

2FEL_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|3-carboxy-cis,cis-muconate lactonizing enzyme|Agrobacterium tumefaciens (358)
>4IDS_1|Chain A|Delta-1-pyrroline-5-carboxylate dehydrogenase|Mycobacterium tuberculosis (83332)
>7YWL_1|Chain A|DNA (50-MER)|DNA molecule (2853804)
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 \(w=f(c)\)
2FEL , Knot 141 359 0.77 38 171 324 
MSLSPFEHPFLSGLFGDSEIIELFSAKADIDAMIRFETALAQAEAEASIFADDEAEAIVSGLSEFAADMSALRHGVAKDGVVVPELIRQMRAAVAGQAADKVHFGATSQDVIDTSLMLRLKMAAEIIATRLGHLIDTLGDLASRDGHKPLTGYTRMQAAIGITVADRAAGWIAPLERHLLRLETFAQNGFALQFGGAAGTLEKLGDNAGAVRADLAKRLGLADRPQWHNQRDGIAEFANLLSLVTGTLGKFGQDIALMAEIGSEIRLSGGGGSSAMPHKQNPVNAETLVTLARFNAVQISALHQSLVQEQERSGAGWMLEWLTLPQMVTATGTSLLVAERLAAQIDRLGADESHHHHHH
4IDS , Knot 226 563 0.84 40 246 518 
MGSSHHHHHHSSGLVPRGSHMDAITQVPVPANEPVHDYAPKSPERTRLRTELASLADHPIDLPHVIGGRHRMGDGERIDVVQPHRHAARLGTLTNATHADAAAAVEAAMSAKSDWAALPFDERAAVFLRAADLLAGPWREKIAAATMLGQSKSVYQAEIDAVCELIDFWRFNVAFARQILEQQPISGPGEWNRIDYRPLDGFVYAITPFNFTSIAGNLPTAPALMGNTVIWKPSITQTLAAYLTMQLLEAAGLPPGVINLVTGDGFAVSDVALADPRLAGIHFTGSTATFGHLWQWVGTNIGRYHSYPRLVGETGGKDFVVAHASARPDVLRTALIRGAFDYQGQKCSAVSRAFIAHSVWQRMGDELLAKAAELRYGDITDLSNYGGALIDQRAFVKNVDAIERAKGAAAVTVAVGGEYDDSEGYFVRPTVLLSDDPTDESFVIEYFGPLLSVHVYPDERYEQILDVIDTGSRYALTGAVIADDRQAVLTALDRLRFAAGNFYVNDKPTGAVVGRQPFGGARGSDTNDKAGSPLNLLRWTSARSIKETFVAATDHIYPHMAVD
7YWL , Knot 19 50 0.49 8 16 37 
AGCGAACGTGGATTTTGTCCGACATCGGCAAGCTCCCTTTTTCGACTATT

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 \(c\).

\(|P_{f(2FEL_1)}(2) \setminus P_{f(4IDS_1)}(2)|=45\), \(|P_{f(4IDS_1)}(2) \setminus P_{f(2FEL_1)}(2)|=120\). 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 1:10101100111011110001101101010101110100111010101011100010111011001110101100111001111101100101111101100101110000110001110101110111001101100110110001001101000101111101100111111110001101001100111101111110100110011110101100111100101000001110110110110101101100111110110010101111001110000110100110110101101011000110000001111110110110110101001111001110100111000000000
Pair \(Z_2\) Length of longest common subsequence
2FEL_1,4IDS_1 165 7
2FEL_1,7YWL_1 171 3
4IDS_1,7YWL_1 246 3

Newick tree

 
[
	7YWL_1:11.65,
	[
		2FEL_1:82.5,4IDS_1:82.5
	]:30.15
]

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 \((0.85)(0.8)(\frac{922 }{\log_{20} 922}-\frac{359}{\log_{20}359})=150.\)
Status Protein1 Protein2 d d1/2
Query variables 2FEL_1 4IDS_1 188 149.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]