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Parikh vectors
7LYJ_1 3ZXL_1 3ZIL_1 Letter Amino acid
18 2 7 C Cysteine
0 11 19 K Lycine
0 17 5 W Tryptophan
0 37 22 V Valine
0 43 18 R Arginine
0 34 17 D Aspartic acid
0 31 11 P Proline
14 48 31 A Alanine
0 17 27 E Glutamic acid
0 15 8 H Histidine
0 9 8 M Methionine
0 23 15 F Phenylalanine
0 29 27 S Serine
0 26 20 N Asparagine
0 14 13 Q Glutamine
21 56 12 G Glycine
0 22 18 I Isoleucine
0 33 60 L Leucine
0 47 27 T Threonine
0 28 13 Y Tyrosine 

7LYJ_1|Chain A|RNA (66-MER)|Severe acute respiratory syndrome coronavirus 2 (2697049)
>3ZXL_1|Chains A, B|HIAXHD3|HUMICOLA INSOLENS (85995)
>3ZIL_1|Chain A|AAR187CP|EREMOTHECIUM GOSSYPII (33169)
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 \(w=f(c)\)
7LYJ , Knot 23 66 0.48 8 16 42 
CGGUGUAAGUGCAGCCCGUCUUACACCGUGCGGCACAGCGGAAACGCUGAUGUCGUAUACAGGGCU
3ZXL , Knot 221 542 0.85 40 253 502 
MPRQASTFTNPVLWEDHPDLEVFRVGSVFYYSSSTFAYSPGAPVLKSYDLVHWTPVTHSVPRLNFGSNYDLPSGTPGAYVKGIWASTLRYRRSNDRFYWYGCVEGRTYLWTSPGGNALANNGEVPPSAWNWQHTATIDNCYADAGLLIDDDDTMYIAYGNPTINVAQLSPDGTRQVRVQQRVYAHPQGQTVAGARMYKIRGNYYILVTRPADAEYVLRSTTGSPFGPYEARTLVSRIQGPLANAGFAHQGGIVDAPDGTWHYVAFMDAYPGGRIPVVAPLRWTADGWPEVVTDSQGRWGTSYPIPVRGAKNATEGLASTDLDEFRGTRFSEHWEWNHNPDTSKFTLLGGNEGGLILRTATVTGDLFAARNTLTRRIAGPKASGIFRLDVRGMRDGDRAGAVLFRDRAAYIGVWKQGNEARIVMVDDLRLNEDGWRTASTGRVAANGPVIDTNAQQDIWLRIDADITPAFGTNTERTTTFYYSIDGGRTYTRLGPAFAMTNSWRYFTGYRFGVFNFSTKSLGGEVKVKGFKMNMILEHHHHHH
3ZIL , Knot 157 378 0.82 40 203 354 
DEALSRHFNELRTMGETLKYSEDLDFILSDNSMTTPEHRRNNMLRLCLDMMNNEDLCQYIVKYRHREVWEWCFQGTDPKQKVTSLLQCFIADKIPLLRHDKRWAMLSLENFILPLATDEVFPKKIAGSRLVKLNYQDLLRKLKFTNTCEYALYIWATYLLYTEAVYGAVPALARLISRGQLKDWDTACSLLENNIVAAPSGSDIEEYAQAFQTLAGLSREKLTNEGVLKCLIKLTNHTTVLELSADLLPSLVRSLAMSVQLHQNNIVSSISEIKTNLLILQLGLLLNIVSEATTAASTEELTNFGAVFRSVFVKKPTEMSFVLQLFLLVYAYSAGAAGVQLPPAEADFLKSELEAFATDVSSYNHNIHTRITRVLETL

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 \(c\).

\(|P_{f(7LYJ_1)}(2) \setminus P_{f(3ZXL_1)}(2)|=11\), \(|P_{f(3ZXL_1)}(2) \setminus P_{f(7LYJ_1)}(2)|=248\). 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 1:011010111010110001000010100101011010110111110100110100101010111100
Pair \(Z_2\) Length of longest common subsequence
7LYJ_1,3ZXL_1 259 2
7LYJ_1,3ZIL_1 211 3
3ZXL_1,3ZIL_1 176 3

Newick tree

 
[
	7LYJ_1:12.56,
	[
		3ZIL_1:88,3ZXL_1:88
	]:38.56
]

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 \((0.85)(0.8)(\frac{608 }{\log_{20} 608}-\frac{66}{\log_{20}66})=161.\)
Status Protein1 Protein2 d d1/2
Query variables 7LYJ_1 3ZXL_1 218 119
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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