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Parikh vectors
2KRB_1 5LIE_1 6LNL_1 Letter Amino acid
5 15 12 I Isoleucine
4 7 6 Y Tyrosine
2 41 4 R Arginine
8 28 6 D Aspartic acid
0 8 5 M Methionine
5 19 6 F Phenylalanine
5 34 11 G Glycine
3 12 11 H Histidine
2 9 5 Q Glutamine
4 30 13 E Glutamic acid
4 46 15 L Leucine
10 4 17 K Lycine
3 23 9 S Serine
3 25 6 T Threonine
5 10 8 N Asparagine
0 2 2 C Cysteine
0 6 2 W Tryptophan
9 31 8 V Valine
5 38 11 A Alanine
4 26 13 P Proline 

2KRB_1|Chain A|Eukaryotic translation initiation factor 3 subunit B|Homo sapiens (9606)
>5LIE_1|Chains A, B|Putative cytochrome P450 126|Mycobacterium tuberculosis (1773)
>6LNL_1|Chains A, B, C|60 kDa polyprotein|African swine fever virus (10497)
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 \(w=f(c)\)
2KRB , Knot 44 81 0.79 34 68 79 
DSVIVVDNVPQVGPDRLEKLKNVIHKIFSKFGKITNDFYPEEDGKTKGYIFLEYASPAHAVDAVKNADGYKLDKQHTFRVN
5LIE , Knot 168 414 0.81 40 195 385 
MTTAAGLSGIDLTDLDNFADGFPHHLFAIHRREAPVYWHRPTEHTPDGEGFWSVATYAETLEVLRDPVTYSSVTGGQRRFGGTVLQDLPVAGQVLNMMDDPRHTRIRRLVSSGLTPRMIRRVEDDLRRRARGLLDGVEPGAPFDFVVEIAAELPMQMICILLGVPETDRHWLFEAVEPGFDFRGSRRATMPRLNVEDAGSRLYTYALELIAGKRAEPADDMLSVVANATIDDPDAPALSDAELYLFFHLLFSAGAETTRNSIAGGLLALAENPDQLQTLRSDFELLPTAIEEIVRWTSPSPSKRRTASRAVSLGGQPIEAGQKVVVWEGSANRDPSVFDRADEFDITRKPNPHLGFGQGVHYCLGANLARLELRVLFEELLSRFGSVRVVEPAEWTRSNRHTGIRHLVVELRGG
6LNL , Knot 83 170 0.83 40 126 162 
MPSNMKQFCKISVWLQQHDPDLLEIINNLCMLGNLSAAKYKHGVTFIYPKQAKIRDEIKKHAYSNDPSQAIKTLESLILPFYIPTPAEFTGEIGSYTGVKLEVEKTEANKVILKNGEAVLVPAADFKPFPDRRLAVWIMESGSMPLEGPPYKRKKEGGGNLEHHHHHHHH

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 \(c\).

\(|P_{f(2KRB_1)}(2) \setminus P_{f(5LIE_1)}(2)|=34\), \(|P_{f(5LIE_1)}(2) \setminus P_{f(2KRB_1)}(2)|=161\). 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 1:001111001101110010010011001100110100010100010001011100101101101100101001000001010
Pair \(Z_2\) Length of longest common subsequence
2KRB_1,5LIE_1 195 3
2KRB_1,6LNL_1 138 3
5LIE_1,6LNL_1 187 3

Newick tree

 
[
	5LIE_1:10.85,
	[
		2KRB_1:69,6LNL_1:69
	]:33.85
]

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 \((0.85)(0.8)(\frac{495 }{\log_{20} 495}-\frac{81}{\log_{20}81})=124.\)
Status Protein1 Protein2 d d1/2
Query variables 2KRB_1 5LIE_1 156 93.5
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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