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Parikh vectors
9KML_1 8CAC_1 2RDO_1 Letter Amino acid
9 29 0 L Leucine
7 12 0 Y Tyrosine
7 17 23 A Alanine
2 21 0 N Asparagine
4 13 0 Q Glutamine
13 26 41 G Glycine
10 11 0 R Arginine
4 11 0 I Isoleucine
3 10 0 M Methionine
16 16 0 S Serine
4 17 0 D Aspartic acid
3 11 0 K Lycine
2 13 0 P Proline
8 23 0 T Threonine
3 3 0 W Tryptophan
8 26 0 V Valine
2 12 36 C Cysteine
8 9 0 E Glutamic acid
1 6 0 H Histidine
4 16 0 F Phenylalanine 

9KML_1|Chain A[auth H]|heavy chain of 9D5 fab|Mus musculus (10090)
>8CAC_1|Chains A[auth AAA], B[auth BBB]|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
>2RDO_1|Chain A|5S RIBOSOMAL RNA|Escherichia coli (562)
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 \(w=f(c)\)
9KML , Knot 59 118 0.79 40 91 114 
EVQLVESGGGLVKPGGSLKLSCAASGFTFSSYAMSWVRQSPEKRLEWVAEISSGGRYIYYSDTVTGRFTISRDNARNILHLEMSSLRSEDTAMYYCARGEVRQRGFDYWGQGTTLTVS
8CAC , Knot 133 302 0.83 40 193 286 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVYAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSG
2RDO , Knot 34 120 0.45 8 15 46 
UGCCUGGCGGCCGUAGCGCGGUGGUCCCACCUGACCCCAUGCCGAACUCAGAAGUGAAACGCCGUAGCGCCGAUGGUAGUGUGGGGUCUCCCCAUGCGAGAGUAGGGAACUGCCAGGCAU

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 \(c\).

\(|P_{f(9KML_1)}(2) \setminus P_{f(8CAC_1)}(2)|=42\), \(|P_{f(8CAC_1)}(2) \setminus P_{f(9KML_1)}(2)|=144\). 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 1:0101100111110111010100110110100011011000100010111010011001000001010101000010011010100100000110001010100011001101001010
Pair \(Z_2\) Length of longest common subsequence
9KML_1,8CAC_1 186 3
9KML_1,2RDO_1 100 3
8CAC_1,2RDO_1 196 3

Newick tree

 
[
	8CAC_1:10.46,
	[
		9KML_1:50,2RDO_1:50
	]:56.46
]

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 \((0.85)(0.8)(\frac{420 }{\log_{20} 420}-\frac{118}{\log_{20}118})=91.2\)
Status Protein1 Protein2 d d1/2
Query variables 9KML_1 8CAC_1 117 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]