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Parikh vectors
2KWO_1 5RFB_1 6PXN_1 Letter Amino acid
0 13 19 P Proline
1 16 35 S Serine
0 24 22 T Threonine
1 17 22 A Alanine
0 17 21 D Aspartic acid
0 12 6 C Cysteine
1 29 39 L Leucine
5 11 24 K Lycine
0 11 18 Y Tyrosine
3 11 40 R Arginine
0 14 13 Q Glutamine
1 7 12 H Histidine
0 17 16 F Phenylalanine
0 9 23 E Glutamic acid
0 10 13 M Methionine
0 3 3 W Tryptophan
0 27 19 V Valine
0 21 16 N Asparagine
8 26 33 G Glycine
0 11 21 I Isoleucine 

2KWO_1|Chain A[auth B]|Histone peptide|null
>5RFB_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>6PXN_1|Chains A, B|Casein kinase I isoform delta|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 \(w=f(c)\)
2KWO , Knot 10 20 0.50 14 14 15 
SGRGKGGKGLGKGGAKRHRK
5RFB , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
6PXN , Knot 178 415 0.86 40 232 403 
MELRVGNRYRLGRKIGSGSFGDIYLGTDIAAGEEVAIKLECVKTKHPQLHIESKIYKMMQGGVGIPTIRWCGAEGDYNVMVMELLGPSLEDLFNFCSRKFSLKTVLLLADQMISRIEYIHSKNFIHRDVKPDNFLMGLGKKGNLVYIIDFGLAKKYRDARTHQHIPYRENKNLTGTACYASINTHLGIEQSRRDDLESLGYVLMYFNLGSLPWQGLKAATKRQKYERISEKKMSTPIEVLCKGYPSEFATYLNFCRSLRFDDKPDYSYLRQLFRNLFHRQGFSYDYVFDWNMLKFGASRAADDAERERRDREERLRHSRNPATRGLPSTASGRLRGTQEVAPPTPLTPTSHTANTSPRPVSGMERERKVSMRLHRGAPVNISSSDLTGRQDTSRMSTSQIPGRVASSGLQSVVHR

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 \(c\).

\(|P_{f(2KWO_1)}(2) \setminus P_{f(5RFB_1)}(2)|=6\), \(|P_{f(5RFB_1)}(2) \setminus P_{f(2KWO_1)}(2)|=188\). 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 1:01010110111011100000
Pair \(Z_2\) Length of longest common subsequence
2KWO_1,5RFB_1 194 2
2KWO_1,6PXN_1 218 4
5RFB_1,6PXN_1 190 3

Newick tree

 
[
	2KWO_1:10.75,
	[
		5RFB_1:95,6PXN_1:95
	]:10.75
]

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 \((0.85)(0.8)(\frac{326 }{\log_{20} 326}-\frac{20}{\log_{20}20})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 2KWO_1 5RFB_1 127 67
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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