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Parikh vectors
2FVQ_1 7ATS_1 6DEU_1 Letter Amino acid
0 7 7 Q Glutamine
0 29 27 L Leucine
0 20 20 K Lycine
0 15 18 S Serine
0 10 10 Y Tyrosine
0 23 18 V Valine
6 9 19 A Alanine
0 18 20 D Aspartic acid
0 21 21 E Glutamic acid
0 17 13 I Isoleucine
0 12 7 M Methionine
0 12 11 N Asparagine
2 8 10 C Cysteine
2 22 19 G Glycine
6 12 17 T Threonine
0 4 2 W Tryptophan
0 26 17 R Arginine
0 10 18 H Histidine
0 16 18 F Phenylalanine
0 19 10 P Proline

2FVQ_1|Chain A[auth B]|5'-D(*CP*TP*TP*TP*CP*AP*TP*TP*AP*AP*TP*GP*AP*AP*AP*G)-3'|
>7ATS_1|Chain A|LIM domain kinase 1|Homo sapiens (9606)
>6DEU_1|Chains A, B|Caspase-6|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 \(w=f(c)\)
2FVQ , Knot 8 16 0.46 8 10 14
CTTTCATTAATGAAAG
7ATS , Knot 137 310 0.84 40 198 297
SMPHRIFRPSDLIHGEVLGKGCFGQAIKVTHRETGEVMVMKELIRFDEETQRTFLKEVKVMRCLEHPNVLKFIGVLYKDKRLNFITEYIKGGTLRGIIKSMDSQYPWSQRVSFAKDIASGMAYLHSMNIIHRDLNSHNCLVRENKNVVVADFGLARLMVDEKTQPEGLRSLKKPDRKKRYTVVGNPYWMAPEMINGRSYDEKVDVFSFGIVLCEIIGRVNADPDYLPRTMDFGLNVRGFLDRYCPPNCPPSFFPITVRCCDLDPEKRPSFVKLEHWLETLRMHLAGHLPLGPQLEQLDRGFWETYRRGES
6DEU , Knot 134 302 0.84 40 197 290
MASSASGLRRGHPAGGEENMTETDAFYKREMFDPAEKYKMDHRRRGIALIFNHERFFWHLTLPERRGTCADRDNLTRRFSDLGFEVKCFNDLKAEELLLKIHEVSTVSHTDADCFVCVFLSHGEGNHIYAYDAKIEIQTLTGLFKGDKCHSLVGKPKIFIIQACRGNQHDVPVIPLDVVDNQTEKLDTNITEVDAASVYTLPAGADFLMCYSVAEGYYSHRETVNGSWYIQDLCEMLGKYGSSLEFTELLTLVNRKVSQRRVDFCKDPSAIGKKQVPCFASMLTKKLHFFPKSNLEHHHHHH

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 \(c\).

\(|P_{f(2FVQ_1)}(2) \setminus P_{f(7ATS_1)}(2)|=8\), \(|P_{f(7ATS_1)}(2) \setminus P_{f(2FVQ_1)}(2)|=196\). 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 1:0000010011011111
Pair \(Z_2\) Length of longest common subsequence
2FVQ_1,7ATS_1 204 2
2FVQ_1,6DEU_1 195 3
7ATS_1,6DEU_1 175 4

Newick tree

 
[
	2FVQ_1:10.54,
	[
		6DEU_1:87.5,7ATS_1:87.5
	]:16.04
]

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 \((0.85)(0.8)(\frac{326 }{\log_{20} 326}-\frac{16}{\log_{20}16})=103.\)
Status Protein1 Protein2 d d1/2
Query variables 2FVQ_1 7ATS_1 135 71
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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