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Parikh vectors
2JXT_1 7CNR_1 6UEF_1 Letter Amino acid
13 32 0 E Glutamic acid
3 33 4 G Glycine
7 5 0 H Histidine
6 29 0 I Isoleucine
3 8 0 M Methionine
4 15 0 F Phenylalanine
6 15 0 R Arginine
11 28 0 K Lycine
0 3 0 W Tryptophan
2 22 0 D Aspartic acid
0 3 6 C Cysteine
4 24 0 S Serine
2 20 5 T Threonine
2 19 0 Y Tyrosine
2 38 6 A Alanine
3 4 0 Q Glutamine
6 34 0 L Leucine
4 16 0 P Proline
7 26 0 V Valine
1 12 0 N Asparagine

2JXT_1|Chain A|50S ribosomal protein LX|Methanothermobacter thermautotrophicus (187420)
>7CNR_1|Chains A, C, E, G|DUF521 domain-containing protein|Thermococcus kodakarensis (strain ATCC BAA-918 / JCM 12380 / KOD1) (69014)
>6UEF_1|Chain A[auth B]|DNA (5'-D(*CP*AP*AP*TP*GP*AP*CP*TP*CP*AP*TP*GP*CP*TP*CP*AP*TP*CP*GP*GP*A)-3')|synthetic construct (32630)
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 \(w=f(c)\)
2JXT , Knot 45 86 0.77 36 65 78
MKMKTKIFRVKGKFLMGDKLQPFTKELNAIREEEIYERLYSEFGSKHRVPRSKVKIEEIEEISPEEVQDPVVKALVQRLEHHHHHH
7CNR , Knot 164 386 0.84 40 209 369
MYLTKEEELILAGEYGYALQKAMEILVALGDIYGADRLIPIKSAQVAGVSYKNIGDAGIEFLRDFVEAGAKVSVYTTLNPAGIGDDEFMEKQMEVLELYRKMGIEVTSTCTPYYGANLPKFGDHIAWSESSAVSFANSILGARTNREGGPSSLAAAIVGKTPNYGLHLDENRKATVIVDVKAKVKTFADYSVLGYHVGKTLGNDVPYFKNLKPEKTEFLKELGAAMGATGSIALYHVEGETPEYREAITDKLETITVEDSDLKAVRESFQDDWSDIDMILIGCPHASLPEVKEIAELLRMRGKPLKIPLFITASRAVKALADALGYTEIIERYNGKIIPDSCFVVSPIKGWYRGIATNSGKSAFYFRSFGFSVRLDDVENLIKEAP
6UEF , Knot 10 21 0.48 8 11 15
CAATGACTCATGCTCATCGGA

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 \(c\).

\(|P_{f(2JXT_1)}(2) \setminus P_{f(7CNR_1)}(2)|=21\), \(|P_{f(7CNR_1)}(2) \setminus P_{f(2JXT_1)}(2)|=165\). 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 1:10100011010101111001011000101100001000100011000011000101001001010010011101110010000000
Pair \(Z_2\) Length of longest common subsequence
2JXT_1,7CNR_1 186 4
2JXT_1,6UEF_1 76 1
7CNR_1,6UEF_1 204 3

Newick tree

 
[
	7CNR_1:11.54,
	[
		2JXT_1:38,6UEF_1:38
	]:72.54
]

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 \((0.85)(0.8)(\frac{472 }{\log_{20} 472}-\frac{86}{\log_{20}86})=116.\)
Status Protein1 Protein2 d d1/2
Query variables 2JXT_1 7CNR_1 149 89.5
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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