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Parikh vectors
6XXE_1 2YLS_1 7WJC_1 Letter Amino acid
16 45 38 A Alanine
2 3 1 C Cysteine
2 46 69 E Glutamic acid
10 27 61 S Serine
7 21 38 N Asparagine
4 15 29 Q Glutamine
0 12 25 H Histidine
15 34 34 T Threonine
1 11 19 W Tryptophan
4 40 27 R Arginine
10 26 46 I Isoleucine
2 16 50 K Lycine
4 26 46 F Phenylalanine
3 29 29 P Proline
1 25 38 Y Tyrosine
11 43 36 V Valine
6 29 42 D Aspartic acid
7 44 49 G Glycine
6 43 66 L Leucine
0 7 16 M Methionine 

6XXE_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P|Uncharacterized protein|Thermus thermophilus (strain HB27 / ATCC BAA-163 / DSM 7039) (262724)
>2YLS_1|Chain A|PHENYLACETONE MONOOXYGENASE|THERMOBIFIDA FUSCA (2021)
>7WJC_1|Chain A|Alpha-xylosidase|Lactococcus lactis subsp. cremoris MG1363 (416870)
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 \(w=f(c)\)
6XXE , Knot 52 111 0.73 36 84 105 
FTLIELAIVIVIIGILVAIAVPRFVDLTDQANQANVDATAAAVRSAYAIATVQAKGIPTCDQVFANPEGGSTSGSTWTSSDNSTTVSCNASADTFTISRGGKTRTLNLTVN
2YLS , Knot 217 542 0.84 40 248 510 
MAGQTTVDSRRQPPEEVDVLVVGAGFSGLYALYRLRELGRSVHVIETAGDVGGVWYWNRYPGARCDIESIEYCYSFSEEVLQEWNWTERYASQPEILRYINFVADKFDLRSGITFHTTVTAAAFDEATNTWTVDTNHGDRIRARYLIMASGQLSVPQLPNFPGLKDFAGNLYHTGNWPHEPVDFSGQRVGVIGTGSSGIQVSPQIAKQAAELFVFQRTPHFAVPARNAPLDPEFLADLKKRYAEFREESRNTPGGTHRYQGPKSALEVSDEELVETLERYWQEGGPDILAAYRDILRDRDANERVAEFIRNKIRNTVRDPEVAERLVPKGYPFGTKRLILEIDYYEMFNRDNVHLVDTLSAPIETITPRGVRTSEREYELDSLVLATGFDALTGALFKIDIRGVGNVALKEKWAAGPRTYLGLSTAGFPNLFFIAGPGSPSALSNMLVSIEQHVEWVTDHIAYMFKNGLTRSEAVLEKEDEWVEHVNEIADETLYPMTASWYTGANVPGKPRVFMLYVGGFHRYRQICDEVAAKGYEGFVLT
7WJC , Knot 294 759 0.85 40 297 688 
MGSSHHHHHHSSGLVPRGSHMVSELESKYMNNNIIKFDKARFTVLTEHLIRIEYSETGEFEERMTQMVQNREFSEVNFDIIEKEETIEIITSTVHLYYNGGEFTNASLFADVKFNFSVYSNRWYFGEKSDGNLKGTTRTLDMIDGECPLEDGIMSKNGFAVLADKGKVLTEVGDIAGNSVSTIDLYLFAYGRDYRQALKDFYQLTGNTPKLPRFALGNWWSRYYDYSDKSYLALMDKFTDKKVPLSVSVIDMDWHKVSEVPSRFGSGWTGYSWNKKLFPNPENFIDELHQRKLKVTLNDHPADGIRAFEDPYPQVAQTLDLNTELEEAAKFDFDNLKFRKAYFEEVHGPLEKEGVDFWWIDWQQGAISKSGVDPLWLLNHYQYQNAQKKHKNNIILSRYAGPGSHRYPLGFSGASVISWASLDFQPYFTSTASNIGYTWWSHDIGGHMQGYKDAELSLRWLQFGVFSPINRLHSSKSEFTSKEPWHFDAVIEQSMIDFLQLRHQLIPYLYSANLITASEGRALVEPLYYEYPMEEEAYQHRNQYLFGEQLMVAPITEKMNSLLQMGSVEVWFPEGTWYDFFSGQPYDGKVSLKVYREITEMPVFAKAGAIIPLDKNPLKKEEIPSEIIWKIFPGADGEYLLLEEDNETKAEFVNGIFTVTSKKESSRKHTIIYGEHEIVSAKRGEFSIDLNGKEENFDWNFSTALFRRLDIAEISYEQKDEILQQLSLIEEHEKQVAFIKTNENQELQNSLFELLYSGK

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 \(c\).

\(|P_{f(6XXE_1)}(2) \setminus P_{f(2YLS_1)}(2)|=18\), \(|P_{f(2YLS_1)}(2) \setminus P_{f(6XXE_1)}(2)|=182\). 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 1:101101111111111111111101101000100101010111100101110101011100001110101100010010000000010001010010100110000101010
Pair \(Z_2\) Length of longest common subsequence
6XXE_1,2YLS_1 200 4
6XXE_1,7WJC_1 237 4
2YLS_1,7WJC_1 135 5

Newick tree

 
[
	6XXE_1:12.45,
	[
		2YLS_1:67.5,7WJC_1:67.5
	]:52.95
]

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 \((0.85)(0.8)(\frac{653 }{\log_{20} 653}-\frac{111}{\log_{20}111})=157.\)
Status Protein1 Protein2 d d1/2
Query variables 6XXE_1 2YLS_1 196 116
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]