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Parikh vectors
2HOO_1 6UBI_1 1RMX_1 Letter Amino acid
0 12 0 P Proline
0 33 0 S Serine
0 21 0 V Valine
0 15 0 K Lycine
0 7 0 F Phenylalanine
0 6 0 I Isoleucine
0 15 0 L Leucine
0 1 0 M Methionine
0 4 0 W Tryptophan
19 15 2 A Alanine
0 11 0 D Aspartic acid
0 9 0 Y Tyrosine
0 4 0 N Asparagine
0 9 0 Q Glutamine
0 6 0 E Glutamic acid
26 22 3 G Glycine
0 7 0 H Histidine
0 20 2 T Threonine
0 7 0 R Arginine
21 5 3 C Cysteine 

2HOO_1|Chain A|thi-box riboswitch|null
>6UBI_1|Chains A, D|VRC34.05 heavy chain|Homo sapiens (9606)
>1RMX_1|Chains A, B|5'-D(*CP*GP*AP*CP*TP*AP*GP*TP*CP*G)-3'|
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 \(w=f(c)\)
2HOO , Knot 28 83 0.49 8 16 51 
GCGACUCGGGGUGCCCUUCUGCGUGAAGGCUGAGAAAUACCCGUAUCACCUGAUCUGGAUAAUGCCAGCGUAGGGAAGUCGCA
6UBI , Knot 102 229 0.80 40 144 221 
SQYLAQSGSEVKKPGASVKVSCRLHGDKFGAHYIHWVRQAPGQGLEWLGFFHPGTGDAVSAQKFQGRISLTRDTSISTGYLEVRRLSSDDTAVYYCARDKTYSDEATGMDIWGQGTTVIVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSCDKTH
1RMX , Knot 7 10 0.53 8 8 8 
CGACTAGTCG

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 \(c\).

\(|P_{f(2HOO_1)}(2) \setminus P_{f(6UBI_1)}(2)|=11\), \(|P_{f(6UBI_1)}(2) \setminus P_{f(2HOO_1)}(2)|=139\). 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 1:10110001111010000000101011111001111110100010100100011000111011010011010111111100101
Pair \(Z_2\) Length of longest common subsequence
2HOO_1,6UBI_1 150 2
2HOO_1,1RMX_1 16 4
6UBI_1,1RMX_1 146 2

Newick tree

 
[
	6UBI_1:85.33,
	[
		2HOO_1:8,1RMX_1:8
	]:77.33
]

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 \((0.85)(0.8)(\frac{312 }{\log_{20} 312}-\frac{83}{\log_{20}83})=72.4\)
Status Protein1 Protein2 d d1/2
Query variables 2HOO_1 6UBI_1 98 62
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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