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Parikh vectors
6NOY_1 1DDN_1 6LHA_1 Letter Amino acid
19 0 8 E Glutamic acid
2 3 16 G Glycine
7 0 13 I Isoleucine
10 0 22 P Proline
7 0 20 V Valine
10 0 15 R Arginine
7 0 19 N Asparagine
3 0 6 H Histidine
15 0 20 L Leucine
1 0 4 W Tryptophan
2 3 4 C Cysteine
12 0 15 Q Glutamine
12 0 11 K Lycine
3 0 10 M Methionine
2 0 13 F Phenylalanine
3 0 12 Y Tyrosine
9 12 23 A Alanine
8 0 16 D Aspartic acid
15 0 20 S Serine
12 15 30 T Threonine 

6NOY_1|Chains A, B, C[auth G], D[auth H]|Maintenance of carboxysome positioning B protein, Mcsb|Cyanothece (43988)
>1DDN_1|Chain A[auth E]|33 BASE DNA CONTAINING TOXIN OPERATOR|
>6LHA_1|Chain A|VP1 protein|Coxsackievirus A16 (31704)
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 \(w=f(c)\)
6NOY , Knot 73 159 0.77 40 113 149 
GSHMSNNALDRLINKQKPKVPPRNDVVSESVSNDIKTQGQQELNTSLPPSDTKATPEEMPTSHESETSLSQDQKPKLSPDTFETVRNTIRIESEVDESLRQLCHEERITKETWLEAAYLYLCEKPEELAQVIQLAQERLSQRKAIADYKRAKTMQERFL
1DDN , Knot 12 33 0.42 8 11 18 
ATATAATTAGGATAGCTTTACCTAATTATTTTA
6LHA , Knot 134 297 0.85 40 198 287 
GDPIADMIDQTVNNQVNRSLTALQVLPTAANTEASSHRLGTGVVPALQAAETGASSNASDKNLIETRCVLNHHSTQETAIGNFFSRAGLVSIITMPTTDTQNTDGYVNWDIDLMGYAQLRRKCELFTYMRFDAEFTFVVAKPNGVLVPQLLQYMYVPPGAPKPTSRDSFAWQTATNPSVFVKMTDPPAQVSVPFMSPASAYQWFYDGYPTFGEHLQANDLDYGQCPNNMMGTFSIRTVGTEKSPHSITLRVYMRIKHVRAWIPRPLRNQPYLFKTNPNYKGNDIKCTSTSRDKITTL

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 \(c\).

\(|P_{f(6NOY_1)}(2) \setminus P_{f(1DDN_1)}(2)|=111\), \(|P_{f(1DDN_1)}(2) \setminus P_{f(6NOY_1)}(2)|=9\). 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 1:100100011001100001011100011000100010001000100011100001010011000000001000001010100100100010100010001001000001000011011010100010011011011000100001110000100100011
Pair \(Z_2\) Length of longest common subsequence
6NOY_1,1DDN_1 120 2
6NOY_1,6LHA_1 177 4
1DDN_1,6LHA_1 195 3

Newick tree

 
[
	6LHA_1:10.77,
	[
		6NOY_1:60,1DDN_1:60
	]:41.77
]

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 \((0.85)(0.8)(\frac{192 }{\log_{20} 192}-\frac{33}{\log_{20}33})=55.1\)
Status Protein1 Protein2 d d1/2
Query variables 6NOY_1 1DDN_1 71 40.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]