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Parikh vectors
6IVR_1 1AJL_1 1RBD_1 Letter Amino acid
3 2 0 C Cysteine
14 3 0 G Glycine
5 0 2 K Lycine
7 0 0 M Methionine
14 0 0 P Proline
12 0 1 D Aspartic acid
17 0 2 E Glutamic acid
9 0 1 H Histidine
15 0 1 F Phenylalanine
24 4 4 A Alanine
20 0 1 R Arginine
22 0 0 I Isoleucine
49 0 0 L Leucine
5 0 0 W Tryptophan
15 0 0 V Valine
12 0 0 N Asparagine
8 0 1 Q Glutamine
19 0 1 S Serine
18 0 1 T Threonine
9 0 0 Y Tyrosine 

6IVR_1|Chains A, B, C, D, E|Ibestrophin|Klebsiella pneumoniae (573)
>1AJL_1|Chain A|RNA (5'-R(*GP*GP*UP*AP*AP*UP*AP*AP*GP*CP*UP*C)-3')|Tetrahymena thermophila (5911)
>1RBD_1|Chain A[auth S]|RIBONUCLEASE S (S-PEPTIDE)|Bos taurus (9913)
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 \(w=f(c)\)
6IVR , Knot 130 297 0.83 40 179 281 
SNAMIIRPEQHWFLRLFDAHGSVLSKIIFRLLLNVLMSIIAIISYQWYEQLGIHLTVAPFSLLGIAIAIFLGFRNSASYSRFVEARNLWGTVLIAERTLVRQLRNILPAEHDAHRRIVSYLVAFSWSLKHQLRKTDPTADLRRLLPEERVTEILASSMPTNRILLLAGNEIGQLREAGKLSDITYGLMDNKLDELAHVLGGCERLATTPVPFAYTLILQRTVYLFCTLLPFALVGDLHYMTPFVSVFISYTFLSWDSLAEELEDPFGTAANDLPLNAMCNTIERNLLDMTGQHPLPE
1AJL , Knot 7 12 0.48 8 9 9 
GGUAAUAAGCUC
1RBD , Knot 12 16 0.69 22 14 14 
KETAAAKFERQHADSX

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 \(c\).

\(|P_{f(6IVR_1)}(2) \setminus P_{f(1AJL_1)}(2)|=175\), \(|P_{f(1AJL_1)}(2) \setminus P_{f(6IVR_1)}(2)|=5\). 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 1:001111010001110110101011001110111011101111100010001110101111011111111111100010000110100111011110001100100111100010001100111101010001000010101001110001001110011000111111001101001101001001110001001101111000110011111001110001011001111111101001011101110001101001100100111011001110110001000110101001110
Pair \(Z_2\) Length of longest common subsequence
6IVR_1,1AJL_1 180 2
6IVR_1,1RBD_1 179 3
1AJL_1,1RBD_1 21 2

Newick tree

 
[
	6IVR_1:10.45,
	[
		1RBD_1:10.5,1AJL_1:10.5
	]:92.95
]

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 \((0.85)(0.8)(\frac{309 }{\log_{20} 309}-\frac{12}{\log_{20}12})=99.9\)
Status Protein1 Protein2 d d1/2
Query variables 6IVR_1 1AJL_1 128 66.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]