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 \(c\).
\(|P_{f(7TUE_1)}(2) \setminus P_{f(1RAW_1)}(2)|=178\),
\(|P_{f(1RAW_1)}(2) \setminus P_{f(7TUE_1)}(2)|=9\).
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 1:1000100100110011010101101101000111010001001000101111000110010000010000000000010011000000011001100101001110101101000010010001110001001011001101000010110110000101011010010001001000100101100010001100001010011111011010101000100000000110001110001001111111010000000010001110110101
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 \((0.85)(0.8)(\frac{310
}{\log_{20}
310}-\frac{36}{\log_{20}36})=89.6\)
Status
Protein1
Protein2
d
d1/2
Query variables
7TUE_1
1RAW_1
120
66
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]