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 \(c\).
\(|P_{f(8PCW_1)}(2) \setminus P_{f(9EJG_1)}(2)|=117\),
\(|P_{f(9EJG_1)}(2) \setminus P_{f(8PCW_1)}(2)|=51\).
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 1:110111111011100011001001111011000010011111000010001010011101110001011100111000010110111001001100000000011101001010100111110010110101101001001000011000000100110100000101100010001001001110001001100100011101100100110100100010011001000011011000010000001101010101000010100011010010011100010000111100000010000101100001101000101000111110100000011001011000110011111001001100000100001010001001110010
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 \((0.85)(0.8)(\frac{573
}{\log_{20}
573}-\frac{183}{\log_{20}183})=112.\)
Status
Protein1
Protein2
d
d1/2
Query variables
8PCW_1
9EJG_1
142
104
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]