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 \(c\).
\(|P_{f(4CYO_1)}(2) \setminus P_{f(5QOR_1)}(2)|=162\),
\(|P_{f(5QOR_1)}(2) \setminus P_{f(4CYO_1)}(2)|=44\).
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 1:101110001110000000011111110010011011001011100101101010110010110011000010000011010000011011101100110101110001000111111111101011010010101000101001100001001001011010001000011111100100010000110110011111101010100100010100110101011110000100111110000011011000110010100110100111001001011111001010001110011110011000001001101001100111000001101101000110011100111011111000110100110110000110010111101010001001101010100111111
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 \((0.85)(0.8)(\frac{578
}{\log_{20}
578}-\frac{167}{\log_{20}167})=118.\)
Status
Protein1
Protein2
d
d1/2
Query variables
4CYO_1
5QOR_1
156
107
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]