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 \(c\).
\(|P_{f(5UOG_1)}(2) \setminus P_{f(8TDH_1)}(2)|=50\),
\(|P_{f(8TDH_1)}(2) \setminus P_{f(5UOG_1)}(2)|=124\).
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 1:10000000011011000101001001011111010101100110110010100101111010100101111010111111011101011101111001101001110111100010110001100111111001011101001100101100111110110101001111111011111100101111011000001001111000101111101100111111101001011010110111101111011010010011110110010111111011000101101110110101110110101100011001110010111001011011100110001100
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 \((0.85)(0.8)(\frac{795
}{\log_{20}
795}-\frac{344}{\log_{20}344})=122.\)
Status
Protein1
Protein2
d
d1/2
Query variables
5UOG_1
8TDH_1
161
138
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]