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 \(c\).
\(|P_{f(9AUV_1)}(2) \setminus P_{f(3CNR_1)}(2)|=136\),
\(|P_{f(3CNR_1)}(2) \setminus P_{f(9AUV_1)}(2)|=28\).
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 1:10000001001010101101100110100111111000111001010001001101011110111001000011111100111111000101110110100100101101000100000011010111111011001001011101110111100101001111001011000110101111011010111111011101101111110100001111111101011001101100011111011101010110111111001111011110001110101101000010011101111111010100010000111001110110101100111101100111110001100101110010001011010011100001001010001100011
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 \((0.85)(0.8)(\frac{512
}{\log_{20}
512}-\frac{117}{\log_{20}117})=117.\)
Status
Protein1
Protein2
d
d1/2
Query variables
9AUV_1
3CNR_1
139
89
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]