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 \(c\).
\(|P_{f(7SFE_1)}(2) \setminus P_{f(5ISX_1)}(2)|=99\),
\(|P_{f(5ISX_1)}(2) \setminus P_{f(7SFE_1)}(2)|=32\).
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 1:0100101110110001000000010101001011001011100000110110101110000010110101101100011110001101111000001010010001011001100011101110100110100100010011000001010011000100000101010010110100001101100100100011000100011100110110111011010101001100100011000101000000000101001011010011010011010000101000010101001001000000011000101011010000111010110100010010011001010011110010110100100001001100100110010101010101000100100101010110100101101011100110011100011110110111011010011001100000111011111000000100110010101101111001101100100000001000111011000000010111100100110100011101010011011000011110110011100000111111111001111101101111010010111000011001001001110010100010011010011011010001010011000101100011100010001011111010011111100100110101010010110010000000001000011101100010110100111001001111011001000001111010101011100010010111001011010000110100010001110000111011000001101111111011110101011101
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 \((0.85)(0.8)(\frac{1447
}{\log_{20}
1447}-\frac{573}{\log_{20}573})=221.\)
Status
Protein1
Protein2
d
d1/2
Query variables
7SFE_1
5ISX_1
283
232
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]