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 \(c\).
\(|P_{f(6BOH_1)}(2) \setminus P_{f(6BPO_1)}(2)|=10\),
\(|P_{f(6BPO_1)}(2) \setminus P_{f(6BOH_1)}(2)|=258\).
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 1:0011111100011000011000111101110100110110101000111101010111001010111001011110000100001011001101101110111011101101010111011000100011111111111101100011111110001110011000000101011100010000001111010100011111100001000100000111011100010100001001100110011011110110110001001111011011011101100110001111111011001100101111101001111010111000010000010111111011011001111100000010110111010111000110111101101001000111111111110000001111010111000001110001111011110000011111111110011011010011110110110100110011000010100110110010110110101111110101110100100011100010011101011111101010111011000111101000010101111110010110001100101111111010111101010001110011101101111111110110111100000111101101101111010101110100111111110100110110111110110010001100010001011010011110101111101011111101110011100111010001110110001010000111011010101001110000011100000011111001111001101010011101010010001111110101100101111001111000111111100110111110001010111011011110101011000110001111011010111111000010011100001101010011111100011101111100011110100001011111111000011010111010010101100100100110001010010111101001110011100001011011101011000001001001100100110110001100111010000110111100100010111110111111111111111101101000110011010110000010110001110110101010100101101000100101111011010010001101101111110011001011111110111000110001110011110001011000110000101111001111001001101100101110011001010010110111010100000111000010101010010001001010010111110111000010001111001001111100010111011101001111101111000101100111101111001011011110110010100111111010110011100
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 \((0.85)(0.8)(\frac{2234
}{\log_{20}
2234}-\frac{727}{\log_{20}727})=365.\)
Status
Protein1
Protein2
d
d1/2
Query variables
6BOH_1
6BPO_1
271
270.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]