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 \(c\).
\(|P_{f(4TXT_1)}(2) \setminus P_{f(5KKA_1)}(2)|=146\),
\(|P_{f(5KKA_1)}(2) \setminus P_{f(4TXT_1)}(2)|=28\).
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 1:10100010111001001111100100110101000111000100110011001010000110001110110101010100100110010001110100011000010011001101001000101101011110011000110001001101101110100101010010110010110010011000110011010100101111011101110000000010000110101011010011011100010100100011011011001001110001011100000111101000100110100111111011101011000101100011111111000010100101100110010001010011001011111110001010000011101010111001011000110001111011010011000010100011111001101100110100010111100101010100101100100010101100100111010110111000110000111001100110011001101000001101100010000110001011111110110101100110110100000001011010110001011010000111000111101000111100000100111110000000
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 \((0.85)(0.8)(\frac{968
}{\log_{20}
968}-\frac{312}{\log_{20}312})=176.\)
Status
Protein1
Protein2
d
d1/2
Query variables
4TXT_1
5KKA_1
225
162
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]