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 \(c\).
\(|P_{f(5UZP_1)}(2) \setminus P_{f(8FOC_1)}(2)|=75\),
\(|P_{f(8FOC_1)}(2) \setminus P_{f(5UZP_1)}(2)|=67\).
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 1:100000000110110001010001000010011101110001010010000100111010101101110110111000011010011010110110000111010110011101111111010110000101100011001111001101100110010110010111011000001101010110000010110000101110110111010001000101111100010100010011100000100100101010000011010100001110110010101111101111110111000111110010001100100001000110010010111101011100001000000011100110011101110100111011100101001110101001111000110010000111110011111101110011111100100100011101100001
Pair
\(Z_2\)
Length of longest common subsequence
5UZP_1,8FOC_1
142
5
5UZP_1,5WNN_1
165
6
8FOC_1,5WNN_1
179
4
Newick tree
[
5WNN_1:90.53,
[
5UZP_1:71,8FOC_1:71
]:19.53
]
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 \((0.85)(0.8)(\frac{990
}{\log_{20}
990}-\frac{462}{\log_{20}462})=138.\)
Status
Protein1
Protein2
d
d1/2
Query variables
5UZP_1
8FOC_1
171
163
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]