4AYJ_1|Chains A, B, C, D|BOGT - METAL-INDEPENDENT GLYCOSYLTRANSFERASE|BACTEROIDES OVATUS (28116)
>7EHQ_1|Chain A|Chitin oligosaccharide binding protein NagB2|Paenibacillus sp. FPU-7 (762821)
>2OXK_1|Chain A|hybrid alpha/beta peptide based on the GCN4-pLI sequence; heptad positions b and f substituted with beta-amino acids|null
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 \(c\).
\(|P_{f(4AYJ_1)}(2) \setminus P_{f(7EHQ_1)}(2)|=62\),
\(|P_{f(7EHQ_1)}(2) \setminus P_{f(4AYJ_1)}(2)|=106\).
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 1:101111010010001110010101000110000111000110001010000000010010000111100010010111010001000000111101011100111001111000011110101110001000100000010010110101000011110110001010100010011000100011111000011000110011110101101010111111011111000001001100110000
Pair
\(Z_2\)
Length of longest common subsequence
4AYJ_1,7EHQ_1
168
3
4AYJ_1,2OXK_1
162
3
7EHQ_1,2OXK_1
212
3
Newick tree
[
7EHQ_1:10.03,
[
4AYJ_1:81,2OXK_1:81
]:19.03
]
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 \((0.85)(0.8)(\frac{686
}{\log_{20}
686}-\frac{246}{\log_{20}246})=122.\)
Status
Protein1
Protein2
d
d1/2
Query variables
4AYJ_1
7EHQ_1
155
121.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]