3TMP_1|Chains A, C, E, G|OTU domain-containing protein 5|Homo sapiens (9606)
>7HVG_1|Chain A|Protease 2A|Coxsackievirus A16 (31704)
>5IYY_1|Chains A, B|Neuropilin-1|Homo sapiens (9606)
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 \(c\).
\(|P_{f(3TMP_1)}(2) \setminus P_{f(7HVG_1)}(2)|=101\),
\(|P_{f(7HVG_1)}(2) \setminus P_{f(3TMP_1)}(2)|=66\).
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 1:1001111000000001111010110110100000110011000011110010001101101110010100010011000010011001001000100010001000000000100101011101000110100000100110110010110000001101000001000011010010111111
Pair
\(Z_2\)
Length of longest common subsequence
3TMP_1,7HVG_1
167
3
3TMP_1,5IYY_1
177
4
7HVG_1,5IYY_1
146
3
Newick tree
[
3TMP_1:89.96,
[
7HVG_1:73,5IYY_1:73
]:16.96
]
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 \((0.85)(0.8)(\frac{328
}{\log_{20}
328}-\frac{144}{\log_{20}144})=56.3\)
Status
Protein1
Protein2
d
d1/2
Query variables
3TMP_1
7HVG_1
73
64.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]