4QAC_1|Chains A, B, C, D, E, F, G, H, I, J|Acetylcholine-binding protein|Lymnaea stagnalis (6523)
>1EJQ_1|Chains A, B|SYNDECAN-4|null
>4JQD_1|Chains A, B, E, F|Csp231I C protein|Citrobacter sp. RFL231 (315237)
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 \(c\).
\(|P_{f(4QAC_1)}(2) \setminus P_{f(1EJQ_1)}(2)|=135\),
\(|P_{f(1EJQ_1)}(2) \setminus P_{f(4QAC_1)}(2)|=14\).
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 1:0000000010010110010000010111000001111010101101101001000101111000010000111000001001011100111101110011001011010110110010110110100010001011000011000101101000000101010000000000100000101101000000100000101000101010100010001
Pair
\(Z_2\)
Length of longest common subsequence
4QAC_1,1EJQ_1
149
3
4QAC_1,4JQD_1
149
3
1EJQ_1,4JQD_1
80
3
Newick tree
[
4QAC_1:82.86,
[
1EJQ_1:40,4JQD_1:40
]:42.86
]
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 \((0.85)(0.8)(\frac{245
}{\log_{20}
245}-\frac{28}{\log_{20}28})=73.6\)
Status
Protein1
Protein2
d
d1/2
Query variables
4QAC_1
1EJQ_1
92
51.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]