3LQR_1|Chains A, B|Cell death protein 4|Caenorhabditis elegans (6239)
>4FCE_1|Chain A|Bifunctional protein GlmU|Yersinia pestis CO92 (214092)
>4FYV_1|Chains A, C|Aspartate carbamoyltransferase catalytic chain|Escherichia coli (83333)
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 \(c\).
\(|P_{f(3LQR_1)}(2) \setminus P_{f(4FCE_1)}(2)|=100\),
\(|P_{f(4FCE_1)}(2) \setminus P_{f(3LQR_1)}(2)|=52\).
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 1:110010001100100011001010011001010011000000110010001001101101000010011111011000000011011000101110010110111111010001100011110110010001000010011001001001001111101011010011100110000011110000111100010110001011001111100000110110100100111001100111001001111001100001011001010011000010100110000011010010100000110101111111000001100010100101101111100001001001101000100011111001010000011111000101100000011111111111101110110011110100000001000110010010001111010011110101001101110011010011011011000110110001011000110010010000100101000000110100110110100010001001100
Pair
\(Z_2\)
Length of longest common subsequence
3LQR_1,4FCE_1
152
4
3LQR_1,4FYV_1
174
4
4FCE_1,4FYV_1
142
6
Newick tree
[
3LQR_1:84.94,
[
4FCE_1:71,4FYV_1:71
]:13.94
]
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 \((0.85)(0.8)(\frac{1008
}{\log_{20}
1008}-\frac{459}{\log_{20}459})=144.\)
Status
Protein1
Protein2
d
d1/2
Query variables
3LQR_1
4FCE_1
185
167
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]