1BGQ_1|Chain A|HEAT SHOCK PROTEIN 90|Saccharomyces cerevisiae (4932)
>4NQZ_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P|Enoyl-[acyl-carrier-protein] reductase [NADH] FabI|Pseudomonas aeruginosa (208964)
>7CWN_1|Chains A, B, C|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(c\).
\(|P_{f(1BGQ_1)}(2) \setminus P_{f(4NQZ_1)}(2)|=70\),
\(|P_{f(4NQZ_1)}(2) \setminus P_{f(1BGQ_1)}(2)|=84\).
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 1:101000000011100010101010011011100100000111001100100110010000100100100010111010101000110100011110010110011011001001110110111010111011111001111100101100000000011000111010101001000110101101110000100100001001100000111011011100010
Pair
\(Z_2\)
Length of longest common subsequence
1BGQ_1,4NQZ_1
154
6
1BGQ_1,7CWN_1
208
4
4NQZ_1,7CWN_1
202
5
Newick tree
[
7CWN_1:10.70,
[
1BGQ_1:77,4NQZ_1:77
]:32.70
]
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 \((0.85)(0.8)(\frac{498
}{\log_{20}
498}-\frac{225}{\log_{20}225})=78.7\)
Status
Protein1
Protein2
d
d1/2
Query variables
1BGQ_1
4NQZ_1
98
89.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]