3ELM_1|Chains A, B|Collagenase 3|Homo sapiens (9606)
>7BLD_1|Chain A|Bromodomain adjacent to zinc finger domain protein 2A|Homo sapiens (9606)
>1PSF_1|Chain A|PHOTOSYSTEM I ACCESSORY PROTEIN E|Synechococcus sp. (32049)
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 \(c\).
\(|P_{f(3ELM_1)}(2) \setminus P_{f(7BLD_1)}(2)|=87\),
\(|P_{f(7BLD_1)}(2) \setminus P_{f(3ELM_1)}(2)|=49\).
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 1:001110010100101000110001010000100110011011001011010010011101110111000101011011011110111111001101010000010000010011111100110011100000111111110000100011110001011001011100010
Pair
\(Z_2\)
Length of longest common subsequence
3ELM_1,7BLD_1
136
3
3ELM_1,1PSF_1
144
3
7BLD_1,1PSF_1
116
2
Newick tree
[
3ELM_1:73.60,
[
7BLD_1:58,1PSF_1:58
]:15.60
]
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 \((0.85)(0.8)(\frac{276
}{\log_{20}
276}-\frac{105}{\log_{20}105})=54.0\)
Status
Protein1
Protein2
d
d1/2
Query variables
3ELM_1
7BLD_1
70
55
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]