1LVM_1|Chains A, B|CATALYTIC DOMAIN OF THE NUCLEAR INCLUSION PROTEIN A (NIA)|Tobacco etch virus (12227)
>3URB_1|Chains A, B|Parathion hydrolase|Brevundimonas diminuta (293)
>6BWS_1|Chains A, B, C, D|Glycolate utilization protein|Methylobacterium extorquens (408)
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 \(c\).
\(|P_{f(1LVM_1)}(2) \setminus P_{f(3URB_1)}(2)|=73\),
\(|P_{f(3URB_1)}(2) \setminus P_{f(1LVM_1)}(2)|=107\).
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 1:1000000010011011000011000100100000100001011111111100001100001011100101110100000100011010011110110011111001010010000010110001000010011000000110001111001100001001011100001111110010010000001001100110110000100110110101001111100111001
Pair
\(Z_2\)
Length of longest common subsequence
1LVM_1,3URB_1
180
3
1LVM_1,6BWS_1
172
6
3URB_1,6BWS_1
162
4
Newick tree
[
1LVM_1:90.24,
[
6BWS_1:81,3URB_1:81
]:9.24
]
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 \((0.85)(0.8)(\frac{556
}{\log_{20}
556}-\frac{229}{\log_{20}229})=93.3\)
Status
Protein1
Protein2
d
d1/2
Query variables
1LVM_1
3URB_1
119
101
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]