2EWU_1|Chain A|Cytochrome c3|Desulfovibrio vulgaris str. 'Miyazaki F' (883)
>1SMC_1|Chains A, B, C|Deoxyuridine 5'-triphosphate nucleotidohydrolase|Mycobacterium tuberculosis (1773)
>6VHQ_1|Chains A, B|Glycoside hydrolase family 68 protein|Bacillus subtilis (1423)
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 \(c\).
\(|P_{f(2EWU_1)}(2) \setminus P_{f(1SMC_1)}(2)|=52\),
\(|P_{f(1SMC_1)}(2) \setminus P_{f(2EWU_1)}(2)|=82\).
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 1:11011101101000001110000000110010000110100000001011000010000001010001100010010001100100111011000010100100000
Pair
\(Z_2\)
Length of longest common subsequence
2EWU_1,1SMC_1
134
3
2EWU_1,6VHQ_1
203
4
1SMC_1,6VHQ_1
189
6
Newick tree
[
6VHQ_1:10.42,
[
2EWU_1:67,1SMC_1:67
]:39.42
]
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 \((0.85)(0.8)(\frac{281
}{\log_{20}
281}-\frac{107}{\log_{20}107})=54.8\)
Status
Protein1
Protein2
d
d1/2
Query variables
2EWU_1
1SMC_1
64
52.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]