5SPL_1|Chains A, B|Non-structural protein 3|Severe acute respiratory syndrome coronavirus 2 (2697049)
>5SKM_1|Chains A, B, C, D|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>3BNQ_1|Chains A, B, C|A site of human mitochondrial ribosome, A chain|
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 \(c\).
\(|P_{f(5SPL_1)}(2) \setminus P_{f(5SKM_1)}(2)|=52\),
\(|P_{f(5SKM_1)}(2) \setminus P_{f(5SPL_1)}(2)|=154\).
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 1:0110010101010001010010110010010101110110101001111111100100011010000011001110111001101001100010111101001001011001000100001111111011111101100101010010001011110001000110011
Pair
\(Z_2\)
Length of longest common subsequence
5SPL_1,5SKM_1
206
3
5SPL_1,3BNQ_1
126
2
5SKM_1,3BNQ_1
228
2
Newick tree
[
5SKM_1:12.05,
[
5SPL_1:63,3BNQ_1:63
]:57.05
]
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 \((0.85)(0.8)(\frac{512
}{\log_{20}
512}-\frac{169}{\log_{20}169})=100.\)
Status
Protein1
Protein2
d
d1/2
Query variables
5SPL_1
5SKM_1
133
98
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]