Opening the paper…
Algorithmic Thinking in Bioinformatics, End Term
Your lab has bought a new mass spectrometer and you are asked to test the accuracy of the same. You use the machine to generate the spectrum for the peptide . The spectrum generated is given below:
0 113 186 226 299 299 412 415
Use Figure 1 given below to calculate the percentage of error of the machine.
| G | A | S | P | V | T | C | I | L | N | D | K | Q | E | M | H | F | R | Y | W |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 57 | 71 | 87 | 97 | 99 | 101 | 103 | 113 | 113 | 114 | 115 | 128 | 128 | 129 | 131 | 137 | 147 | 156 | 163 | 186 |
Figure 1: Masses of different amino acids
(Error is calculated by dividing the total number of missing and false masses, by the length of the theoretical spectrum.)
Round up the answer to 2 decimal places.
Your lab has bought a new mass spectrometer and you are asked to test the accuracy of the same. You use the machine to generate the spectrum for the peptide $\mathit{Peptide} = \mathit{WIL}$. The spectrum generated is given below: 0 113 186 226 299 299 412 415 Use Figure 1 given below to calculate the percentage of error of the machine. | G | A | S | P | V | T | C | I | L | N | D | K | Q | E | M | H | F | R | Y | W | |---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| | 57 | 71 | 87 | 97 | 99 | 101 | 103 | 113 | 113 | 114 | 115 | 128 | 128 | 129 | 131 | 137 | 147 | 156 | 163 | 186 | Figure 1: Masses of different amino acids (Error is calculated by dividing the total number of missing and false masses, by the length of the theoretical spectrum.) *Round up the answer to 2 decimal places.* An evil warlord wants to mutate a human chromosome into the DNA sequence of a dangerous virus and implant it in cyborgs to create his robotic army. The synteny blocks of the two species are given below: $$\begin{aligned} \mathit{Human\ DNA} &: -5 -1 -2 -4 +3 \\ \mathit{Virus} &: -5 +4 +1 -2 -3 \end{aligned}$$ The most sophisticated machines available require 1 hour to apply a single 2-break operation. Use breakpoint graphs to determine the minimum number of hours needed by the evil warlord to complete the transformation. In a soft K-means clustering process, a dataset is clustered into two groups. A data point has distances $d_1 = 3$ and $d_2 = 6$ from the two cluster centroids. Using the soft K-means formula with $\beta = 1$, compute the probabilities of the data point belonging to each cluster. After assigning probabilities, update the centroid $\mu_1$ given that the current centroid is $\mu_1 = 4$ and this data point's value is $x = 5$. Assume no other points are assigned to cluster 1. Use the centroid update formula: $$\mu_k^{\text{new}} = \frac{\sum_i P(C_k \mid x_i) x_i}{\sum_i P(C_k \mid x_i)}$$ where $P(C_k \mid x)$ is computed using the softmax-like probability formula: $$P(C_k \mid x) = \frac{e^{-\beta d_k}}{\sum_{j=1}^{K} e^{-\beta d_j}}$$