Algorithmic Thinking in Bioinformatics · End Term · Jan 2026 · FN

You are given two DNA sequences

and

of length

and

respectively. Assume

to be the scoring function. A pseudocode for an algorithm that calculates the optimal global alignment score between the two sequences is given below. Fill in the blanks for the algorithm appropriately.

The number of occurrences of the four nucleotides in the genome sequence of some virus is given in Table 1.

The suffix array of the genome sequence is:

. Assume $ is present at the end of the original genome sequence for all computations. Which of the following represents the correct genome sequence?

Consider the following profile matrix.

Find the profile-most probable

-mer for the sequence

.

Let

be a random sample from a distribution with density:

Find the maximum likelihood estimator (MLE) of

.

A mass spectrometer generates the following spectrum

for the peptide ''

HEQN''.

The figure given below depicts the mass of all amino acids.

The criteria to trim peptides in the leaderboard based cyclopeptide sequencing algorithm is modified as follows: "Suppose the algorithm is considering the peptide

. Let the number of elements in the theoretical spectrum of

be

. If

(

,

)

, then the peptide is trimmed''. Which of the following peptides will be trimmed?

Given below are a set of genetic sequences and the position (sites) of their nucleotides.

You construct the following rooted binary phylogenetic tree from this. Calculate the parsimony score for the tree. Enter the value as a single integer.

Consider the below table containing sample data from a sequencing experiment. Each trial corresponds to 5 independent expression measurements. Each measurement is classified as either: • H: high expression signal • L: low expression signal Assume that each trial is generated from one of two hidden biological states, each with its own probability of producing a high signal.

Let

and

denote the probability of observing a high signal (H) in biological states 1 and 2, respectively. Given:

Here, π represents the prior probability of the two biological states. What is the probability that **Trial 3** was generated by biological state 1? Answer correct to two decimal places.

A researcher is analyzing gene expression levels from five tissue samples. Gene expression measures how active a gene is in a given sample; higher values mean the gene is more active. The researcher believes the samples come from three different biological subtypes and uses a univariate Gaussian Mixture Model (GMM) with 3 components to model them. Suppose for component 2, you are given the following expression levels and corresponding responsibilities. Calculate the value of

?

Answer correct to two decimal places.

The overlap graph of some linear (i.e., non-circular) genome

has

nodes. Answer the given subquestions about the de Bruijn graph constructed on the same set of k-mers. Remember that

can be reconstructed by using both the graphs when answering these questions.

What is the number of edges in the de Bruijn graph? Enter the value as a single integer.

The overlap graph of some linear (i.e., non-circular) genome

has

nodes. Answer the given subquestions about the de Bruijn graph constructed on the same set of k-mers. Remember that

can be reconstructed by using both the graphs when answering these questions.

What is the maximum number of nodes possible in the de Bruijn graph? Enter the value as a single integer.

Consider a dataset of six genes. Each gene is represented by its expression levels under two experimental conditions (Condition A and Condition B), so each gene corresponds to a point in

.

A researcher applies **K-means clustering** with

to group genes with similar expression patterns. The cluster centroids are initialized as follows: • Cluster 1 centroid:

(low-expression genes) • Cluster 2 centroid:

(high-expression genes) Based on the above data, answer the given subquestions.

If

is the centroid of the first cluster after convergence, find the value of

. Enter the value as a single integer.

Consider a dataset of six genes. Each gene is represented by its expression levels under two experimental conditions (Condition A and Condition B), so each gene corresponds to a point in

.

A researcher applies **K-means clustering** with

to group genes with similar expression patterns. The cluster centroids are initialized as follows: • Cluster 1 centroid:

(low-expression genes) • Cluster 2 centroid:

(high-expression genes) Based on the above data, answer the given subquestions.

If

is the centroid of the second cluster after convergence, find the value of

. Enter the value as a single integer.