这个作业是用Python解决DNA序列相关的编程

COMPSCI369 – S1 2020

Assignment 3

0 Instructions

This assignment is worth 7.5% of the final grade. It is marked out of 75 points.

Provide a solution as a Python notebook that includes well documented code with the code/test

calls to reproduce your results. Include markdown cells with explanation of the results for each

question. Submit to Canvas

• the .ipynb file with outputs from the executed code

• a .html version of the notebook with all outputs of executed code showing. (To get this

format, export from the notebook viewer or use nbconvert.)

Within the notebook, set the random seed to some integer of your choosing (using random.seed)

so that the marker can recreate the same output that you get. You can reset the seed before each

question if you like.

1 Genome Assembly

Due to limitations of the modern sequencing technology, we can only obtain short continuous sequence fragments (or reads) from the genome sequences at a time. Given millions of such short

reads, can we reconstruct the full DNA sequences as close as possible? This is essentially the DNA

sequence assembly problem, that can be approximated to the Shortest Common Superstring (SCS)

problem: Given a set of strings s1, s2, . . . , sn, find a shortest string s that contains all of them as

substrings.

SCS problem is a NP-complete problem, so the early DNA sequences algorithms used a simple

greedy strategy to the assembly problem, that find the SCS by iteratively joining and merging

overlapping reads until all reads have been merged.

In this assignment you will implement the greedy sequence assembler. You will also implement the

read generator, i.e simulate the shotgun sequencing process, that randomly partitions a genome

sequence S into fragments of certain length l. The process is repeated a large number of times

(also known as cloning) to amplify the biological signal, needed for proper identification of the

short reads. In the lecture, you saw example of greedy DNA reconstruction given all the l-length

reads defined over the original DNA sequence for a fixed value of l. Here, we will not assume that

all possible reads of length l will be given (generated), and we will allow for reads with different

length. But, we will keep the assumption that the reads will be error free.

Question 1: Shotgun Sequencing (10 Points)

Implement a class ShotgunSequencing with the following attributes and methods:

(a) sequence

stores a DNA sequence.

(b) readSequence(filename, i=1)

reads only the i-th sequence from the filename, a file in fasta format, and stores

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the sequence in sequence. The parameter i can take only positive values; if the

file does not have i sequences, then return None.

(c) shotgun(l min,l max)

returns the sequence sequence as an array of fragments with random length

len(f) that is uniformly distributed between l min and l max. Note that the

last generated fragment can be shorter than l min. You can safely assume that

the fragments cover the whole sequence, and no fragment gets lost.

Example: S=‘ATTCGGT’ could be fragmented as ‘AT’, ‘TCGG’, ‘T’ for 2 ≤

len(f) ≤ 4.

(d) cloning(l min,l max,n)

calls the function shotgun(min, max) n times and returns one sorted array

with all fragments.

Question 2: Sequence Assembler (35 Points)

Implement a class SequenceAssembler which assembles the fragments from the above

exercise, with the following attributes and methods:

(a) graph

stores the overlap graph.

Hint: Think about the below given methods which you have to implement

before you decide on how to store your graph. You need to have easy access

to all in-coming and out-going edges of a node. You will need to remove nodes

and their corresponding edges. Why are adjacency lists the best representation

for graphs to use for this problem?

(b) calculateOverlap(fragmentA,fragmentB)

returns the length of the overlap if fragmentB follows fragmentA.

Example: calculateOverlap(‘AAT’,‘ATG’) should return 2, while calculateOverlap(‘ATG’, ‘AAT’) should return 0.

(c) createOverlapGraph(fragments)

creates an overlap graph where each fragment is considered as node. Edges

are directed and weighted, with the weights representing length of fragment

overlaps. Keep edges that have non-zero weights. Nodes representing fragments

that are substrings of other fragments (nodes) can be removed from the graph.

(d) getMaxEdge()

returns the edge with highest weight.

(e) assembling()

implements the greedy algorithm for Shortest Common Superstring where you

merge the nodes until one is left and return the final sequence.

Test your solution for different combinations of l min, l max and n

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Sequence l min l max n

5 10

Test 10 20 3,5,10

20 30

50 100

Real mRNA 100 200 5,10,15

200 500

and interpret the result for the reconstruction of the two sequences (short-length

test sequence, and real-length mRNA from the human genome) provided in the file

A3 DNAs.fasta. When interpreting the results, take into consideration the following

questions:

• How well is the sequence reconstructed as the fragments vary in size?

• Does the reconstructed sequence have a similar length to the original sequence?

• What is the effect of cloning on the two sequences?

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2 Stochastic simulation

A standard model in epidemiology is the SIR model of infectious disease spread. It has a population

of N hosts is divided into 3 compartments, so is known as a compartmental model:

• the S compartment of those who are susceptible to the disease

• the I compartment of those who are infectious with the disease

• the R compartment of those who are recovered from the disease and now immune (or, more

generally, those who are removed from the epidemic either through recovery with immunity

or due to death).

We assume that S + I + R = N.

The model can be thought of as deterministic or stochastic. We consider the stochastic version

here. Times between all events are exponentially distributed with the following rates which depend

on the current state of the outbreak, assumed to be (S, I, R):

• the rate of transmissions is βSI and the new state is (S − 1, I + 1, R), and

• the rate of recoveries is γI and the new state is (S, I − 1, R + 1).

Question 3: Simulating outbreaks (30 Points)

(a) At what point will the epidemic finish?

(b) Write method rand exp that takes a rate parameter λ as input and produces

as output an exponentially distributed random variable with rate parameter λ.

(c) Write method sim SIR that takes as inputs N, S0, β, γ and produces as output

a list of the event times and the number susceptible, infected and recovered at

each time point. All outbreaks start at time t = 0.

(d) Run a simulation with N = 1000, S0 = 10, β = 2.2, γ = 2 and plot the number

infected through time.

(e) Run an experiment and report the results to approximate the probability that

a large outbreak occurs using the same parameters as above but with only one

initial infected. What has usually happened if there is no outbreak?

(f) The reproduction number R0 = β/γ of the epidemic is the mean number of

transmissions by a single infected in an otherwise susceptible population. Using

the same parameters as above but allowing β to vary, select five values of R0

near to or at 1 and explore whether or not you get an outbreak. Report and

explain your results.

(g) Suppose now that the infectious period is fixed, so that hosts are infectious

for exactly 1 time unit. Is the process still Markov? How would you go about

writing code to simulate such an epidemic? (You do not have to actually write

the code here.)

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