Algorithms for Bioinformatics– Introductory lectureVELI MÄKINEN, AUTUMN 2019

HTTPS://COURSES.HELSINKI.FI/FI/LSI31001/130408680

Course formatVideo lecture -> Friday lecture -> Monday study group->Thursday exercises

◦ First week a special case: ◦ Thursday python crash course, introduction to Rosalind

◦ Friday (this lecture)

◦ Video lecture + other material

◦ Monday study group

Grading:◦ To pass, you need to attend all study groups:

◦ Check course moodle for compensatory assignments

◦ Exercises 12 points (30% ⇒ 1, 85% ⇒ 12)

◦ Exam 48 points (to take part, you need at least 1 point from exercises)

◦ Total points 30 ⇒ 1, ∼ 50 ⇒ 5

Lectures and study groups are given by Veli Mäkinen (parts 0-2), Leena Salmela (parts 3-4), and Jarkko Toivonen (part 5). Exercises are given by Jarkko Toivonen (parts 0-4) and Veli Mäkinen (part 5).

Course overviewIntroduction to algorithms in the context of molecular biology

Targeted for ◦ first year bioinformatics students

◦ biology and medicine students

◦ CS / Math / Statistics students thinking of specializing in bioinformatics

Some programming skills and high school level biology are sufficient background◦ We will use Python in this course (no advanced features)

◦ Central dogma of molecular biology will be covered in Monday study group

Not as systematic as other CS algorithm courses: emphasis is on learning some design principles and techniques with the biological realm as motivation

Algorithms for BioinformaticsState-of-the-art algorithms in bioinformatics are rather involved

Instead, we study toy problems motivated by biology (but not too far from reality) that have clean and introductory level algorithmic solutions

The goal is to arouse interest to study the real advanced algorithms in bioinformatics!

We mostly avoid statistical notions to give algorithmic concepts the priority

Continue to further bioinformatics courses to learn the practical realm

AlgorithmWell-defined problem Solution to problem

input output

Homework: Find out what the following algorithm running time notions mean:

Number of steps: f(size of input)

…

Algorithms in BioinformaticsWeakly defined problem Solution to problem

input output=input2 output2=… outputN

Reasons: Biological problems usually too complex to admit a simple algorithmic formulation

Problem modeling sometimes leads to statistical notions

Problematic for CS theory: Optimal solutions to subproblems do not necessarily lead to best global solution

Algorithms in BioinformaticsPlenty of important subproblems where algorithmic techniques have been vital:

◦ Fragment assembly⇒ human genome

◦ Design of microarrays⇒ gene expression measurements

◦ Sequence comparison⇒ comparative genomics

◦ Phylogenetic tree construction⇒ evolution modeling

◦ Genome rearrangements ⇒ comparative genomics, evolution

◦ Motif finding ⇒ gene regulatory mechanism

◦ Biomolecular secondary structure prediction ⇒ function

◦ Analysis of high-throughput sequencing data ⇒ genomic variations in populations

Course contentPart 0: Getting familiar with biological sequences using Python

Part 1: Exhaustive search and randomized algorithms for motif discovery

Part 2: Graph Algorithms for Genome Assembly

Part 3: Dynamic Programming and Sequence Alignment

Part 4: Combinatorial Algorithms and Genomic Rearrangements

Part 5: Combinatorial Pattern Matching

Exam: Friday 18.10

Some motivating examplesSplicing graphs, transcript prediction, variation graphs

AG

ATG

ATG

CA

GAT

GG

ATG

AA

Source: wikipedia

DN

A=

DNA

transcription

binding

promoterenhancer

silencer

protein-protein

interaction

gene 1

pre-mRNA

mature mRNA transcripts

intron exon

alternative splicing

translation

proteins

TFBS

gene 2

...

Next week (part 1) coversthe discovery of these

TranscriptomicsStudy of RNA biology

genome

Transcription, alternative splicing

1203x

gene

87x

234xHow to measure these?

RNA-seq split read alignment

genome

…

align

gene

Splicing graph

1603 1508 1380 1597

95

1511

220

1198 13031203x

87x

234x

Find paths that best explainthe graph, e.g:

These numbers should reflect the average coverageof a position inside a transcript / exon / junction(how many reads span over a position, on average).Realistic concrete numbers are as shown divided by 100.

Annotated transcript expressionestimation

1603 1508 1380 1597

95

1511

220

1198 1303?x

?x

?x

Assume we know the possible transcriptsbut their relative abundancies are unknown

a

b

c

(1603-(a+b+c))2+(95-b) 2 +(1511-(a+c)) 2 +(1508-(a+c)) 2 +(220-c) 2 +(1198-a) 2 +(1380-(a+b)) 2 +(1303-(a+b)) 2 +(1597-(a+b+c)) 2

f(a,b,c)=Least squares problem:

Minimize

Least squares problemf(a,b,c) receives minimum when all partial derivates of f are zero.

f’a(a,b,c) = 2(a+b+c-1603)+ 2(a+c-1511) +2(a+c-1508) + 2(a-1198) + 2(a+b-1380) +2(a+b-1303) + 2(a+b+c-1597)

f’b(a,b,c) = 2(a+b+c-1603)+ 2(b-95) +2(a+b-1380) +2(a+b-1303) + 2(a+b+c-1597)

f’c(a,b,c) = 2(a+b+c-1603) + 2(a+c-1511) +2(a+c-1508) + 2(c-220) + 2(a+b+c-1597)

7a+4b+4c=101004a+5b+2c=59784a+2b+5c=6439 This system has a unique solution, which is

{ a = 21032/17, b = 5260/51, c = 13097/51 }.

Google: linear equations solver, click first link, copy-paste, click ”solve the system”, copy-paste the result

Solution

1603 1508 1380 1597

95

1511

220

1198 13031237 x

103 x

257 x

a

b

c

Splicing graphs and this courseWe need a way to align short DNA fragments on the genome, allowing splicing.

We will cover basic principles of such alignment algorithms (part 3) and take a look at data structures that enable fast pattern matching (part 5).

More on advanced alignment algorithms:◦ Biological Sequence Analysis, period III, Spring 2020.

What if there is no genome available?

…

align???

gene

One can exploit read overlaps (part 2)

…

align

gene

Genome rearrangements

1 2 3 4

1 234

Species A with 4 genes

Species B with 4 genes

During evolution, some chromosome level rearrangements happen

These can be modeled using signed permutations

We will cover some basic algorithms (part 4).

More on evolution related algorithms in the new course Elements of Bioinformatics, Autumn 2020.

Pan-genomics1000 Genomes Project and other high-throughput sequencing based projects have gathered a huge catalogue of human variation.

Such datasets can be represented as variation graphs

Alignment algorithms need to be revisited to work on graphs

More on this next Spring: Biological Sequence Analysis