DNA Analysis: Principles and Sequencing Algorithms

Veronika Abramova

, Bruno Cabral

and Jorge Bernardino

1,2

Polytechnic Institute of Coimbra, ISEC - Coimbra Institute of Engineering, Coimbra, Portugal

University of Coimbra – CISUC, Centre for Informatics and Systems of University Coimbra, Coimbra, Portugal

Keywords: DNA, Genome Assembly, Graph, Assemblers, Algorithms.

Abstract: DNA discovery has put humans one step closer to deciphering their own structure stored as biological data.

Such data could provide us with a huge amount of information, necessary for studying ourselves and learn

all the variants that pre-determine one's characteristics. Although, these days, we are able to extract DNA

from our cells and transform it into sequences, there is still a long road ahead since DNA has not been easy

to process or even extract in one go. Over the past years, bioinformatics has been evolving more and more,

constantly aiding biologists on the attempts to “break” the code. In this paper, we present some of the most

relevant algorithms and principles applied on the analysis of our DNA. We attempt to provide basic genome

overview but, moreover, the focus of our study is on assembly, one of the main phases of DNA analysis.

1 INTRODUCTION

Deoxyribonucleic acid, known as DNA, was firstly

discovered and introduced by Watson and Crick

(Watson and Crick, 1953). Authors stated that any

existing organism’s molecule stores all the necessary

data for its living and grown by carrying instructions

that are necessary for constant development and

overall organism’s functioning (Saenger and

Wolfram, 1984), (Alberts et. al, 2002). For us,

humans, DNA contains most of our characteristics

as a person, such as, adaptation, character and so on

but, more importantly, information about creation of

proteins that form all of our parts. This protein is

used by our organism to produce all the necessary

substances, for example, keratin or our hair and

nails, bio functioning proteins that transport oxygen

inside our body and so on. DNA structure is

presented as double helix, where on one helix are

located Adenine (A) and Guanine (G) and on the

other helix Thymine (T) and Cytosine (C). While

creating the double helix, A connects with T and,

respectively, C with G. Those are called base pairs.

Currently, there are several challenges related to

the DNA study and manipulation. One of the

limitations of the current technology is the capability

of extracting the entire DNA chain, only parts of

DNA may be read. That means that, these days, it is

not possible to extract the entire genome. More than

that, extracted parts can be easily corrupted, either

by extraction errors or by transcription errors.

Moreover, even if the part of DNA that is analyzed

was correctly processed, there is a possibility of that

sequence being just a part of necessary sequence or

not meaning anything (trash). That means that even

if the code was extracted correctly, the extracted

sequence may not have expected importance.

Another challenging task that follows is genome

assembly.

In this paper we attempt describing some of the

challenges that are related to the genome assembly

as well as some of the current possibilities. Currently

there are a lot of studies and papers, focusing on

extracting ever more of the necessary and important

data. However, we consider that it may be

challenging for someone to begin study

bioinformatics. Therefore, we describe the

assembling algorithms and the origin of those as

well as their base, so readers can understand some of

the associated challenges with genome sequencing.

The remaining of the paper is structured as

follows: Section 2 describes related work and some

of the studies that have been performed over the past

years. Section 3 describes some of the available

assemblers that are used for extracting and

sequencing DNA. Section 4 provides an overview

over algorithms that are used for DNA sequencing

(genome assembly). Finally, section 5 presents our

conclusions and future work.

Abramova, V., Cabral, B. and Bernardino, J.

DNA Analysis: Principles and Sequencing Algorithms.

DOI: 10.5220/0006084102450250

In Proceedings of the 8th International Joint Conference on Computational Intelligence (IJCCI 2016) - Volume 1: ECTA, pages 245-250

ISBN: 978-989-758-201-1

245

2 RELATED WORK

DNA study has been a hardly invested area over the

past years and, therefore, there is a lot of data about

genetic study and evolution. Munib et al. (2015)

present and describe the entire process of shotgun

sequence assembly in the realm of high-performance

computing. They describe main phases of genome

assemble and some of the algorithms that may be

used among those phases. Also, Mount (2004)

provides an examination of the computational

methods needed for analyzing DNA, RNA –

structure that DNA is transformed after has been

extracted from the nucleus of the cell, and protein

data, as well as genomes. Differently, we focus our

paper on one specific area, providing more detail,

instead of entire process overview. Polyanovsky et

al. (2011) present a comparison approach between

alignment algorithms. Authors based they work

mainly on Polyanovsky et al. (2008), Sunyaev et al.

(2004), Domingues et al. (2000) and compared

results produced by local and global alignment and

concluded that both local and the global alignment

algorithms rely on positions and relative lengths of

the parts of the sequences that will be aligned and

depending of the sequence positioning, global or

local algorithms provide better results. Global

algorithm proved to that when the core part of one

sequence was positioned above the core of the other

sequence but when the cores were positioned

asymmetrically, the local algorithm was more stable.

Posada (2009) describes methods to analyze DNA

sequences as well as some available tools that are

free to use, describing recognition of similar

sequences using BLAST, sequence alignment, DNA

compositions and molecular evolution and other.

This book is more oriented for biologists that do not

have much knowledge about computer science and,

moreover, have a bigger biological background that

most of computer engineers do not have. Jones and

Pavel (2004

) provide a large overview over existing

algorithms that are used in bioinformatics by

presenting the foundations of algorithms, describing

principles that drove their design, and their most

important results. DNA sequencing challenges and

processing are described in El-Metwally et al.

(2013), Niedringhaus et al. (2011), Voelkerding et

al. (2009), Zhou et al. (2010), Wheeler et al. (2008).

Authors describe some of the past and current

technologies, solutions for DNA sequencing and

available next-generation sequencing (NGS)

platforms and their future (Hert et al., 2008). NGS

platforms perform sequencing of millions of small

fragments of DNA in parallel which means that

millions of small fragments of DNA can be

sequenced at the same time, creating a massive pool

of data. All the sequence fragments are analysed

several times in order to reduce error possibility.

3 GENOME ASSEMBLERS

After years of genome study and research there is a

variety of assemblers used to extract and transcript

genome. Constant interest and technological

evolution have been contributing for different

generations of assemblers, attempting to provide

better results and surpass each other. The first next-

generation DNA sequencing machine, the GS20,

was introduced to the market by 454 Life Sciences

in 2005 (Gilles et al., 2011) That technology was

based on a large-scale parallel pyrosequencing

system, which relies on fixing DNA fragments to

small DNA-capture beads in a water-in-oil emulsion.

While trying to understand what is genome

assembling and what its stages are and elements that

are take part, one of the first things we hear of is de-

novo assembly. So what is de-novo how it is

important? De-novo is a method of new generation

sequencing that attempts to sequence genome

without any reference. That means that short reads

are not mapped against original sequence (when it is

available). On the other hand, reference assembling

considers available parts of the sequence (reads) and

only considers those that can be mapped into an

original sequence. It may be used to assemble

genomes of already extinct organisms (Era7, 2016).

One of the first challenges consisted of the

extractions of the DNA from the cells. Biological

advance and evolution had contributed to this task

and currently it is possible to extract DNA. That

possibility would provide all of the answers to one’s

“construction” and allow us to manipulate our own

constituent and fight many diseases. DNA structure

is presented as double helix, where on one helix are

located Adenine (A) and Guanine (G) and on the

other helix Thymine (T) and Cytosine (C). While

creating the double helix, A connects with T and,

respectively, C with G. Those are called base pairs.

After extracting a DNA sequence (input), it is

processed by overlapping the extracted sequences.

This overlap process is called sequence alignment

and it allows creating a larger sequence that contains

parts of small pieces. The output of an assembler is

generally decomposed into contigs, or contiguous

regions of the genome which are nearly completely

resolved, and scaffolds, or sets of contigs which are

approximately placed and oriented with respect to

ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications

246

each other (Gregory, 2005). Currently DNA

sequencing technology allows short reads of 500 and

up to 700 nucleotides. This sequences are parts from

one complete DNA genome.

Genome assembling from shorter sequences is

like reassembling the magazine from the millions of

small pieces of each page. In both cases will exist

errors. In case of magazine it would be ragged edges

that difficult putting pieces together. In case of

genome assembly those would be reading errors.

More than that, pieces may be lost in both cases and

also, in case of DNA, nucleotides may be

transcripted incorrectly. Nevertheless, efforts to

determine the DNA sequence of organisms have

been remarkably successful, even in the face of these

difficulties. Salzberg et al. (2011) describe some of

the most popular Assemblers.

4 ALGORITHMS

In the 1950s, Seymour Benzer applied graph theory

to show that genes are linear (Jones and Pevzner,

2004). Therefore, in this section we will describe

some of the most popular algorithms for genome

assembly, while most of those being Graph

algorithms. Short read assemblers generally use one

of two basic algorithms: overlap graphs and de

Bruijn graphs. The overlaps between each pair of

reads is computed and compiled into a graph, in

which each node represents a single sequence read.

This algorithm is more computationally intensive

than de Bruijn graphs, and most effective in

assembling fewer reads with a high degree of

overlap (Illumina¸ 2010). De Brujin Graph started

from Bridges of Königsberg problem (Compeau et

al., 2011). The bridges problem is presented on the

Figure 1.

Figure 1: Bridges of Königsberg (Compeau et al.,2011).

The problem statement consisted on passing

each bridge only once considering that the islands

could only be reached by the bridges and every

bridge once accessed must be crossed to its other

end. The starting and ending points of the route may

or may not be the same. This problem was firstly

solved by Leonard Euler, a Swiss mathematician,

physicist, astronomer and logician. At first Euler

analysed the problem and decided that it could not

be solved (Paoletti, 2011). However, Euler could

not just accept that. He decided to create a logical

formula for this type of problems. Euler observed

that in order to be able to solve this type of problems

it would be necessary zero or two nodes with odd

degree. This theory was posteriorly proved by Carl

Hierholzer. This author stated that in order to be able

to solve a graph using Euler’s path, each connected

node has to have an even degree, except for the

starting and terminal nodes (Barnett, 2009). On

August 26, 1735, Euler presented a paper containing

the solution to the Konigsberg bridge problem. He

addressed Bridges of Königsberg, problem as well

as provided a general solution where any number of

bridges could be used (Hopkins and Wilson, 2004).

In this section we describe some of the basic

DNA assembly algorithms and problems that those

try to solve.

4.1 Shortest Superstring Problem

Since all the DNA reads are performed as parts, it is

necessary to be able to overlap those and create one

superstring that would better represent and include

considered pieces of sequences. This is important

since different sequences may be part of the same

superstring. However, this superstring creation may

be challenging. As more simplistic approach,

superstring could result from complete

concatenation of available reads. But this approach

would not be very correct. Best superstring created

should be the shortest one possible. That would

represent the sequence that somehow concatenates

available reads but, also, does not contain

unnecessary information.

INPUTS: Set of sequences.

OUTPUT: One sequence that contains all the

input sequences while being as short as possible.

In order to be able to create one superstring it is

necessary to align input sequences and be able to

identify which ones may be same part of different

reads. We should be able to define any overlapping

regions and after that create one complete sequence.

Below we present an example of Shortest

Superstring Solution. Given:

INPUTS: {00, 01, 10, 11}

FULL SEQUENCE: 00011011

SHORTEST SUPERSTRING:

DNA Analysis: Principles and Sequencing Algorithms

247

001011

As it is possible to understand, instead of just

concatenating all the available stings, in order to

solve Shortest Superstring Problem, it is necessary

to evaluate all the sequences and find overlaps. After

those overlaps are considered, final sequence is

shorter than just full sequence concatenation.

As computational approach, in order to solve

these problems may be used greedy algorithms

(Vazirani¸ 2001). Those algorithms continuously

build up the final solution, through interactive

cycles. Each cycle the algorithm attempts to find

optimal solution. It is important to notice that greedy

algorithms are not exhaustive and when the problem

has considerable difficulty it may not be possible to

obtain the best optimal solution, instead just local

maximum. Also, depending on the problem

difficulty, those algorithms require a considerable

amount of cycles in order to be able to produce

optimal solution that may, never less, be local.

While applied to the Shortest Superstring Problem,

greedy algorithms iterate input sequences and

integrate (assemble) those one by one. In the

approach presented below the algorithm considers

two of the most similar sequences and overlap them,

creating just one sequence. After, this sequence will

be aligned with the third one and so on, for example:

INPUT: {ACTG, CTGA, GACC, TGAC,

ACCC}

STAGE 1 – consider most similar string ACTG

and CTGA

ACTG

CTGA -> ACTGA

STAGE 2 – consider most similar ACTGA and

TGAC

ACTGA

TGAC -> ACTGAC

STAGE 3 – consider most similar ACTGAC

and GACC

ACTGAC

GACC -> ACTGACC

STAGE 4 – overlap the rest – ACTGACC and

ACCC

ACTGACC

ACCC -> ACTGACCC

OUTPUT: ACTGACCC

As we can see, in the previous example, greedy

algorithm was able to create a shortest superstring

with 4 steps. However, the problem presented is

very simplistic. In real case scenario, inputs string

would have been larger and number of inputs would

be bigger. Therefore, it may be difficult for the

algorithm to find the best superstring. Also, the

algorithm may consider different possibilities of

sequences to match, especially at start. This also

highly affects the final sequence.

4.2 Hamiltonian Path Problem

Hamiltonian Path in an undirected graph is a path

that visits each vertex exactly once. A cycle that

uses every vertex in a graph exactly once is called a

Hamilton cycle. It is important to notice that in order

for Hamiltonian Path to exist, graph edges must be

biconnected. That means that two or more vertices

of the graph when removed could not disconnect the

graph. Problem statement is, as follows:

INPUT: Read sequences

OUTPUT: Created graph as well as Spectrum S

Available sequences must be connected if there is an

overlap. For example,

INPUT: {ATG, TGG, TGC, GTG, GGC}

OUTPUT:

ATGGCGTGC

In this example there is a possibility of the

second path that could be obtained by overlapping

sequences in different order (way):

OUTPUT:

ATGCGTGGC

This simple example allows us to create different

path by overlapping existing sequences. Due to the

nature of the sequences (available nucleotides) there

were two possible path to choose from. However, in

the more complex problem the solution is not a

trivial one.

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As first approach could be used brute-force

(exhaustive) search. But, a better approach is

presented by Frank Rubin Author proposed an

algorithm that divides a complete problem into

pieces, each being solved easier than them all

together (Rubin, 1974). All the available graphs are

divided into three categories: used in path, not used

in path and undecided. The functioning of this

algorithm (identification and study of small

problems) resembles dynamic programming

principles, where each stage of the problem (part) is

independent from previous stages (Vazirani¸2001).

Also, Michael Held and Richard M. Karp

presented their solution using dynamic programming

and based on the traveling-salesman problem (Held

and Karp, 1962). Traveling-salesman problem is a

well knows problem, similarly to the Bridges of

Königsberg problem. Salesman must visit each city

just once and using shortest route. Therefore, authors

provided a solution as cyclic iteration of vertices and

verify if there is a possibility of covering a path in

set of vertices S. For further vertices the path is

evaluated only if it existed in the previous stage.

4.3 Eulerian Path Problem

Similarly, to the previously stated problem, the

purpose of the Eulerian Path is to find a route to visit

each node of the graph just once. Euler Circuit is a

circuit that uses each vertex of the graph just once.

The main difference between Eulerian path and

Circuit is that path ends on the different vertex,

while circuit represents the complete cycle where it

starts and end with the same vertex. Differently from

the Hamiltonian Path problem, while working with

Eulerian Path, we shall consider more linear

traveling approach. That means that sequences are

connected linearly (v1 -> v2 -> …) which not

happens in Hamiltonian Path. Moreover, while

working with Eulerian path it is necessary to

consider the following theorem: “A connected graph

is Eulerian if and only if each of its vertices is

balanced.” (Jones and Pevzner

, 2004). Consider that

vertex is balanced when indegree = outdegree for

presented vertex. In order to create a Eulerian cycle,

it is necessary to start drawing path from the

arbitrary vertex v and traversing edges that have not

already been used. We stop the path when we

encounter a vertex with no way out, that is, a vertex

whose outgoing edges has already been used in the

path.

Below is presented an example of the Eulerian

Path problem:

INPUT: {ATG, TGG, TGC, GTG, GGC}

STAGE 1: Create vertices of lengh k-1

{AT, TG, GG, GC, CG, GT}

OUTPUT:

ATGGCGTGC

As we have seen in the previous sub-section,

there is another path:

OUTPUT:

ATGCGTGGC

In order to solve Eulerian path problems there are

two main algorithms: Fleury's algorithm and Cycle

finding algorithm. Fleury's algorithm was originally

created in 1883 to find Eulerian paths (Fleury,

1883). It proceeds by repeatedly removing edges

from the graph in such way, that the graph remains

Eulerian. The algorithm starts at a vertex of odd

degree, or, if the graph has none, it starts with an

arbitrarily chosen vertex. At each step it chooses the

next edge in the path to be removed considering that

that edge would not disconnect the graph itself (is

not a bridge). If there is no such edge algorithm

cannot proceed. It then moves to the other endpoint

of that vertex and deletes the chosen edge. At the

end of the algorithm there are no edges left, and the

sequence from which the edges were chosen

(removed) forms a Eulerian cycle if the graph has no

vertices of odd degree, or a Eulerian trail if there are

exactly two vertices of odd degree.

5 CONCLUSIONS

This work provides a basic overview over genome

assembly processes and their challenges. We started

by describing the overall genome sequencing

problem and discussing its relevance. Posteriorly,

we portrayed some of the most popular assemblers

and their inner workings. Most of the assemblers,

including some not mentioned in this work, use de

Bruijn graphs for sequence assembling. But,

DNA Analysis: Principles and Sequencing Algorithms

249

sequence alignment, used for creating common

substrings (overlaps) also has an high impact and

weight in DNA sequencing performance. Finally, to

provide a clear insight for computer scientists into

genome assembly algorithms, we draw some

parallelism between the Selling-travelers problem,

as well as with the Bridges of Königsberg problem,

with the genome sequencing problems, showing that

both have highly contributed to the evolution and the

development of graph algorithms and their use in

bioinformatics.

After many years of research and work, genome

assembly is still a hard and cumbersome task. As

future work, we plan to implement and optimize

some of the described approaches using state of the

art parallel and distributed computing strategies.

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