Introduction to Computational Biology

Maps, Sequences and Genomes

Michael S. Waterman

• Publisher: Chapman and Hall/CRC
• Year: 2018
• eBook ISBN:
  9781351437080
• Print ISBN:
  9780412993916
• Subtopic: Programming Algorithms

Biology is in the midst of a era yielding many significant discoveries and promising many more. Unique to this era is the exponential growth in the size of information-packed databases. Inspired by a pressing need to analyze that data, Introduction to Computational Biology explores a new area of expertise that emerged from this fertile field- the combination of biological and information sciences. This introduction describes the mathematical structure of biological data, especially from sequences and chromosomes. After a brief survey of molecular biology, it studies restriction maps of DNA, rough landmark maps of the underlying sequences, and clones and clone maps. It examines problems associated with reading DNA sequences and comparing sequences to finding common patterns. The author then considers that statistics of pattern counts in sequences, RNA secondary structure, and the inference of evolutionary history of related sequences. Introduction to Computational Biology exposes the reader to the fascinating structure of biological data and explains how to treat related combinatorial and statistical problems. Written to describe mathematical formulation and development, this book helps set the stage for even more, truly interdisciplinary work in biology.

Chapter 1

Some Molecular Biology

The purpose of this chapter is to provide a brief introduction to molecular biology, especially to DNA and protein sequences. Ideally, the reader has taken a beginning course in molecular biology or biochemistry and can go directly to Chapter 2. Introductory textbooks often exceed 1000 pages; here we just give a few basics. In later chapters we introduce more biological details for motivation.

One of the basic problems of biology is to understand inheritance. In 1865 Mendel gave an abstract, essentially mathematical model of inheritance in which the basic unit of inheritance was a gene. Although Mendel’s work was forgotten until 1900, early in this century it was taken up again and underwent intense mathematical development. Still the nature of the gene was unknown. Only in 1944 was the gene known to be made of DNA; and, it was not until 1953 that James Watson and Francis Crick proposed the now famous double helical structure for DNA. The double helix gives a physical model for how one DNA molecule can divide and become two identical molecules. In their paper appears one of the most famous sentences of science: “It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.” That copying mechanism is the basis of modern molecular genetics. In the model of Mendel the gene was abstract. The model of Watson and Crick describes the gene itself, providing the basis for a deeper understanding of inheritance.

The molecules of the cell are of two classes: large and small. The large molecules, known as macromolecules, are of three types: DNA, RNA, and proteins. These are the molecules of most interest to us and they are made by joining certain small molecules together in polymers. We next discuss some of the general properties of macromolecules, including how DNA is used to make RNA and proteins. Then we give some more details of the biological chemistry that are the basis of these properties.

1.1 DNA and Proteins

DNA is the basis of heredity and it is a polymer, made up of small molecules called nucleotides. These nucleotides are four in number and can be distinguished by the four bases: adenine (A), ctyosine (C), guanine (G), and thymine (T). For our purposes a DNA molecule is a word over this four letter alphabet, $\mathcal{A}$ = { A,C,G,T}. DNA is a nucleic acid and there is one other nucleic acid in the cell, RNA. RNA is a word over another four letter alphabet of ribonucleotides, $\mathcal{A}$ = {A,C,G,U} where thymine is replaced by uracil. These molecules have a distinguishable direction, and for reasons detailed later, one end (usually the left) is labeled 5’ and the other 3’.

Proteins are also polymers and here the word is over an alphabet of 20 amino acids. See Table 1.1 for a list of the amino acids and their one and three letter abbreviations. Proteins also have directionality.

How much DNA does an organism need to function? We can only answer a simpler question: How much DNA does an organism have? The intestinal bacterium Escherichia coli (E. coli) is an organism with one cell and has about 5 × 10⁶ letters per cell. The DNA contained in the cell is known as the genome. In contrast to the simpler E. coli, the genome of a human is about 3 × 10⁹ letters. Each human cell contains the same DNA.

Both RNA and proteins are made from instructions in the DNA, and new DNA molecules are made from copying existing DNA molecules. These processes are discussed next.

1.1.1 The Double Helix

The key feature of DNA that suggested the copying mechanism is the complementary basepairs; that is, the bases pair with A pairing T and G pairing C. This so-called pairing is by hydrogen bonds; more on that later. The idea is that a single word (or strand) of DNA (written in the 5’ to 3’ direction)

$5\text{'}\text{ACCTGAC3}\text{'}$

is paired to a complementary strand running in the opposite direction:

There are seven basepairs in this illustration. The A-T and G-C pairs are formed by hydrogen bonds, here indicated by a heavy bar. DNA usually occurs double stranded and its length is often measured by number of basepairs.

The three-dimensional structure is helical. In the next figure we show the letters or bases as attached to a string or backbone; note that the bars indicating the hydrogen bonds have been deleted. To properly view this figure, imagine a ribbon with edges corresponding to the backbones twisted into a helix.

1.2 The Central Dogma

DNA carries the genetic material–the information required by an organism to function. (There are exceptions in the case of certain viruses where the genetic material is RNA.) DNA is also the means by which organisms transfer genetic information to their descendants. In organisms with a nucleus (eukaryotes), DNA remains in the nucleus; whereas proteins are made in the cytoplasm outside of the nucleus. The intermediate molecule carrying the information out of the nucleus is RNA. The information flow in biology is summarized by the “central dogma,” put forward by Francis Crick in 1958:

The central dogma states that once ‘information’ has passed into protein it cannot get out again. The transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein, may be possible, but transfer from protein to protein, or from protein to nucleic acid, is impossible. Information means here the precise determination of sequence, either of bases in...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• 0 Introduction
• 1 Some Molecular Biology
• 2 Restriction Maps
• 3 Multiple Maps
• 4 Algorithms for DDP
• 5 Cloning and Clone Libraries
• 6 Physical Genome Maps: Oceans, Islands and Anchors
• 7 Sequence Assembly
• 8 Databases and Rapid Sequence Analysis
• 9 Dynamic Programming Alignment of Two Sequences
• 10 Multiple Sequence Alignment
• 11 Probability and Statistics for Sequence Alignment
• 12 Probability and Statistics for Sequence Patterns
• 13 RNA Secondary Structure
• 14 Trees and Sequences
• 15 Sources and Perspectives
• References
• I Problem Solutions and Hints
• II Mathematical Notation
• Algorithm Index
• Author Index
• Subject Index