Über die Autorin bzw. den Autor

Matthew He, PhD, is Full Professor and Director of the Division of Math, Science, and Technology of Nova Southeastern University, Florida. He is Full Professor and Grand PhD from the World Information Distributed University, Belgium, since 2004. Dr. He has published more than 100 research papers in mathematics, computer science, information theory, and bioinformatics, and is an editor of both International Journal of Biological Systems and International Journal of Cognitive Informatics and Natural Intelligence.

Sergey Petoukhov, PhD, is a chief scientist of the Department of Biomechanics, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, as well as Full Professor and Grand PhD from the World Information Distributed University. He has published more than 150 research papers in biomechanics, bioinformatics, mathematical and theoretical biology, the theory of symmetries and its applications, and mathematics.

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Mathematical methods that illuminate fundamental problems related to the genetic code and bioinformatics

Mathematics of Bioinformatics: Theory, Practice, and Applications provides a comprehensive blueprint for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. It offers valuable knowledge about mathematical tools, phenomenological results, and interdisciplinary connections in the fields of molecular genetics, bioinformatics, and informatics.

Each chapter is divided into sections based on bioinformatics topics and related mathematical theory and methods. Each topic is comprised of an introduction to the biological problems in bioinformatics; a presentation of topics in mathematical theory and methods relevant to the problems; and an integrative overview that draws the connections and interfaces between the problems, theory, methods, and applications. This practical resource:

• Covers genetic codes, sequences, structures, functions, biological networks/systems, and interfaces with mathematics, making connections between mathematics and bioinformatics for the bioinformatics specialist
• Provides integrative models for potential simulations, modeling, and implementation utilizing algorithms and analysis for the computer scientist
• Details recent research covering other branches of mathematics such as linear algebra, topology, differential geometry, fractals, and chaos theory that have found useful applications in bioinformatics
• Emphasizes applications of mathematics in bioinformatics while eschewing mathematical proofs and deep theories

Mathematics of Bioinformatics is intended for scientists, researchers, and upper-level undergraduate and graduate students in bioinformatics, mathematics, computer informatics, theoretical biology, mathematical biology, and biotechnology who seek information on the possibilities and challenges of interface between mathematics and bioinformatics. Readers with a foundation in calculus can also adapt to the mathematical topics introduced throughout.

Aus dem Klappentext

Mathematical methods that illuminate fundamental problems related to the genetic code and bioinformatics

Mathematics of Bioinformatics: Theory, Practice, and Applications provides a comprehensive blueprint for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. It offers valuable knowledge about mathematical tools, phenomenological results, and interdisciplinary connections in the fields of molecular genetics, bioinformatics, and informatics.

Each chapter is divided into sections based on bioinformatics topics and related mathematical theory and methods. Each topic is comprised of an introduction to the biological problems in bioinformatics; a presentation of topics in mathematical theory and methods relevant to the problems; and an integrative overview that draws the connections and interfaces between the problems, theory, methods, and applications. This practical resource:

• Covers genetic codes, sequences, structures, functions, biological networks/systems, and interfaces with mathematics, making connections between mathematics and bioinformatics for the bioinformatics specialist
• Provides integrative models for potential simulations, modeling, and implementation utilizing algorithms and analysis for the computer scientist
• Details recent research covering other branches of mathematics such as linear algebra, topology, differential geometry, fractals, and chaos theory that have found useful applications in bioinformatics
• Emphasizes applications of mathematics in bioinformatics while eschewing mathematical proofs and deep theories

Mathematics of Bioinformatics is intended for scientists, researchers, and upper-level undergraduate and graduate students in bioinformatics, mathematics, computer informatics, theoretical biology, mathematical biology, and biotechnology who seek information on the possibilities and challenges of interface between mathematics and bioinformatics. Readers with a foundation in calculus can also adapt to the mathematical topics introduced throughout.

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Mathematics of Bioinformatics

John Wiley & Sons

Chapter One

Traditionally, the study of biology is from morphology to cytology and then to the atomic and molecular level, from physiology to microscopic regulation, and from phenotype to genotype. The recent development of bioinformatics begins with research on genes and moves to the molecular sequence, then to molecular conformation, from structure to function, from systems biology to network biology, and further investigates the interactions and relationships among, genes, proteins, and structures. This new reverse paradigm sets a theoretical starting point for a biological investigation. It sets a new line of investigation with a unifying principle and uses mathematical tools extensively to clarify the ever-changing phenomena of life quantitatively and analytically.

It is well known that there is more to life than the genomic blueprint of each organism. Life functions within the natural laws that we know and those that we do not know. Life is founded on mathematical patterns of the physical world. Genetics exploits and organizes these patterns. Mathematical regularities are exploited by the organic world at every level of form, structure, pattern, behavior, interaction, and evolution. Essentially all knowledge is intrinsically unified and relies on a small number of natural laws. Mathematics helps us understand how monomers become polymers necessary for the assembly of cells. Mathematics can be used to understand life from the molecular to the biosphere levels, including the origin and evolution of organisms, the nature of genomic blueprints, and the universal genetic code as well as ecological relationships.

Mathematics and biological data have a synergistic relationship. Biological information creates interesting problems, mathematical theory and methods provide models for understanding them, and biology validates the mathematical models. A model is a representation of a real system. Real systems are too complicated, and observation may change the real system. A good system model should be simple, yet powerful enough to capture the behavior of the real system. Models are especially useful in bioinformatics. In this chapter we provide an overview of bioinformatics history, genetic code and mathematics, background mathematics for bioinformatics, and the big picture of bioinformatics–informatics.

1.1 INTRODUCTION

Mendel's Genetic Experiments and Laws of Heredity The discovery of genetic inheritance by Gregor Mendel back in 1865 was considered as the start of bioinformatics history. He did experiments on the cross-fertilization of different colors of the same species. Mendel's genetic experiments with pea plants took him eight years (1856–1863). During this time, Mendel grew over 10,000 pea plants, keeping track of progeny number and type. He recorded the data carefully and performed mathematical analysis of the data. Mendel illustrated that the process of inheritance of traits could be explained more easily if it was controlled by factors passed down from generation to generation. He concluded that genes come in pairs. Genes are inherited as distinct units, one from each parent. He also recorded the segregation of parental genes and their appearance in the offspring as dominant or recessive traits. He published his results in 1865. He recognized the mathematical patterns of inheritance from one generation to the next. Mendel's laws of heredity are usually stated as follows:

• The law of segregation. A gene pair defines each inherited trait. Parental genes are randomly separated by the sex cells, so that sex cells contain only one gene of the pair. Offspring therefore inherit one genetic allele from each parent. • The law of independent assortment. Genes for different traits are sorted from one another in such a way that the inheritance of one trait is not dependent on the inheritance of another. • The law of dominance. An organism with alternate forms of a gene will express the form that is dominant.

In 1900, Mendel's work was rediscovered independently by DeVries, Correns, and Tschermak, each of whom confirmed Mendel's discoveries. Mendel's own method of research is based on the identification of significant variables, isolating their effects, measuring these meticulously, and eventually subjecting the resulting data to mathematical analysis. Thus, his work is connected directly to contemporary theories of mathematics, statistics, and physics.

Origin of Species Charles Darwin published On the Origin of Species by Means of Natural Selection (Darwin, 1859) or "The Preservation of Favored Races in the Struggle for Life." His key work was that evolution occurs through the selection of inheritance and involves transmissible rather than acquired characteristics between individual members of a species. Darwin's landmark theory did not specify the means by which characteristics are inherited. The mechanism of heredity had not been determined at that time.

First Genetic Map In 1910, after the rediscovery of Mendel's work, Thomas Hunt Morgan at Columbia University carried out crossing experiments with the fruit fly (Drosophila melanogaster). He proved that the genes responsible for the appearance of a specific phenotype were located on chromosomes. He also found that genes on the same chromosome do not always assort independently. Furthermore, he suggested that the strength of linkage between genes depended on the distance between them on the chromosome. That is, the closer two genes lie to each other on a chromosome, the greater the chance that they will be inherited together. Similarly, the farther away they are from each other, the greater the chance of that they will be separated in the process of crossing over. The genes are separated when a crossover takes place in the distance between the two genes during cell division. Morgan's experiments also lead to Drosophila's unusual position as, to this day, one of the best studied organisms and most useful tools in genetic research. In 1911, Alfred Sturtevant, then an undergraduate researcher in the laboratory of Thomas Hunt Morgan, mapped the locations of the fruit fly genes, creating the first genetic map ever made.

Transposable Genetic Elements In 1944, Barbara McClintock discovered that genes can move on a chromosome and can jump from one chromosome to another. She studied the inheritance of color and pigment distribution in corn kernels at the Carnegie Institution Department of Genetics in Cold Spring Harbor, New York. At age 81 she was awarded a Nobel prize. It is believed that transposons may be linked to such genetic disorders as hemophilia, leukemia, and breast cancer; and transposons may have played a crucial role in evolution.

DNA Double Helix In 1953, James Watson and Francis Crick proposed a double-helix model of DNA. DNA is made of three basic components: a sugar, an acid, and an organic "base." The base was always one of the four nucleotides: adenine (A), cytosine (C), guanine (G), or thymine (T). These four different bases are categorized in two groups: purines (adenine and guanine) and pyrimidines (thymine and cytosine). In 1950, Erwin Chargaff found that the amounts of adenine (A) and thymine...