This textbook introduces bioinformatics to students in mathematics with no biology background assumed and it provides solid mathematical tools for biology students along with an understanding of how to implement them in bioinformatics problems. In addition to the basics, the text offers new approaches to understanding biological sequences. The concise presentation distinguishes itself from others on the subject, discussing and providing principles that relate to current open problems in bioinformatics as well as considering a variety of models. The convex hull principle is highlighted, opening a new interdisciplinary research area at the intersection of biology, mathematics, and computer science. Prerequisites include first courses in linear algebra, probability and statistics, and mathematical analysis. Researchers in mathematics, biology, and math-biology, will also find aspects of this text useful.

This textbook is written based on the authors' research works that have been published in various journals along with the lecture notes used when teaching bioinformatics courses at the University of Illinois at Chicago and at Tsinghua University. The content may be divided into two parts. The first part includes three chapters, introducing some basic concepts. Chapter 1 provides biological background in molecular biology for mathematicians. Chapter 2 describes biological databases that are commonly used. Chapter 3 is concerned with alignment methods including global/local alignment, heuristic alignment, and multiple alignment. The second part consisting of five chapters, describes several bioinformatics principles using a rigorous mathematical formulation. Chapter 4 introduces the time-frequency spectral principle and its applications in bioinformatics. In Chapters 5 and 6, two strategies are used, the graphical representation and the natural vector method, to represent biological sequences, and conduct sequence comparison and phylogenetic analysis without alignment. Chapter 7 presents the convex hull principle and shows how it can be used to mathematically determine whether a certain amino acid sequence can be a protein. The last chapter summarizes additional mathematical ideas relating to sequence comparisons, such as new feature vectors and metrics. This part focuses on the governing principle in biology and provides plenty of alignment-free methods, which cannot be found in any other book.

Focuses on alignment-free methods in sequence comparison, which are neglected in many books on bioinformatics Introduces the method to form a practical genome/protein space and proposes the convex hull principle Based on the author's research works, bioinformatics from the view of a mathematician

Autorentext

Stephen Shing-Toung Yau (Life Fellow, IEEE) received the Ph.D. degree in mathematics from the State University of New York, Stony Brook, NY, USA, in 1976. He was a Member of the Institute of Advanced Study, Princeton, NJ, USA, from 1976 to 1977 and 1981 to 1982. He was a Benjamin Pierce Assistant Professor with Harvard University, Cambridge, MA, USA, from 1977 to 1980. He then joined the Department of Mathematics, Statistics and Computer Science (MSCS), University of Illinois at Chicago (UIC), Chicago, IL, USA, and served for more than 30 years. From 2005 to 2011, he was a Joint Professor with the Department of Electrical and Computer Engineering, MSCS, UIC. After retiring in 2011, he joined the Department of Mathematical Sciences at Tsinghua University in Beijing, China, where he served for over 10 years. In 2022, he became a research fellow at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) in Beijing, China, to begin his new research. His research interests include nonlinear filtering, bioinformatics, complex algebraic geometry, Cauchy-Riemann geometry, and singularities theory. Dr. Yau has been the Managing Editor and Founder of Journal of Algebraic Geometry since 1991 and the Editor-in-Chief and Founder of Communications in Information and Systems since 2000. He was the General Chairman of the 1995 IEEE International Conference on Control and Information. He received the Sloan Fellowship in 1980, the Guggenheim Fellowship in 2000, and the American Mathematical Society Fellow Award in 2013. In 2005, he was entitled the UIC Distinguished Professor. In 2019, He won the Chern Prize of Lifetime Achievement in Mathematics. Xiuqiong Chen received the B.S. degree in the School of Mathematical Sciences, Beihang University, Beijing, China, in 2014, and the Ph.D. degree in applied mathematics from the Department of Mathematical Sciences, Tsinghua University, Beijing, China in 2019. After her graduation, she was a Postdoctoral Scholar with Yau Mathematical Sciences Center, Tsinghua University, Beijing, China, from 2019 to 2021. She joined in Renmin University of China, Beijing, China, since 2021. She is currently an Assistant Professor with School of Mathematics, Renmin University of China. Her research interests include nonlinear filtering and deep learning. Xiaopei Jiao received his Bachelor's degree from Shanghai Jiao Tong University in 2017 and completed his Ph.D. from the Department of Mathematics at Tsinghua University in 2022. From 2022 to 2024, he worked as a postdoctoral researcher at the Beijing Institute of Mathematical Science and Application. He is currently employed at the University of Twente in the Netherlands as postdoctoral researcher. His research focuses on nonlinear filtering, Lie estimation algebra, physics-informed deep learning, and bioinformatics. Jiayi Kang received the B.S. degree from the college of mathematics, Sichuan University, Chengdu, China, in 2019 and Ph.D. degree from Department of Mathematical Sciences at Tsinghua University, China in 2024. He is currently an assistant professor at the Beijing Institute of Mathematical Sciences and Applications in Beijing, China. Zeju Sun received the B.S. degree from Department of Mathematical Sciences, Tsinghua University, Beijing, China, in 2020. He is currently pursuing the Ph.D. degree in mathematics with the department of Mathematical Sciences, Tsinghua University, Beijing, China. Yangtianze Tao received the B.S degree in College of Mathematics, Sichuan University, Sichuan, China in 2019. Now he is pursuing Ph.D. degree with Department of Mathematical Sciences, Tsinghua University, Beijing, China, under the supervision of Prof. Stephen Yau in the field of applied mathematics. His research interests include deep learning, machine learning and nonlinear filtering.

Inhalt

Preface.- 1 Biological Overview.- 2 Bioinformatics Databases.- 3 Sequence Alignment.- 4 The Time-Frequency Spectral Analysis and Applications in Bioinformatics.- 5 Graphical Representation of Sequences and Its Application.- 6 The Development and Applications of the Natural Vector Method.- 7 Convex Hull Principle and Distinguishing Proteins from Arbitrary Amino Acid Sequences.- 8 New Features or Metric on Sequence Comparison.- References.