This book grew out of a course for graduate students in the first year of the MSc bioinformatics program that the author teaches every year at Saarland University. Also included is some material from a special lecture on cell simulations. The book is designed as a textbook, placing emphasis on transmitting the main ideas of a problem, outlining algorithmic strategies for solving these, and describing possible complications or connections to other parts of the book. The main challenge during the writing of the book was the concentration on conceptual points that may be of general educative value rather than including the latest research results of this fascinating fast‐moving field. It is considered more important for a textbook to give a cohesive picture rather than mentioning all possible drawbacks and special cases where particular general guidelines may not apply. We apologize to those whose work could not be mentioned because of space constraints.

The intended audience includes students of bioinformatics and from life science disciplines. Consequently, some basic knowledge in molecular biology is taken for granted. The language used is not very formal. Previous knowledge of computer science is not required, but a certain adeptness in basic mathematics is necessary. The book introduces all of the mathematical concepts needed to understand the material covered. In particular, Chapter 2 introduces mathematical graphs and algorithms on graphs used in classifying protein–protein interaction networks. Chapter 6 introduces linear and convex algebra typically being used in the description of metabolic networks. Chapter 7 discusses ordinary and stochastic differential equations used in the kinetic modeling of signal transduction pathways. Chapter 8 introduces the method of Fourier transformation for protein–protein docking and pattern matching. Also introduced are Bayesian networks in Chapter 4 as a way to judge the reliability of protein–protein interactions and inference techniques to model gene regulatory networks. We note, however, that the emphasis of this book is placed on discrete mathematics rather than on statistical methods. Not included yet are classical network flow algorithms such as Menger's theorem or the max‐flow min‐cut theorem as they are currently rarely used in cellular modeling. The book focuses on proteins and the genes coding for them, as well as on metabolites. Less room is given to DNA, RNA, or lipid membranes that would, of course, also deserve a great deal of attention. The main reason for this was to provide a homogenous background for discussing algorithmic concepts.

The author is very grateful to Dr. Tihamér Geyer who coordinated the assignments for the lectures for valuable comments on the manuscript and for many solved examples and problems for this book. The following coworkers from Saarbrücken and elsewhere have provided valuable suggestions on different portions of the text: Kerstin Kunz, Jan Christoph, and Florian Lauck. I thank Dr. Hawoong Jeong, Dr. Julio Collado‐Vides, Dr. Agustino Martínez‐Antonio, Dr. Ruth Sperling, Dr. James R. Williamson, Dr. Joanna Trylska, Dr. Claude Antony, and Dr. Nicholas Luscombe for sending me high‐resolution versions of their graphics. I thank Dr. Andreas Sendtko and the publishing staff at Wiley‐VCH for their generous support of this book project, for their seemingly endless patience during the revision stage, and for excellent typesetting.

I also thank the Center of Theoretical Biophysics at the University of California, San Diego, for their hospitality during a sabbatical visit in summer 2007 that finally allowed to complete this work. Finally, this book would not have been possible without the support and patience of my wife Regina and our two daughters.

March 2008

About 10 years after the publication of the first edition, I finally managed to prepare this expanded second edition of this book. Its main spirit remained the same: it is designed as a textbook, placing emphasis on transmitting the main ideas of a problem, outlining algorithmic strategies for solving these, and describing possible complications or connections to other parts of the book. Because of the feedback from colleagues, I have reordered the content, starting now in Chapter 2 with an introduction into the structures of protein–protein complexes before we enter into the world of protein interaction networks. I refrain from listing all the rearrangements here. Usually, I tried to keep subsections intact and simply shifted them around. A few sections were removed from the text because I now felt that they were too specialized. About 50% of new content has been added. In terms of mathematical methods, much more room is now given to statistical methods. In terms of biology, several new chapters now address protein–DNA interactions, epigenetic modifications, and microRNAs. Still not covered are biophysical topics related to intracellular transport, cytoskeletal dynamics, and processes taking place at and across biological membranes. Maybe, there will be a need for a third edition eventually?

In addition to those who contributed to the first edition, the author is very grateful to Thorsten Will and Maryam Nazarieh for solved examples and problems for this book. The following coworkers from Saarbrücken and elsewhere have provided valuable suggestions on different portions of the text: Mohamed Hamed Fahmy, Dania Humaidan, Olga Kalinina, Heiko Rieger, and Thorsten Will. I thank my group members of the past years with whom I had the privilege to work on exciting research projects related to the content of this book and I thank our secretary Kerstin Gronow‐Pudelek for technical assistance.