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This cybertextbook is needed by advanced undergraduate and graduate students and professionals in the biomedical sciences or in biomedical engineering who want or need to use modern computer modeling approaches to test theories against experimental data. The cybertextbook is focussed on practical application; it is a handbook, a guidebook, and a map for the process of formulating and testing biological models. The reader will learn a step-by-step method, applicable to a wide range of biological problems. The aim is to add useful and powerful tools to the reader's repertoire of scientific skills, and to make the reader self-sufficient in the use of these tools.

I am writing for biologists. This book represents an approach to systems biology that emerges from more than 40 years at the interface between experimental and computational biology. It is not intended to convey the "state of the art," nor is it a collection of standard practices. I agree with the unnamed editor who, in a 2010 Nature opinion piece, asserted that a textbook is "One person's view of a field, accumulated through personal experience, years of research, and face-to-face interaction with students." This is the ideal I aim to reach.

Systems biology has its roots in many disciplines. I am a cardiovascular cell physiologist, but I also have deep roots in electrical engineering, biomedical engineering, and molecular cell biology. Other phrases might be used to describe the arena in which this book does battle. You could describe it as computational cell biology, or computer modeling, or kinetics, or biological control systems. In talks and lectures and discussions with students I have used all these phrases to describe what we do. But each of these phrases means different things to different scientists. Consequently, I need to say more explicitly what this book is about.

Let me attempt a description from the perspective of a prospective reader. This is a book about biology from a systems perspective; the book could be titled Analysis of Complex Biological Systems or Practical Kinetic Modeling of Biological Systems or Integrative Bioinformatics. If you are an experimental biologist working on a system you feel is complex, this book may be for you. For my purposes, complexity is defined by how many variables you want to understand - that is, how many things are changing with time in the biological system you are studying. If that number is greater than 10, I am writing for you.

Scientists are always taught the virtues of the controlled experiment - an experiment in which only one thing is changed so that a rational comparison can be made between the "control" and the "experimental" results. This is the foundation of the reductionist paradigm and underlies most of scientific hypothesis testing. But reductionism has its limits.

If successful, 21st century biomedical science will make the transition from reductionism to synthesis or integration. This is not because the end of reductionist experimentation is in sight. It is fundamentally because the goal of publically funded scientific research is improvement of the human condition. An assumption of this text is that synthesis and integration can only be achieved if we confront complexity on its own terms. In other words, biomedical scientists whose goals are synthetic of integrative must have tools to deal with complexity. The human brain is palpably incapable of predicting the behavior of any interconnected system that meets my simple complexity criterion. Most of us cannot predict the behavior of a system of even five such variables, let alone ten.

In the future there may be an entirely new science of complexity whose form I cannot imagine, but I think it is reasonable to assume that any such science will be mathematical and computational. Mathematics and computation are the right tools for complex problems. The more complex your problem, the more this is true. But scientific tools only become widely useful when they are accessible to a large community. My aim is to make mathematical and computational modeling accessible to all biomedical scientists.

Chapter 1