Theories, Models, and Equations in Systems Biology

Kenneth F. Schaffner

This contributions begins with a review of some claims made by biologists such as Waddington and von Bertalanffy, and others, that biology should seek general theories similar to those found in physics, for example in Newton's theory of gravitation and its elaboration in the Principia, some treatments of Maxwell's electromagnetic theory, or thermodynamics, quantum mechanics, and relativity theories. I disagree with that view, and describe an alternative framework for biological theories as collections of prototypical interlevel models that can be extrapolated by analogy to different organisms. I look at two cases in particular: the development of the Hodgkin-Huxley giant squid model for action potentials, and at a more recent model of Ferr_e and Lockery for worm (C. elegans) chemotaxis. The Hodgkin-Huxley strategy uses equations, but in specialized ways involving heuristic approximations, to build their model. In the worm example, model building proceeds from the organismal level down. It starts from a model of the nematode body which captures the head and neck turning movements (head-sweep), then seeks a neural implementation of the head-sweep mechanism, arguing that the neural model is well-based on the worm's neurophysiology. Though both approaches use the tools of biophysics and other theories of physics, the manner of their implementation is quite different from physics, but can be generalized as an approach for systems biology.