Theories , Models , and Equations in Systems Biology

This paper 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. In these domains, broadly applicable differential equations system states and potential trajectories are found. I disagree with that view, and describe an alternative framework for biological theories as collections of prototypical interlevel largely qualitative causal models that can be extrapolated by analogy to different organisms. However, in the rare area of intersection between prototypical models which are largely qualitative and the equation-based models of physics, there are some significant accomplishments that may point the way toward important systems approaches in biology. I look at two cases in particular in this intersection area: the development of the Hodgkin-Huxley giant squid model for action potentials, and at a more recent model of Ferrée and Lockery for worm (C. elegans) chemotaxis. The Hodgkin-Huxley strategy uses equations, but in specialized ways involving empirical curve-fitting and 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 using tools from compartment theory. The proponents of this model argue that their neural model is well-based on the worm’s neurophysiology but only weakly, at this point, on the organism’s neuroanatomy. Though both approaches use some of the tools of biophysics and other mathematically sophisticated theories of physics, the manner of their implementation is quite different from physics, but may be generalizable as an approach for systems biology.