F = m a of Biology?

I will describe my participation over the past few years in an effort to find fundamental mathematical laws in biology.  I will discuss a theory for understanding the emergence of multi-scale, hierarchical structure in biology.  I will describe how modular structure in proteins, genetics, and biological networks may arise and how it can be understood.  I will show the implications of the theory for engineering design, and I will discuss additional examples of structure formation in ecological food networks, developmental pathways, physiology, and social networks.  I will then turn to theories of the immune system and describe a theory of the immune response to vaccines.  I will illustrate this theory by application to design of the annual influenza vaccine.  I will use this theory to explain limitations in the vaccine for dengue fever and to suggest a transport-inspired amelioration of these limitations.  I will conclude with a discussion of the immune system in bacteria.