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.
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