Models in Mathematical Biology: A Feedback Perspective II

University Of Florida, Gainesville FL

Investigators

Abstract

In this golden era of research in biological systems, there is an increasing need to make sense of the overwhelming amount of available data from lab experiments and clinical trials. This new knowledge will not substantially impact society unless it is organized and interpreted correctly. A crucial step in this process is the development of theories that explain why the data are what they are. This is where the current proposal aims at making a contribution. Many biological systems are extremely complex, especially those in molecular cell biology. The inner workings of single cell hold many mysteries, even today. Why does a cell become cancerous? How and why does it move? Why can cell A be infected by a virus, while cell B cannot? The answer to these questions hinges upon the understanding of the dynamics of the chemical networks inside the cell. We have all seen graphical representations of these networks consisting of thousands of nodes and arrows. It is therefore not surprising that to go a step further by inquiring about the dynamics, and not just the structure of these systems, is a very challenging problem. An idea that comes naturally is to break the networks into smaller parts, and study these in isolation. Later we can then put the pieces back together to understand the overall system. It often happens that the isolated subsystems have particular properties. One such property is monotonicity, and this proposal explores the consequences for the full network whenever it consists of monotone subsystems. The current state of the art in this area is geared towards showing global stability. This proposal aims at broadening this spectrum by focusing on results that predict more complicated behavior such as bistability or the existence of periodic solutions. A second component of this proposal is the design of feedback control laws for bioreactors containing several competing species. An important application area of this research is the commercial production of growth factor. In this case, the reactor contains species with DNA containing a plasmid that codes for the production of growth factor. Upon cell division however, this plasmid can be lost, leading to a wildlife competitor that is not burdened by the production of growth factor, yet consumes nutrient for growth. It is clear that controlling such reactors is an important economical problem. The design of feedback control laws in this proposal could be helpful in this context.