Modeling Nanoscale Transport Systems

Mathematical formulation and physical models are the foundation of scientific understanding and technological advancement. Our ability to design experiments effectively is heavily dependent on our physical understanding of the system under investigation, and careful mathematical analysis is required in order to effectively progress from scientific concepts towards viable technologies. With increasing system complexity, the focus of mathematical formulation has shifted from simple, elegant models which rely on basic physical concepts to tailored, increasingly complex solutions using high-powered simulations and numerical solutions. While these methods may provide insights into specific systems, adapting these models to different systems is generally difficult, even when the systems under question operate according to the same physical laws. This is especially evident in nanobiotechnology, where the complexity of the systems studied has given rise to experiment-driven focus. Our aim is to focus on the mathematical modeling of transport processes in nanoscale systems, and to construct generalized, conceptual models for three model systems, which in turn could be applied to many biological and engineered systems. The three model systems we use - enzyme cascades, coupled molecular motors and self-assembling molecular shuttles provide a broad basis for generalized transport systems in nanoscale systems. These systems combine diffusive and active transport, as well as diverse assembly conditions and multi-scale systems with size scales spanning nano- to millimeter sizes and system complexity ranging from isolated two-component systems to multimolecular, highly-coupled systems. By applying and adapting these basic models to increasingly complex systems, we can both understand the physics behind nanoscale systems, as well as design these systems with increased robustness, scalability and repeatability.