Co-Design of Resource Limited Genetic Networks Tuning System Parameters to Satisfy Specifications

Abstract

Modular composition is a very powerful and widely used tool in engineering disciplines, as it aids in maintaining the system complexity tractable. Its main idea is that parts of the systems can be encapsulated into black box models characterized only by its input to output behavior, which eliminates the need to consider the complex dynamics inside the black box. Moreover, this process can be done iteratively, allowing the design of highly complex systems, such as computer chips. But this powerful tool is not always available, like in synthetic biology, where engineered systems in cells have very complex and intricate interconnections between subsystems, which makes encapsulating parts of theses systems a very challenging endeavor. There are many reasons for this failure in modularity in biological systems, such as load effects (retroactivity), unknown interactions and resource competition, which is our focus for this work. Recent efforts to achieve modular design in systems with resource competition, have focused in adding additional machinery to the cell to either try to isolate the subsystems or control the availability of the shared resource. In this work we explore a co-design approach, where instead of adding additional machinery to the cell, we aim to tune some systems parameters to satisfy some specification. To this end we provide conditions on the systems parameters for a network of subsystems to meet a given specification, which are derived using mathematical logic and ideas on how to tackle similar problems. With this, this work lays the foundations for further development of co-design techniques for genetic networks with production and/or degradation resources, where one may be able to mitigate the effects of one type of resource sharing by tuning the other.