Design constraints for biological systems that achieve adaptation and disturbance rejection

Many processes in natural biological systems, such as chemotaxis in bacteria and osmoregulation in yeast, rely on control architectures fundamentally equivalent to commonly used motifs from electrical and control engineering. However, difficulties arise when designing and implementing these architectures in a biological context due to uncertainties inherent in the behaviour of biological systems, and physical limitations of the available parts. In this paper we discuss recent developments in the study of biological control systems, which are increasingly necessary for realisation of complex synthetic biological constructs, focusing on methods for their design and implementation. We establish a range of desirable properties that ease implementation of biological constructs, and apply classical control theory to derive a set of constraints to aid the design of systems that achieve adaptation or disturbance rejection. We demonstrate how these constraints can be used in practice, first deriving the necessary structure for a linear system that achieves adaptation, and then embedding this in a non-linear model of biological relevance that could be built in the laboratory