Control-theoretic methods for biological networks

Feedback is both a pillar of control theory and a pervasive principle of nature. For this reason, control-theoretic methods are powerful to analyse the dynamic behaviour of biological systems and mathematically explain their properties, as well as to engineer biological systems so that they perform a specific task by design. This paper illustrates the relevance of control-theoretic methods for biological systems. The first part gives an overview of biological control and of the versatile ways in which cells use feedback. By employing control-theoretic methods, the complexity of interlaced feedback loops in the cell can be revealed and explained, and layered feedback loops can be designed in the cell to induce the desired behaviours, such as oscillations, multi-stability and activity regulation. The second part is mainly devoted to modelling uncertainty in biology and understanding the robustness of biological phenomena due to their inherent structure. Important control-theoretic tools used in systems biology are surveyed. The third part is focused on tools for model discrimination in systems biology. A deeper understanding of molecular pathways and feedback loops, as well as qualitative information on biological networks, can be achieved by studying the 'dynamic response phenotypes' that appear in temporal responses. Several applications to the analysis of biological systems are showcased.