Aivar Sootla (University of Oxford)

Title: Applications of Monotone Systems Theory to Synthetic Biology

Abstract: In this talk, we will discuss some mathematical problems arising in the fast developing field of synthetic biology. Synthetic biology is concerned with creating genetically modified bacteria for the production of useful chemical compounds (e.g., drugs, bio-degradable plastic, fuels etc), for detecting viruses, toxins or prohibited substances (e.g. in a biological sample, water supply), and even for new methods of drug delivery. Due to complexity and variability of bacterial systems modelling presents a serious challenge. Furthermore, quantitative data analysis is impeded by technological and physical constraints, therefore scientists often rely on qualitative analysis of their designs. From the modelling perspective, qualitative analysis is not always straightforward unless models have specific properties. We will argue that a class of models called monotone can offer effective tools for qualitative analysis of biological processes. Monotone systems often appear in biological modelling and possess a powerful property: a partial order in their trajectories. Partial order enables a number of stability results, which are crucial for simplified analysis and control of nonlinear systems. Equipped with the Koopman operator framework, we present methods for analysis and control of monotone systems, which are computationally efficient and can provide answers for a range of parameters.