The last years have witnessed a transition of the biological sciences from a qualitative to a quantitative (hard) science. However, this transition can only take place if biologists become familiar with the mathematical instruments that are the basis for studying the systems quantitatively. In this course, we will discuss several approaches to the modelling of biological systems, giving particular attention to regulatory circuits (transcriptional or sRNA-dependent and their integration) and metabolic systems with a discussion of how these models can be exploited to rationalize the process of metabolic engineering.

To achieve this task, we will present a few fundamental concepts of the field to then show how complicate dynamical behaviours can originate from relatively simple circuits thanks to the non-linearity and high interconnectedness that is intrinsic of biological systems.

We will also show how it is possible to provide a detailed characterisation of these behaviours through mathematics tools. The course will integrate theory and practical lessons, the latter using a software developed to provide help to modellers, called Copasi, in addition to the generic platform R.

During the course we will also introduce related concepts to show how the structure of the network onto which a process takes place can have huge effects on the dynamics of a system, a concept which is particularly useful when studying epidemic spreading that is particularly important in these days. Expected learning outcomes After this course, the student will be able to:

• Use biological information about a cellular system or population to build a workable mathematical model;
• Use experimental data of different kinds to estimate the parameters of the models under analysis;
• Reasoning critically about the possible assumptions at the basis of each model; -Be able to communicate their results by using a rigorous terminology, which is at the basis of providing a fully understandable message to the audience.