Non linear dynamics in quantitative biology

A.Y. 2021/2022
Overall hours
BIO/11 BIO/18 BIO/19
Learning objectives
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.
Course syllabus and organization

Single session

Lesson period
First semester
Teaching will be online, if needed, depending on the rules.
Course syllabus
· Models are wrong. (frontal)
· Translating systems of interactions (regulatory, enzymatic, reproductive, predatory ) into quantitative models (frontal || practice).
· From gene regulatory circuits to signaling cascades and small metabolic systems - the many ways for obtaining quantitative descriptions for a biological system. (Group practical activity and student-to-student teaching).
· Fitting the elephant. From general to specific models: using experimental data to parameterize models; quantifying the importance of parameters with sensitivity analysis. (practice with theory)
· The behavior of systems after infinitesimal perturbations in the variables: stability analysis, relaxation time, oscillations - in one word the Jacobian. (practice with theory)
· What's Metabolic Control Theory? The summation theorems, flux and concentration control coefficients, elasticities. (frontal + practice)
· Periodic systems: playing with the cell cycle. (Group practical activity and student-to-student teaching)
· Do I really need parameters? Exploring parameter space and the Structural Kinetic Modelling approach. (practice)
· Roleplay: (
· Forgetting about mechanistic equations: Flux Balance Analysis and the optimization of metabolic systems (To be defined)
· Open discussion. Models and their characteristics in an evolutionary perspective.
Prerequisites for admission
Teaching methods
The teacher will tentatively exploit the following types of lesson, which, will depend on the students he is working with. In the syllabus I propose a plausible plan, which is however to be considered as a draft and dynamical proposal.
Frontal: these are classical lessons with the aid of slides or the blackboard depending on the needs. Students are stimulated to intervene by questions / small problem solving / hypothesis formulation.
Practice with theory: these are lessons with theory concepts that I will try to highlight by means of workable examples at the computer; as a simple example, how the steady state condition Nv=0 looks like? Is it true (as Metabolic Control Theory states) that the control over a certain reaction is shared by all other enzymes, in different proportions?
Practice: a practical lesson at the computer, generally following a theory part to stress specific concepts and provide technical details on how to access and perform some calculation.
Group practical activity: students are split in groups and let to work on different examples designed to focus on the subject of the lesson. The teacher is here available for technical help and suggestions. These can be problems that the students have to solve by collaborating and applying concepts and technical abilities developed insofar. For instance, given experimental data, identify the parameters of the system and perform sensitivity analysis to...
Student-to-student teaching: when working in groups, students will work different aspects of a model or on the same aspect on slightly different models, such that the students might encounter varying difficulties that should be solved by collective effort. Next, each group will introduce the work done to the students from other groups. A small report might be asked on another group's work.
Open discussion: The lesson is anticipated by some bibliographical suggestions to the students and therefore requires some study time ahead. This is a discussion where the teacher briefly introduces an idea and then lets the students openly discuss about it.
Teaching Resources
Theory is treated in the book Nonlinear dynamics and chaos by Steven Strogatz ISBN 13: 978-0-8133-4910-7 (pbk); additionally, the topic will be based on available papers that will be provided to the student in time to allow a reading before the lesson.
Assessment methods and Criteria
There will be no examination at the end of the course* and students will get a score based on their activities throughout the course (continuous assessment). I will evaluate both your performances in terms of both technical and theoretical level (knowledge and technical skills), your ability to work in group (collaborative skill), to communicate your knowledge to others (communicative skill) and last but not least, your ability to provide constructive criticisms to the work of other students (reviewer skill).
BIO/11 - MOLECULAR BIOLOGY - University credits: 0
BIO/18 - GENETICS - University credits: 0
BIO/19 - MICROBIOLOGY - University credits: 0
Practicals: 32 hours
Lessons: 32 hours
Professor: Brilli Matteo