Mathematical models are powerful tools for understanding biological systems, from molecular interactions to large-scale ecosystems. This course introduces key mathematical concepts through real-world biological applications, with an emphasis on qualitative understanding over technical details.
Each day consists of a lecture presenting core concepts and examples, followed by an interactive discussion where students engage with open discussion. Four topics are tentatively planned for four days, with a fifth day reserved as a buffer to allow for flexibility.
The course is designed for students in bioinformatics and assumes no background in mathematics – zero knowledge and infinite curiosity. Each topic is paired with a fundamental mathematical concept to provide a structured framework, helping students orient themselves between biological phenomena and their mathematical modeling.
Nicola Vassena is a postdoctoral researcher in the Bioinformatics Group at Leipzig University, where he studies the dynamics of metabolic networks. He previously completed his doctoral studies in nonlinear dynamics at the Free University of Berlin under the supervision of Bernold Fiedler. At the Interdisciplinary Center for Bioinformatics (IZBI) in Leipzig, he led a project on zero-eigenvalue bifurcations in chemical reaction networks. His current research focuses on identifying structural network conditions that give rise to oscillations and multistability in dynamical systems, with applications in biochemical, ecological, and epidemiological networks.
A general reference is the classic book Mathematical Biology by James D. Murray. Further more tailored references will be given in the lectures.
How can a deterministic system be unpredictable?
Abstract:
Many biological and ecological systems exhibit unexpected and irregular behaviors, even when governed by fully deterministic rules. This session introduces the concept of chaos, where small changes in initial conditions lead to drastically different outcomes. We explore fundamental ideas behind chaotic systems, such as the butterfly effect and strange attractors. We will also discuss the limits of computational predictability, a relevant perspective for bioinformatics and data-driven sciences.
Mathematical focus: Discrete models
Abstract:
Many biological processes, from metabolic networks to disease outbreaks, can be modeled using ordinary differential equations (ODEs). This session introduces some of the most famous ODE models in biology, including the Lotka-Volterra predator prey system, the SIR epidemic model, and reaction kinetics. We will also touch on the concept of bifurcations, where small parameter changes lead to sudden shifts in system behavior, with applications to tipping points in climate science and ecological systems.
Mathematical focus: Ordinary differential Equations
Abstract:
Biological systems are often best represented as networks of interacting elements, known as reaction (or interaction) networks. Reaction networks provide a versatile frame work that spans systems from biochemistry to ecology, epidemiology, and even economics. In connection with Topic 2, this session explores ODE systems arising from reaction networks and examines how the structure of the network alone constrains their possible dynamical behaviors. Examples will include Feinberg’s deficiency theory and current research advancements in metabolic networks. Emphasis will be placed on the formidable computational challenges involved in analyzing such systems.
Mathematical focus: Graph Theory
Abstract:
How did the leopard get its spots? How do embryonic cells self-organize into complex patterns? This session introduces reaction-diffusion systems and Turing’s instability, whose work on morphogenesis suggests that simple local interactions can give rise to complex global patterns. The key concept to be explored is that identical, individually stable systems can become destabilized by interactions that, in themselves, would appear stabilizing. To provide an accessible mathematical model, we will use a linear algebra metaphor that illustrates the interaction of identical couples of star-crossed lovers.
Mathematical Focus: Reaction-diffusion systems (PDEs)
Location: Onsite - Armenian Bioinformatics Institute, Ezras Hasratyan 7, Yerevan, Armenia
Start date: April 21
End date: April 25
Schedule: Every day. Time to be finalized according to the voting in the registration file.
FREE
Who can register for this course? - Anyone!
Those who wish to enroll must complete the application form. The registration deadline is April 14 at 11:59 PM Yerevan time.
Should you have any questions, feel free to contact us via the following means:
