Below are some of the topics I have taught as TA in biomedical engineering (Pompeu Fabra University, 2012, 2013). Courses of Mathematical Biomodeling, Evolutionary Algorithms and Cell and Tissue Engineering relating to multicellularity and complexity in evolution.
Additionally, I have been secondary PI for the Barcelona iGEM team 2016, performing an advisory role in the theoretical and wet-lab aspects of the project.
As part of outreach activities, I have shown multiple times our CSL lab in Barcelona to the general public during the PRBB open day. Also, brought a plant based exhibition to the ThinkTank museum in Birmingham targeted to children.
Network Percolation
As a primer of more complicated topologies, regular spatial lattices help undestand the phenomena of connectivity and information transfer, for instance in the case of the percolation threshold. This refers to the statistical property of two random nodes in a given graph being connected (i.e. that a path exists between them). By colouring a simple square lattice and destroying random connections we can readily observe the transition from a single connected network spanning almost all nodes to a fragmented system.
Excitable Media
Matter can display different degrees of reactivity and agency. In particular, living matter (but certainly not limited to it, as shown by the famous Belousov–Zhabotinsky reaction) is usually found far removed from equilibrium thermodynamics, allowing it to behave in interesting ways. Similarly to the previous example, cellular automata constitute a basic framework that, nonetheless, offers deep insights into the relation between simple rules, complex behaviors and emergent properties. Two key elements when modeling propagation phenomena in excitable media are the concept of neighborhood and the relaxation period (in which matter remains at rest even if it recieves a trigger for activation). To the left, some snapshots of a cellular automaton with different neighborhoods, update methods and oscillation periods.
Patterns and Scaling
Spatial regularities of biological entities can be striking, as they comprise a beatiful repertoire that has to be recreated through develoment in a tightly controlled and repeatable fashion. Some patterns seem to respond to very simple rules yet can generate a myriad of complex structures. Some pattern forming mechanisms yield scale-free structures such as fractals (characterized by self-similatiry independently of scale), while some display features at a dominant scale or wavelength like Turing Patterns.
Deterministic Chaos
Even in the absence of stochastic elements in the formulation of a given dynamical system, our ability to predict the future is hampered under some circumstances. This is clearly seen in the three-body problem, where motion can be irregular yet aperiodic, and where very small differences in the initial configuration of the system generate diverging solutions. A simple way to demonstrate the relevance of this feature in biology are logistic maps: an equation as simple as a logistic growth operating in a population with discrete timesteps (seasonal reproduction and non-overlaping generations) can generate deterministic chaotic dynamics.