Excitability paper reproduction in Poincare

[olistarosta]

Earlier this year, Yael Lebel and Uri Alon published Excitability as a design principle in the immune system (Sci. Adv. 12, eaeb0921 (2026), DOI: 10.1126/sciadv.aeb0921), exploring how excitable dynamical systems can model the immune system. We liked the paper and found it included exactly the kind of simulation and analysis that would benefit from Poincare, so we re-implemented part of the simulations using our package.

Among other things, Lebel and Alon identified a family of excitable circuits that model cell-cell interactions and analyzed the sensitivity of various metrics to the model's parameters. With some help from the authors, we were able to reproduce their results, which you can find uploaded in a tutorial-style notebook.

Our implementation takes advantage of Poincare's built-in analysis tools for the required parameter sweeps, keeping model definition separate from simulation and allowing for the extraction of symbolic equations directly from the system. To learn more about Poincare and its capabilities see its documentation on dyscolab's page.

Sensitivity of response pulse amplitude with respect to different parameters, calculated with Poincare.