Jérôme Coville (NRAE, Avignon)

Talk title & abstract: TBA

Florence Hubert (Aix-Marseille Université)

Talk title & abstract: TBA

Annalisa Iuorio (Parthenope University of Naples)

A new E-GLIF model for hippocampal CA1 pyramidal neurons and interneurons

Full-scalemorphologically and biophysically realistic model networks, aiming at modeling multiple brain areas, provide an invaluable tool to make significant scientific advances from in-silico experiments on cognitive functions to digital twin implementations. Due to the current technical limitations of supercomputer systems in terms of computational power and memory requirements, these networks must be implemented using (at least) simplified neurons. 

A class of models which achieve a reasonable compromise between accuracy and computational efficiency is given by generalized leaky integrate-and fire models complemented by suitable initial and update conditions. However, we found that these models cannot reproduce the complex and highly variable firing dynamics exhibited by neurons in several brain regions, such as the hippocampus. 

In this talk, we illustrate a novel adaptive generalized leaky integrate-and fire model for hippocampal CA1 neurons and interneurons, in which the nonlinear nature of the firing dynamics is successfully reproduced by linear ordinary differential equations equipped with nonlinear and more realistic initial and update conditions after each spike event, which strictly depends on the external stimulation current. A mathematical analysis of the equilibria stability as well as the monotonicity properties of the analytical solution for the membrane potential allows (i) to determine general constraints on model parameters, reducing the computational cost of an optimization procedure based on spike times in response to a set of constant currents injections; (ii) to identify additional constraints to quantitatively reproduce and predict the experimental traces from 85 neurons and interneurons in response to any stimulation protocol using constant and piecewise constant current injections. Finally, this approach allows to easily implement a procedure to create infinite copies of neurons with mathematically controlled firing properties, statistically indistinguishable from experiments, to better reproduce the full range and variability of the firing scenarios observed in a real network.

[1] A. Marasco, E. Spera, V. De Falco, A. Iuorio, C.A. Lupascu, S. Solinas, M. Migliore. An Adaptive GLIF model for hippocampal CA1 pyramidal neurons and interneurons. Bull. Math. Biol. 85, 109, 2023.

[2] A. Marasco, C. Tribuzi, A. Iuorio, M. Migliore. Mathematical generation of data-driven hippocampal CA1 pyramidal neurons and interneurons copies via A-GLIF models for large-scale networks covering the experimental variability range. Math. Biosci. 371, 109179, 2024.

King-Yeung (Adrian) Lam (Ohio State University)

Control formulation for a road-field population dynamics model

Berestycki, Roquejoffre, and Rossi introduced a reaction-diffusion system for populations that have a distinguished ‘road’ on which they move quickly but do not reproduce.  The goal is to understand invasion behavior (fronts).  This model has attracted enormous interest in the decade since it was introduced, with a nearly complete picture in the case of a straight road.  In this talk, I will discuss a joint work with Adrian Lam in which we provide an optimal control perspective on this problem.  This gives a natural interpretation of the front in terms of balancing speed on the road and growth in the field, and it lets us easily deduce that ‘bent’ line case, which was previously not well-understood, is a simple consequence of the straight line case and some elementary geometry. 

Cinzia Soresina (University of Trento)

Derivation of cross-diffusion models in population dynamics: dichotomy, time-scales, and fast-reaction

In population dynamics, cross-diffusion describes the influence of one species on the diffusion of another. A benchmark problem is the cross-diffusion SKT model, proposed in the context of competing species to account for stable inhomogeneous steady states exhibiting spatial segregation. Even though the reaction part does not present the activator-inhibitor structure, the cross-diffusion terms are the key ingredient for the appearance of spatial patterns [1]. From the modelling perspective, cross-diffusion terms naturally appear in the fast-reaction limit of a ``microscopic'' model (in terms of time scales) presenting only standard diffusion and fast-reaction terms, thus incorporating processes occurring on different time scales [4]. In this talk, recent applications of this approach will be presented, e.g., predator-prey [2] and mutualistic interactions, plant dynamics with autotoxicity effects [3], and epidemiology.

[1] Breden, M., Kuehn, C., Soresina, C. (2021). On the influence of cross-diffusion in pattern formation. Journal of Computational Dynamics 8(2):213--240.
https://doi.org/10.3934/jcd.2021010

[2] Desvillettes, L., Soresina, C. (2019) Non-triangular cross-diffusion systems with predator-prey reaction terms. Ricerche di Matematica 68(1):295--314.
https://doi.org/10.1007/s11587-018-0403-y

[3] Giannino, F., Iuorio, A., Soresina,  C. (in preparation). The effect of auto-toxicity in plant-growth dynamics: a cross-diffusion model.

[4] Kuehn, C., Soresina, C. (2020). Numerical continuation for a fast-reaction system and its cross-diffusion limit. SN Partial Differential Equations and Applications 1:7.
https://doi.org/10.1007/s42985-020-0008-7