An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons

Full-scale morphologically 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 work, we propose an 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 allowed (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.