Extending the integrate-and-fire model to account for metabolic dependencies

It is widely accepted that the brain, like any other physical system, is subjected to physical constraints that restrict its operation. The brain's metabolic demands are particularly critical for proper neuronal function, but the impact of these constraints continues to remain poorly understood. Detailed single-neuron models are recently integrating metabolic constraints, but these models' computational resources make it challenging to explore the dynamics of extended neural networks, which are governed by such constraints. Thus, there is a need for a simplified neuron model that incorporates metabolic activity and allows us to explore the dynamics of neural networks. This work introduces an energy-dependent leaky integrate-and-fire (EDLIF) neuronal model extension to account for the effects of metabolic constraints on the single-neuron behavior. This simple, energy-dependent model could describe the relationship between the average firing rate and the Adenosine triphosphate (ATP) cost as well as replicate a neuron's behavior under a clinical setting such as amyotrophic lateral sclerosis (ALS). Additionally, EDLIF model showed better performance in predicting real spike trains - in the sense of spike coincidence measure - than the classical leaky integrate-and-fire (LIF) model. The simplicity of the energy-dependent model presented here makes it computationally efficient and, thus, suitable for studying the dynamics of large neural networks.