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

Abstract

It is widely accepted that the brain, like any other physical system, is subjected to physical constraints restricting its operation. The brains metabolic demands are particularly critical for proper neuronal function, but the impact of these constraints is still poorly understood. Detailed single-neuron models are recently integrating metabolic constraints, but the computational resources these models need, make it difficult to explore the dynamics of extended neural networks imposed by such constraints. Thus, there is a need for a simple-enough neuron model that incorporates metabolic activity and allows us to explore neural network dynamics. This work introduces an energy-dependent leaky integrate-and-fire (LIF) neuronal model extension to account for the effects of metabolic constraints on the single-neuron behavior (EDLIF). This simple energy-dependent model shows better performance predicting real spikes trains -in spike coincidence measure sense-than the classical leaky integrate-and-fire model. It can describe the relationship between the average firing rate and the ATP cost, and replicate a neurons behavior under a clinical setting such as amyotrophic lateral sclerosis. The simplicity of the energy-dependent model presented here, makes it computationally efficient and thus, suitable to study the dynamics of large neural networks. Author summaryAny physical system or biological tissue is restricted by physical constraints bounding their behavior, and the brain is not free from these constraints. Energetic disorders in the brain have been linked to several neurodegenerative diseases, highlighting the relevance of maintaining a critical balance between energy production and consumption in neurons. These observations motivate the development of mathematical tools that can help to understand the dependence of the brains behavior in metabolism. One of the essential building blocks to achieve this task is the mathematical representation of neurons through models, allowing computational simulations of single-neurons and neural networks. Here we construct a simple and computational cheap energy-dependent neuron model that allows the study of neurons behavior under an energetic perspective. The introduced neuron model is contrasted with one of the widest-used neuron models and shows better prediction capabilities when real neuron recordings are used. Our model is suitable for replicating neurons behavior under a specific neurodegenerative disease, which cannot be achieved by the abovementioned popular model. Our simple model is promising because it allows the simulation and study of neuronal networks under a metabolic-dependent perspective.