Abstract
Overview: We model energy constraints in a network of spiking neurons, while exploring general questions of resource limitation on network function abstractly.Background: Metabolic states like dietary ketosis or hypoglycemia have a large impact on brain function and disease outcomes. Glia provide metabolic support for neurons, among other functions. Yet, in computational models of glia-neuron cooperation, there have been no previous attempts to explore the effects of direct realistic energy costs on network activity in spiking neurons. Currently, biologically realistic spiking neural networks assume that membrane potential is the main driving factor for neural spiking, and do not take into consideration energetic costs.Methods: We define local energy pools to constrain a neuron model, termed Spiking Neuron Energy Pool (SNEP), which explicitly incorporates energy limitations. Each neuron requires energy to spike, and resources in the pool regenerate over time. Our simulation displays an easy-to-use GUI, which can be run locally in a web browser, and is freely available.Results: Energy dependence drastically changes behavior of these neural networks, causing emergent oscillations similar to those in networks of biological neurons. We analyze the system via Lotka-Volterra equations, producing several observations: (1) energy can drive self-sustained oscillations, (2) the energetic cost of spiking modulates the degree and type of oscillations, (3) harmonics emerge with frequencies determined by energy parameters, and (4) varying energetic costs have non-linear effects on energy consumption and firing rates.Conclusions: Models of neuron function which attempt biological realism may benefit from including energy constraints. Further, we assert that observed oscillatory effects of energy limitations exist in networks of many kinds, and that these findings generalize to abstract graphs and technological applications.
Highlights
With health and basic biology in mind, many neurological problems are co-morbid with metabolic disorders, such as diabetes (Reske-Nielsen and Lundbæk, 1963; Dejgaard et al, 1991; Biessels et al, 1994; Duby et al, 2004; Mijnhout et al, 2006)
Energetic metabolism can have a huge impact on brain function and neurological diseases (Gasior et al, 2006; Barañano and Hartman, 2008; Stafstrom and Rho, 2012)
The wellstudied phenomenological neuron model we used is in the family of Spike Response Models (SRM), which is a generalization of integrate-and-fire models
Summary
With health and basic biology in mind, many neurological problems are co-morbid with metabolic disorders, such as diabetes (Reske-Nielsen and Lundbæk, 1963; Dejgaard et al, 1991; Biessels et al, 1994; Duby et al, 2004; Mijnhout et al, 2006). Energetic metabolism can have a huge impact on brain function and neurological diseases (Gasior et al, 2006; Barañano and Hartman, 2008; Stafstrom and Rho, 2012). With biologically inspired technology as a goal, the brain requires a large proportion of the body’s energy, and yet is highly efficient for its absolute power compared to modern supercomputers, with the brain consuming orders of magnitude less energy for more functional processing. Metabolic states like dietary ketosis or hypoglycemia have a large impact on brain function and disease outcomes. In computational models of glia-neuron cooperation, there have been no previous attempts to explore the effects of direct realistic energy costs on network activity in spiking neurons. Biologically realistic spiking neural networks assume that membrane potential is the main driving factor for neural spiking, and do not take into consideration energetic costs
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