Understanding the intricate interplay between neural dynamics and metabolic constraints is crucial for unraveling the mysteries of the brain. Despite the significance of this relationship, specific details concerning the impact of metabolism on neuronal dynamics and neural network architecture remain elusive, creating a notable gap in the existing literature. This study employs an energy-dependent neuron and plasticity model to analyze the role of local metabolic constraints in shaping both the dynamics and structure of Spiking Neural Networks (SNN). Specifically, an energy-dependent version of the leaky integrate-and-fire model is utilized, along with a three-factor learning rule that incorporates postsynaptic available energy as the third factor. These models allow for fine-tuning sensitivity in the presence of energy imbalances. Analytical expressions predicting the network’s activity and structure are derived, and a fixed point analysis reveals the emergence of attractor states characterized by neuronal and synaptic sensitivity to energy imbalances. Analytical findings are validated through numerical simulations using an excitatory-inhibitory network. Furthermore, these simulations enable the study of SNN activity and structure under conditions simulating metabolic impairment. In conclusion, by employing energy-dependent models with adjustable sensitivity to energy imbalances, our study advances the understanding of how metabolic constraints shape SNN dynamics and structure. Moreover, in light of compelling evidence linking neuronal metabolic impairment to neurodegenerative diseases, the incorporation of local metabolic constraints into the investigation of neuronal network structure and activity opens an intriguing avenue for inspiring the development of therapeutic interventions.