Modeling the coexistence of NMDAR-dependent LTP and LTD mediated by changes in AMPAR conductance.

In this work, we develop a mathematical model that captures both the early and late phases of Long-Term Potentiation (LTP) and Long-Term Depression (LTD), incorporating NMDAR-dependent induction and changes in AMPAR conductance. The model combines multiple essential properties. First, it emphasizes a detailed representation of biochemical processes within the postsynaptic neuron, thereby illustrating the interaction between LTD and distinct forms of LTP. Second, the dynamic modulation of postsynaptic AMPA receptor conductance is represented through nonlinear differential equations and algebraic relations. Third, the model incorporates input specificity, associativity, and cooperativity, allowing synaptic changes at one site to influence the strength of neighboring synapses. These features provide a comprehensive description of synaptic dynamics, allowing the simulation of plasticity at both the cellular and the network levels. Overall, the model offers a valuable framework for studying NMDAR-dependent LTP and LTD by explicitly incorporating changes in AMPAR conductance. We believe that this model provides deeper insights into the molecular mechanisms of synaptic plasticity and paves the way for the construction of network-level models by linking multiple cells through AMPA receptor conductance. Significance statement: We present a comprehensive mathematical framework that integrates early (E-LTP), late (L-LTP), and LTD by incorporating NMDAR-dependent signaling and changes in AMPAR conductance. By combining and extending established biochemical models, our approach links molecular signaling, receptor trafficking, and postsynaptic membrane dynamics to changes in synaptic strength. The model reproduces key experimental phenomena, including input specificity, associativity, and cooperativity, and clarifies how pathways, such as CaMKII and PKA govern the stability of synaptic modifications. By capturing both cellular- and network-level properties, this framework provides a foundation for building scalable neural models grounded in the biophysics of learning and memory.