Astrocytes play a crucial role in regulating synaptic strength and orchestrating synaptic plasticity, which is fundamental for learning and memory. However, the specific mechanisms by which astrocytes and their neuroactive transmitters, like D-serine, control these processes remain largely unexplored. D-serine, a co-agonist for the NMDA receptor, has garnered increasing interest as a potential regulatory molecule in synaptic plasticity. Given its activity-dependent release mediated by astrocytes, D-serine is a key player in balancing long-term synaptic depression (LTD) and potentiation (LTP) during learning. This study aims to elucidate the molecular mechanisms underlying D-serine's function, its interaction with other neurotransmitters, and its impact on synaptic plasticity. We develop a computational model of synaptic plasticity incorporating detailed NMDAR activation dynamics, which is validated against spike-timing-dependent plasticity (STDP) and other protocols. Our model explores the hypothesis that two distinct NMDAR groups exist at the synapse, each associated with a distinct pathway leading to either LTP or LTD. By incorporating D-serine modulation, we describe its effects on NMDAR activation and predict its influence on STDP. Our findings highlight that D-serine availability significantly impacts the STDP curve and overall synaptic plasticity, aligning with the phenomenological BCM model of synaptic plasticity. This biophysical model provides a framework for understanding the complex interplay between D-serine and synaptic plasticity, offering insights into the molecular basis of learning and memory. Future work will aim to refine the model with more detailed biological data and further explore the implications of these findings.