Synaptic plasticity involves modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; an increase in AMPAR corresponds to strengthening of synapses while a decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signalling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Previous work in the field of deterministic modelling of CaMKII dynamics has assumed bistable kinetics, while experiments and rule-based modelling have revealed that CaMKII dynamics can be either monostable or ultrasensitive. This raises the following question: how does the choice of model assumptions involving CaMKII dynamics influence AMPAR dynamics at the synapse? To answer this question, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of different signalling and trafficking variations, along with their coupled effects, on AMPAR dynamics at the synaptic site. We find that the properties of the model including network architecture describing different stability features of CaMKII and parameters that capture the endocytosis and exocytosis of AMPAR significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (1) the choice of signalling model (bistable CaMKII or monostable CaMKII dynamics), (2) trafficking versus influx contributions and (3) frequency of stimulus. KEY POINTS: The density of AMPA receptors (AMPARs) at the postsynaptic density of the synapse provides a readout of synaptic plasticity, which involves crosstalk between complex biochemical signalling networks including CaMKII dynamics and trafficking pathways including exocytosis and endocytosis. Here we build a model that integrates CaMKII dynamics and AMPAR trafficking to explore this crosstalk. We compare different models of CaMKII that result in monostable or bistable kinetics and their impact on AMPAR dynamics. Our results show that AMPAR density depends on the coupling between aspects of biochemical signalling and trafficking. Specifically, assumptions regarding CaMKII dynamics and its stability features can alter AMPAR density at the synapse. Our model also predicts that the kinetics of trafficking versus influx of AMPAR from the extrasynaptic space can further impact AMPAR density. Thus, the contributions of both signalling and trafficking should be considered in computational models.