In the mammalian brain, fear memory is associated with fear conditioning-induced synaptic plasticity in the amygdala.An experiment in mice demonstrated that the paraventricular nucleus of the thalamus (PVT) strongly projects to the lateral division of the central amygdala (CeL)and participates in the formation of fear memory via the regulation of a central amygdale fear circuit.Here, we established a mathematical model to investigate the underlying mechanisms for PVT manipulation of synaptic plasticity in the amygdala.In the model, the PVT secretes the brain derived neurotrophic factor (BDNF) to the CeL during fear conditioning, and a positive feedback in postsynaptic BDNF expression was assumed to regulate the maintenance of synaptic potentiation.Model simulations indicated that the postsynaptic firing frequency increases approximately linearly with an increase in the presynaptic Ca2+ concentration, and that a proper strength of the positive feedback of postsynaptic BDNF expression is required to maintain the high presynaptic Ca2+ concentration level for a substantial amount of time following stimulation.Furthermore, we demonstrated that BDNF secretion from the lateral amygdala (LA) to the CeL is important in the regulation of short-term synaptic potentiation.