We study single-electron tunneling (SET) characteristics in crystalline PbS/InP junctions, that exhibit single-electron Coulomb-blockade staircases along with memory and memory-fading behaviors. This gives rise to both short-term and long-term plasticities as well as a convenient non-linear response, making this structure attractive for neuromorphic computing applications. For further insights into this prospect, we predict typical behaviors relevant to the field, obtained by an extrapolation of experimental data in the SET framework. The estimated minimum energy required for a synaptic operation is in the order of 1 fJ, while the maximum frequency of operation can reach the MHz range.