Technical papers sometimes make a distinction between modifiable and non-modifiable synapses. Results on NMDA-NR2A vs. NMDA-NR2B receptors show that a NR2B receptor is required for LTP (learning), and a synapse which contains only NMDA-NR2A and AMPA glutamatergic receptors is not modifiable (except maybe for some LTD).

http://www.ncbi.nlm.nih.gov/pubmed/20164351

“Thus, for LTP induction, the physical presence of NR2B and its cytoplasmic tail are more important than the activation of NR2B–NMDARs, suggesting an essential function of NR2B as a mediator of protein interactions independent of its channel contribution. In contrast, the presence of NR2A is not essential for LTP, and, in fact, the cytoplasmic tail of NR2A seems to inhibit the induction of LTP.”

“The apparent contradiction can be explained by the fact that NR2B, in addition to forming part of a ligand-gated channel, also has a long cytoplasmic tail that binds (directly or indirectly) to a variety of postsynaptic signaling molecules.”

“Our data cannot distinguish whether these collaborating NR2A and NR2B subunits are in the same (triheteromeric) NMDAR complex or in different NMDARs (NR2A–NMDARs and NR2B–NMDARs) that lie near each other.”

“We hypothesize that the NR2A subunit also has a dual function. On one hand, it acts as a channel that facilitates LTP by conducting calcium. On the other hand, it acts as a scaffold that presumably recruits a protein to the synapse that inhibits LTP. Such a protein could act by antagonizing the activation of LTP signaling pathways [e.g., synaptic Ras-GTPase-activating protein (Kim et al., 2005)] or by stimulating the LTD signaling pathways [such as Rap and p38 mitogen-activated protein kinase) (Thomas and Huganir, 2004; Zhu et al., 2005; Li et al., 2006)].”

“Consistent with this idea, changes in plasticity in the visual cortex are correlated with a change in the NR2A/NR2B ratio. Light deprivation lowers the threshold of induction for LTP and is associated with a decrease in synaptic NR2A.”

It is hard to prove a negative, a non-modifiable synapse.  Since NR2B-containing receptors often occur in extrasynaptic positions, stimulation protocols may also recruit them to the synapse.  Triheteromeric receptor complexes do occur, but they may be less common. Also, the role of the NR2D and NR2C subunits, which may also bind to NR1, and which may help in creating Nr2A-type only synapses, is less clear.

Nonetheless it may be justified to make a distinction between “hard-to-modify” synapses and easily modifiable synapses.

This is entirely different from the “silent synapses”, which, because they contain no AMPA receptors, do not contribute (much) to fast signal transmission, but which may be recruited to full synapses, because they do contain NMDA-Nr2B receptors.