Another factor regulating synaptic strength: synaptic columns
It has been well-established for over a decade that synaptic vesicle release further away from a particular receptor cluster is associated with a decreased probability of receptor open state and therefore a decreased postsynaptic current (at least at glutamatergic synapses).
Franks et al 2003; PMC2944019
A few months ago Tang et al published an article in which they reported live imaging of cultured rat hippocampal neurons to investigate this.
They showed that critical vesicle priming and fusion proteins are preferentially found near to one another within presynaptic active zones. Moreover, these regions were associated with higher levels of postsynaptic receptors and scaffolding proteins.
On this basis, the authors suggest that there are transynaptic columns, which they call "nanocolumns" (I employ scare quotes here quite intentionally because I don't prefix any word with nano- until I am absolutely forced to).
They have a nice YouTube video visualizing this arrangement at a synapse:
https://www.youtube.com/watch?v=HPjADfy0O6g
They propose that this arrangement allows the densest presynaptic active zones to match the densest postsynaptic receptor densities, maximizing the efficiency, and therefore strength, of the synapse.
In their most elegant validation experiment of this model, they inhibited synapses by activating postsynaptic NMDA receptors and found that this led to a decreased correspondence between synaptic active zones and postsynaptic densities (PSDs).
Tang et al 2016; doi:10.1038/nature19058
As you can see, the time-scale of the effect of NMDA receptor activation was pretty fast, at only 5 mins. My guess is that this effect is so fast because active positive regulation maintains the column organization, and without it, proteins rapidly diffuse away.
It is almost certain that synaptic cleft adhesion systems or retrograde signaling mechanisms regulate synaptic column organization, and the race is on to identify them and precisely how they work.
In the meantime, Tang et al's work is a great example of synaptic strength variability that is dependent on protein localization, and should inform our models of how the brain works.