A synapse's strength also depends on the number of ion channels it has. Several facts suggest that neurons change the density of receptors on their postsynaptic membranes as a mechanism for changing their own excitability in response to stimuli. In a dynamic process that is maintained in equilibrium, NMDA and AMPA receptors are added to the membrane by exocytosis and removed by endocytosis. These processes, and by extension the number of receptors on the membrane, can be altered by synaptic activity. Experiments have shown that AMPA receptors are delivered to the membrane due to repetitive NMDAR activation .
If the strength of a synapse is only reinforced by stimulation or weakened by its lack, a positive feedback loop will develop, leading some cells never to fire and some to fire too much. But two regulatory forms of plasticity, called scaling and metaplasticity, also exist to provide negative feedback. Synaptic scaling serves to maintain the strengths of synapses relative to each other, lowering amplitudes of small excitatory postsynaptic potentials in response to continual excitation and raising them after prolonged blockage or inhibition. This effect occurs gradually over hours or days, by changing the numbers of NMDA receptors at the synapse (Pérez-Otaño and Ehlers, 2005). Metaplasticity, another form of negative feedback, reduces the effects of plasticity over time. Thus, if a cell has been affected by a lot of plasticity in the past, metaplasticity makes future plasticity less effective. Since LTP and LTD (long-term depression) rely on the influx of Ca2+ through NMDA channels, metaplasticity may be due to changes in NMDA receptors, for example changes in their subunits to allow the concentration of Ca2+ in the cell to be lowered more quickly.
Of these, the first two hypotheses have been recently mathematically examined to have identical calcium-dependent dynamics which provides strong theoretical evidence for a calcium-based model of plasticity, which in a linear model where the total number of receptors are conserved looks like
where is the synaptic weight of the th input axon, is a time constant dependent on the insertion and removal rates of neurotransmitter receptors, which is dependent on , the concentration of calcium. is also a function of the concentration of calcium that depends linearly on the number of receptors on the membrane of the neuron at some fixed point. Both and are found experimentally and agree on results from both hypotheses. The model makes important simplifications that make it unsuited for actual experimental predictions, but provides a significant basis for the hypothesis of a calcium-based synaptic plasticity dependence.