Modifications in the strengths of synapses are thought to underlie memory, learning, and development of cortical circuits. Many cellular mechanisms of synaptic plasticity have been investigated in which differential elevations of postsynaptic calcium concentrations play a key role in determining the direction and magnitude of synaptic changes. We have previously described a model of plasticity that uses calcium currents mediated by N-methyl-Daspartate receptors as the associative signal for Hebbian learning. However, this model is not completely stable. Here, we propose a mechanism of stabilization through homeostatic regulation of intracellular calcium levels. With this model, synapses are stable and exhibit properties such as those observed in metaplasticity and synaptic scaling. In addition, the model displays synaptic competition, allowing structures to emerge in the synaptic space that reflect the statistical properties of the inputs. Therefore, the combination of a fast calcium-dependent learning and a slow stabilization mechanism can account for both the formation of selective receptive fields and the maintenance of neural circuits in a state of equilibrium.S ynaptic plasticity as a physiological basis for learning and memory storage has been extensively investigated. Induction of bidirectional synaptic plasticity has been shown to depend on calcium influx into the postsynaptic cell (1, 2). In a previous paper, we proposed a model of bidirectional activity-dependent synaptic plasticity that depends on the calcium currents mediated by N-methyl-D-aspartate receptors (NMDARs) (3). In this model, which we henceforth denote calcium-dependent plasticity (CaDP), the direction and magnitude of synaptic changes are determined by a function of the intracellular calcium concentration: basal levels of calcium generate no plasticity, moderate ones induce depression, and higher elevations lead to potentiation (4). At a synapse, the amount of neurotransmitter bound to NMDARs provides information on the local, presynaptic activities, whereas back-propagating action potentials signal the global, postsynaptic activities. This association between pre-and postsynaptic activities thus forms the basis for Hebbian learning. Analysis and simulations have shown that this model can explain the rate-, voltage-, and spike timing-dependent plasticity as consequences of, respectively, the temporal integration of calcium transients, the voltage-dependence of NMDAR conductances, and the coincidence-detection property of these receptors (3, 5). In addition, numerous experimental results support the idea that NMDARs play key roles in activity-dependent development and refinement of synapses because of their permeability to calcium ions (6-11).However, typical of associative forms of plasticity rules, CaDP is not completely stable. Excessive neural excitation generates high levels of depolarization, favoring calcium entry into the dendrites and thus promoting synaptic potentiation. Such potentiation further enhances the excitability of the...
