A calciuminfluxdependent plasticity model exhibiting multiple STDP curves Hebbian plasticity means that if the firing of two neurons is correlated, then their connection is strengthened. Conversely, uncorrelated firing causes a decrease in synaptic strength. Spiketimingdependent plasticity (STDP) represents one instantiation of Hebbian plasticity. Under STDP, synaptic changes depend on the relative timing of the pre and postsynaptic firing. By inducing pre and postsynaptic firing at different relative times the STDP curves of many neurons have been determined, and it has been found that there are different curves for different neuron types or synaptic sites. Biophysically, strengthening (longterm potentiation, LTP) or weakening (longterm depression, LTD) of glutamatergic synapses depends on the postsynaptic influx of calcium (Ca2): weak influx leads to LTD, while strong, transient influx causes LTP. The voltagedependent NMDA receptors are the main source of Ca2 influx, but they will only open if a postsynaptic depolarisation coincides with presynaptic neurotransmitter release. Here we present a computational mechanism for Ca2dependent plasticity in which the interplay between the presynaptic neurotransmitter release and the postsynaptic membrane potential leads to distinct Ca2 timecourses, which in turn lead to the change in synaptic strength. It is shown that the model complies with classic STDP results, as well as with results obtained with triplets of spikes. Furthermore, the model is capable of displaying different shapes of STDP curves, as observed in different experimental studies.

Unsupervised Learning of Persistent and Sequential Activity Two strikingly distinct types of activity have been observed in various brain structures during delay periods of delayed response tasks: Persistent activity (PA), in which a subpopulation of neurons maintains an elevated firing rate throughout an entire delay period; and Sequential activity (SA), in which subpopulations of neurons are activated sequentially in time. It has been hypothesized that both types of dynamics can be xe2x80x98learnedxe2x80x99 by the relevant networks from the statistics of their inputs, thanks to mechanisms of synaptic plasticity. However, the necessary conditions for a synaptic plasticity rule and input statistics to learn these two types of dynamics in a stable fashion are still unclear. In particular, it is unclear whether a single learning rule is able to learn both types of activity patterns, depending on the statistics of the inputs driving the network. Here, we first characterize the complete bifurcation diagram of a firing rate model of multiple excitatory populations with an inhibitory mechanism, as a function of the parameters characterizing its connectivity. We then investigate how an unsupervised temporally asymmetric Hebbian plasticity rule shapes the dynamics of the network. Consistent with previous studies, we find that for stable learning of PA and SA, an additional stabilization mechanism is necessary. We show that a generalized version of the standard multiplicative homeostatic plasticity (Renart et al., 2003; Toyoizumi et al., 2014) stabilizes learning by effectively masking excitatory connections during stimulation and unmasking those connections during retrieval. Using the bifurcation diagram derived for fixed connectivity, we study analytically the temporal evolution and the steady state of the learned recurrent architecture as a function of parameters characterizing the external inputs. Slow changing stimuli lead to PA, while fast changing stimuli lead to SA. Our network model shows how a network with plastic synapses can stably and flexibly learn PA and SA in an unsupervised manner.