It has been suggested that excitatory and inhibitory inputs to cortical cells are balanced, and that this balance is important for the highly irregular firing observed in the cortex. There are two hypotheses as to the origin of this balance. One assumes that this balance results from a stable solution of the recurrent neuronal dynamics. This hypothesis can account for a balance of steady state excitation and inhibition without fine tuning of parameters, but not for transient inputs. The second hypothesis suggests that the feed forward excitatory and inhibitory inputs to a postsynaptic cell are already balanced. This latter hypothesis can also account for the balance of transient inputs. However, it remains unclear what mechanism underlies the fine tuning required for balancing feed forward excitatory and inhibitory inputs.

Here we investigated whether inhibitory synaptic plasticity is responsible for the balance of transient feed forward excitation and inhibition. We address this issue in the framework of a model characterizing the stochastic dynamics of temporally asymmetric Hebbian spike timing dependent plasticity of feed-forward excitatory and inhibitory synaptic inputs to a single post-synaptic cell. Our analysis shows that inhibitory Hebbian plasticity generates 'negative feedback' that balances excitation and inhibition. This is in contrast with the 'positive feedback' of excitatory Hebbian synaptic plasticity.

To account for the diversity of the empirically observed STDP rules, we suggest a model in which the STDP rule is represented by two processes that occur in parallel one for potentiation and one for depression. Analysis of the STDP dynamics reveals a critical point. Below this critical point the STDP dynamics is governed by a negative feedback and the synaptic weights are characterized by a unimodal distribution. Above this point, the stability of the STDP dynamics is governed by the synaptic weight dependence of the STDP rule. In the latter case there is a different parameter with a critical value, above which, a bimodal synaptic weight distribution exists. We show that the location of these critical points depends on general properties of the temporal structure of the STDP rule and not on its fine details. These results hold for both excitatory and inhibitory synapses. The symmetry in the learning dynamics of excitatory and inhibitory synapses is discussed.