Balancing Feed-Forward Excitation and Inhibition via Hebbian Inhibitory Synaptic Plasticity

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 it results from a stable solution of the recurrent neuronal dynamics. This model 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 thus does 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 anti-symmetric 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, which contrasts with the ‘positive feedback’ of excitatory Hebbian synaptic plasticity. As a result, this balance may increase the sensitivity of the learning dynamics to the correlation structure of the excitatory inputs. Author Summary: One of the longstanding enigmas in neuroscience is the origin of inherent neural noise. It has been suggested that this noise results from a careful balance of excitatory and inhibitory inputs to neurons. Obtaining this balance requires fine tuning of the relative strengths of the inhibitory and excitatory inputs to each cell. However the mechanism that enables this fine tuning of parameters remains unclear. We suggest that a balance of excitatory and inhibitory inputs can be achieved via a process of unsupervised learning of the inhibitory synaptic strengths. We find that whereas Hebbian learning induces strong positive feedback on excitatory inputs that acts as a force that pulls them towards their boundaries, Hebbian learning of inhibition induces negative feedback. This negative feedback acts to balance the average excitatory input to the cell and makes the learning process less sensitive to the statistics of the inhibitory inputs. Surprisingly, this balance increases the sensitivity of learning to the statistics of the excitatory inputs. Thus, the balance of feed-forward excitation and inhibition emerges as a natural outcome of Hebbian learning applied to the inhibitory inputs to the cell.