Inhibition stabilization and paradoxical effects in recurrent neural networks with short-term plasticity

Inhibition stabilization is considered a ubiquitous property of cortical networks, whereby inhibition controls network activity in the presence of strong recurrent excitation. In networks with fixed connectivity, an identifying characteristic of inhibition stabilization is that increasing (decreasing) excitatory input to the inhibitory population leads to a decrease (increase) in inhibitory firing, known as the paradoxical effect. However, population responses to stimulation are highly nonlinear, and drastic changes in synaptic strengths induced by short-term plasticity (STP) can occur on the timescale of perception. How neuronal nonlinearities and STP affect inhibition stabilization and the paradoxical effect is unclear. Using analytical calculations, we demonstrate that in networks with STP the paradoxical effect implies inhibition stabilization, but inhibition stabilization does not imply the paradoxical effect. Interestingly, networks with neuronal nonlinearities and STP can transition non-monotonically between inhibition-stabilization and non-inhibition-stabilization, and between paradoxically- and non-paradoxically-responding regimes with increasing excitatory activity. Furthermore, we generalize our results to more complex scenarios including networks with multiple interneuron subtypes and any monotonically increasing neuronal nonlinearities. In summary, our work reveals the relationship between inhibition stabilization and the paradoxical effect in the presence of neuronal nonlinearity and STP, yielding several testable predictions.