Short-term plasticity at Purkinje to deep cerebellar nuclear neuron synapses supports a slow gain-control mechanism enabling scaled linear encoding over second-long time windows

Modifications in the sensitivity of neural elements allow the brain to adapt its functions to varying demands. Frequency-dependent short-term synaptic depression (STD) provides a dynamic gain-control mechanism enabling adaptation to different background conditions alongside enhanced sensitivity to input-driven changes in activity. In contrast, synapses displaying frequency-invariant transmission can faithfully transfer ongoing presynaptic rates enabling linear processing, deemed critical for many functions. However, rigid frequency-invariant transmission may lead to runaway dynamics and low sensitivity to changes in rate. Here, I investigated the Purkinje cell to deep cerebellar nuclei neuron synapses (PC_DCNs), which display frequency-invariance, and yet, PCs maintain background-activity at disparate rates, even at rest. Using protracted PC_DCNs activation (120s) in cerebellar slices to mimic background-activity, I identified a previously unrecognized frequency-dependent, slow STD (S_STD) of PC_DCN inhibitory postsynaptic currents. S_STD supports a novel form of gain-control that enabled—over second-long time windows—scaled linear encoding of PC rate changes mimicking behavior-driven/learned PC-signals, alongside adaptation to background-activity. Cell-attached DCN recordings confirmed these results. Experimental and computational modeling results suggest S_STD-gain-control may emerge through a slow depression factor combined with balanced fast-short-term plasticity. Finally, evidence from opto-genetic experiments, statistical analysis and computer simulations pointed to a presynaptic, input-specific and possibly activity-dependent decrease in active synaptic release-sites as the basis for S_STD. This study demonstrates a novel slow gain-control mechanism, which could explain efficient and comprehensive PC_DCN linear transfer of input-driven/learned PC rates over behavioral-relevant time windows despite disparate background-activity, and furthermore, provides an alternative pathway to hone PCs output via background-activity control. SIGNIFICANCE STATEMENT The brain can adapt to varying demands by dynamically changing the gain of its synapses; however, some tasks require linear transfer of presynaptic rates over extended periods, seemingly incompatible with non-linear gain adaptation. Here, I report a novel gain-adaptation mechanism, which enables scaled linear encoding of changes in presynaptic rates over second-long time windows and adaptation to background-activity at longer time-scales at the Purkinje to deep cerebellar nuclear neurons synapses (PC_DCNs). A previously unrecognized PC_DCN slow and frequency-dependent short-term synaptic depression (S_STD), together with frequency-invariant transmission at faster time scales likely explains this process. This slow-gain-control/modulation mechanism may enable efficient linear encoding of second-long presynaptic signals under diverse synaptic background-activity conditions, and flexible fine-tuning of synaptic gains by background-activity modulation.