Robust transmission of rate coding in the inhibitory Purkinje cell to cerebellar nuclei pathway in awake mice

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons allow signals from the cerebellar cortex to influence the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many PC inputs are thought to converge onto each CbN neuron to suppress its firing. It has been proposed that PCs convey information using a rate code, a synchrony and timing code, or both. The influence of PCs on CbN neuron firing was primarily examined for the combined effects of many PC inputs with comparable strengths, and the influence of individual PC inputs has not been extensively studied. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modeling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, individual PC-CbN synapses are suited to concurrently convey rate codes and generate precisely timed responses in CbN neurons. Either synchronous firing or synchronous pauses of PCs promote CbN neuron firing on rapid time scales for nonuniform inputs, but less effectively than for uniform inputs. This is a secondary consequence of variable input sizes elevating the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. These findings may generalize to other brain regions with highly variable inhibitory synapse sizes.

Modeling Synaptic Integration of Bursty and β Oscillatory Inputs in Ventromedial Motor Thalamic Neurons in Normal and Parkinsonian States

The ventromedial motor thalamus (VM) is implicated in multiple motor functions and occupies a central position in the cortico-basal ganglia-thalamocortical loop. It integrates glutamatergic inputs from motor cortex (MC) and motor-related subcortical areas, and it is a major recipient of inhibition from basal ganglia. Previous in vitro experiments performed in mice showed that dopamine depletion enhances the excitability of thalamocortical (TC) neurons in VM due to reduced M-type potassium currents. To understand how these excitability changes impact synaptic integration in vivo, we constructed biophysically detailed mouse VM TC model neurons fit to normal and dopamine-depleted conditions, using the NEURON simulator. These models allowed us to assess the influence of excitability changes with dopamine depletion on the integration of synaptic inputs expected in vivo We found that VM neuron models in the dopamine-depleted state showed increased firing rates with the same synaptic inputs. Synchronous bursting in inhibitory input from the substantia nigra pars reticulata (SNR), as observed in parkinsonian conditions, evoked a postinhibitory firing rate increase with a longer duration in dopamine-depleted than control conditions, due to different M-type potassium channel densities. With β oscillations in the inhibitory inputs from SNR and the excitatory inputs from cortex, we observed spike-phase locking in the activity of the models in normal and dopamine-depleted states, which relayed and amplified the oscillations of the inputs, suggesting that the increased β oscillations observed in VM of parkinsonian animals are predominantly a consequence of changes in the presynaptic activity rather than changes in intrinsic properties.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons convey signals from the cerebellar cortex to the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many uniform sized PC inputs are thought to converge onto each CbN neuron to suppress or eliminate firing. Leading theories maintain that PCs encode information using either a rate code, or by synchrony and precise timing. Individual PCs are thought to have limited influence on CbN neuron firing. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modelling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, PC-CbN synapses are suited to concurrently convey rate codes, and generate precisely-timed responses in CbN neurons. Variable input sizes also elevate the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. Although this reduces the relative influence of PC synchrony on the firing rate of CbN neurons, synchrony can still have important consequences, because synchronizing even two large inputs can significantly increase CbN neuron firing. These findings may be generalized to other brain regions with highly variable sized synapses.

A Slow Short-Term Depression at Purkinje to Deep Cerebellar Nuclear Neuron Synapses Supports Gain-Control and 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_DCN activation (120 s) to mimic background activity in cerebellar slices from mature mice of both sexes, I identified a previously unrecognized, frequency-dependent, slow STD (S-STD), adapting IPSC amplitudes in tens of seconds to minutes. However, after changes in activation rates, over a behavior-relevant second-long time window, S-STD enabled scaled linear encoding of PC rates in synaptic charge transfer and DCN spiking activity. Combined electrophysiology, optogenetics, and statistical analysis suggested that S-STD mechanism is input-specific, involving decreased ready-to-release quanta, and distinct from faster short-term plasticity (f-STP). Accordingly, an S-STD component with a scaling effect (i.e., activity-dependent release sites inactivation), extending a model explaining PC_DCN release on shorter timescales using balanced f-STP, reproduced the experimental results. Thus, these results elucidates a novel slow gain-control mechanism able to support linear transfer of behavior-driven/learned PC rates concurrently with background activity adaptation, and furthermore, provides an alternative pathway to refine PC output.SIGNIFICANCE STATEMENT The brain can adapt to varying demands by dynamically changing the gain of its synapses; however, some tasks require ongoing linear transfer of presynaptic rates, seemingly incompatible with nonlinear gain adaptation. Here, I report a novel slow gain-control mechanism enabling scaled linear encoding of presynaptic rates over behavior-relevant time windows, and adaptation to background activity at the Purkinje to deep cerebellar nuclear neurons synapses (PC_DCNs). A previously unrecognized PC_DCNs slow and frequency-dependent short-term synaptic depression (S-STD) mediates this process. Experimental evidence and simulations suggested that scaled linear encoding emerges from the combination of S-STD slow dynamics and frequency-invariant transmission at faster timescales. These results demonstrate a mechanism reconciling rate code with background activity adaptation and suitable for flexibly tuning PCs output via background activity modulation.

A general method to generate artificial spike train populations matching recorded neurons

We developed a general method to generate populations of artificial spike trains (ASTs) that match the statistics of recorded neurons. The method is based on computing a Gaussian local rate function of the recorded spike trains, which results in rate templates from which ASTs are drawn as gamma distributed processes with a refractory period. Multiple instances of spike trains can be sampled from the same rate templates. Importantly, we can manipulate rate-covariances between spike trains by performing simple algorithmic transformations on the rate templates, such as filtering or amplifying specific frequency bands, and adding behavior related rate modulations. The method was examined for accuracy and limitations using surrogate data such as sine wave rate templates, and was then verified for recorded spike trains from cerebellum and cerebral cortex. We found that ASTs generated with this method can closely follow the firing rate and local as well as global spike time variance and power spectrum. The method is primarily intended to generate well-controlled spike train populations as inputs for dynamic clamp studies or biophysically realistic multicompartmental models. Such inputs are essential to study detailed properties of synaptic integration with well-controlled input patterns that mimic the in vivo situation while allowing manipulation of input rate covariances at different time scales.

Differential Coding Strategies in Glutamatergic and GABAergic Neurons in the Medial Cerebellar Nucleus

The cerebellum drives motor coordination and sequencing of actions at the millisecond timescale through adaptive control of cerebellar nuclear output. Cerebellar nuclei integrate high-frequency information from both the cerebellar cortex and the two main excitatory inputs of the cerebellum: the mossy fibers and the climbing fiber collaterals. However, how nuclear cells process rate and timing of inputs carried by these inputs is still debated. Here, we investigate the influence of the cerebellar cortical output, the Purkinje cells, on identified cerebellar nuclei neurons in vivo in male mice. Using transgenic mice expressing Channelrhodopsin2 specifically in Purkinje cells and tetrode recordings in the medial nucleus, we identified two main groups of neurons based on the waveform of their action potentials. These two groups of neurons coincide with glutamatergic and GABAergic neurons identified by optotagging after Chrimson expression in VGLUT2-cre and GAD-cre mice, respectively. The glutamatergic-like neurons fire at high rate and respond to both rate and timing of Purkinje cell population inputs, whereas GABAergic-like neurons only respond to the mean population firing rate of Purkinje cells at high frequencies. Moreover, synchronous activation of Purkinje cells can entrain the glutamatergic-like, but not the GABAergic-like, cells over a wide range of frequencies. Our results suggest that the downstream effect of synchronous and rhythmic Purkinje cell discharges depends on the type of cerebellar nuclei neurons targeted.SIGNIFICANCE STATEMENT Motor coordination and skilled movements are driven by the permanent discharge of neurons from the cerebellar nuclei that communicate cerebellar computation to other brain areas. Here, we set out to study how specific subtypes of cerebellar nuclear neurons of the medial nucleus are controlled by Purkinje cells, the sole output of the cerebellar cortex. We could isolate different subtypes of nuclear cell that differentially encode Purkinje cell inhibition. Purkinje cell stimulation entrains glutamatergic projection cells at their firing frequency, whereas GABAergic neurons are only inhibited. These differential coding strategies may favor temporal precision of cerebellar excitatory outputs associated with specific features of movement control while setting the global level of cerebellar activity through inhibition via rate coding mechanisms.