TIME REPRESENTATIONS IN PURKINJE CELL DENDRITES Abbreviated title : Time representations in Purkinje cells

Various lines of evidence, most importantly from studies of pavlovian eye blink conditioning, suggest that the cerebellar cortex provides a precise representation of the temporal relationship between successive events in the 0.1 1.5 s range. Current explanations for these timing capabilities rely on spectral decomposition of the inputs carried by parallel fibers (PFs) or delays in activation of PFs synapses on Purkinje cells (PCs). However, based on their length and transmission velocity, PFs cannot produce sufficiently long delays. On the other hand, spectral models cannot explain the trace version of the eye blink paradigm into which the conditioned and unconditioned stimuli are separated by a time gap. Here, we show that intrinsic electrical properties of PCs are sufficient to generate appropriate adaptive timing of the cerebellar cortex output. Using a biophysical model of electric signal integration in PC dendrites, it is shown that brief inputs from climbing fiber (CF) and PFs can trigger longlasting PCs responses with adaptive duration. In both cases, the signals do not propagate actively. The CF-triggered responses invade the dendritic tree only if the CF input is distributed over smooth dendrites, in agreement with the actual anatomical CF synapse distribution. PFs-triggered responses reach the cell soma once a threshold current inversely related to the stimulated area is exceeded. These responses cannot be classified as spikes due to their non-propagating nature nor as electrotonus given their voltage threshold. They therefore represent a novel mechanism of excitability, which allows contextual information from mossy fibers to reliably control duration of PC responses to phasic inputs from PFs and the CF. The cerebellum has been hypothesized to act as an interval timing system (Ivry and Spencer, 2004). This functional hypothesis is best documented in the eye blink conditioning, where paired conditioned (CS) and unconditioned (US) stimuli are repetitively presented to animals. Parallel fibers (PFs, the granule cells axons) convey the CS (Hesslow et al., 1999) while climbing fibers (CFs, axons of inferior olivary neurons) carry the US (Svensson and Ivarsson, 1999) to the cerebellar cortex. With training, animals learn to blink in response to the CS alone at the expected time of the US, with inter-stimulus intervals from 100ms to1200ms (réfférences Llimas). Time encoding of these responses putatively resides in Purkinje cells (PCs) as the CS and US converge on their dendrites. But the physiological mechanisms underlying these dendritic time computations remain obscure. Spectral models use an analogy between PCs and perceptrons to posit that PCs translate patterns of PFs activation into temporal codes. However, perceptrons can only associate concomitant inputs and outputs and these models cannot explain trace conditioning, where a time gap separates the two stimuli (Medina et al., 2000). An alternative hypothesis relies on sustained responses of PCs to brief stimuli. Fiala et al. (1996) have thus shown that dynamics of PCs metabotropic glutamate receptors (Batchelor et al., 1994) can reproduce time characteristics of eye blink conditioning. Induction of correctly timed conditioned responses in mice lacking metabotropic receptors (Aïba et al., 1994) however implicates that other master timing mechanisms are at work in the cerebellum. Dendritic plateau potentials (Llinás and Sugimori, 1992) represent another candidate for trace activities in PCs, as their duration ranges from 100ms to several seconds. Houk and colleagues (Berthier et al., 1993; Barto et al., 1999) have illustrated how plateaus endowed with adaptive duration could sculpt crude commands from the motor cortex to improve motor coordination. Genet and Delord (2002) have embodied this idea by showing in a biophysical model of the plateau mechanism, that tonic synaptic inputs may precisely control plateaus duration. This model also predicts mirror signals, termed ‘valley potentials’, that explain PC pauses in Houk’s model. PCs have complex dendrites. How are plateaus and valleys excited and how do they integrate in the tree to set the timing properties of the neuron? We addressed these questions by investigating the mechanism of Genet and Delord (2002) in the PC dendrites architecture. Simulations in infinite dendrites show that Ca spikes and plateaus / valleys of infinite duration can intrinsically propagate whereas finite plateaus/valleys are non-propagating signals. In equivalent cable representations of a reconstructed PC, activation of the CF triggers traveling waveforms reproducing the diversity of complex spikes shapes. Paradoxically, finite plateaus and valleys triggered in dendrites reach the soma. Their threshold current relates inversely to the stimulated membrane area, like stimuli for propagating spikes in the somatopetal direction. These properties of plateaus / valleys are irreconcilable with features of classical spikes and spreading electrotonus. They lead us to propose that these signals represent a distinct mechanism of electric signaling and our simulations illustrate how PCs may use it to encode timed representations of their MFs and CF inputs.