Our work provides new insights in how olivary AP spikelet distributions may unfold under different conditions. Taking advantage of the control a detailed model gives, we investigated the effect of specific currents on IO neuron firing properties, while also taking into account the effects thereof on parameters available in empirical data, such as AP spikelet count and STO amplitude.
Our three-compartmental model faithfully reproduces earlier findings on olivary neurons such as the frequency and shape of their STOs, their propensity to limit APs to a preferred firing window, and their spike shape as recorded at the soma using whole-cell patch-clamp techniques. There appears to be a difference in the phase range of the firing window reported in earlier work from our lab 
in that the firing window is phase-shifted. However, since the actual shape of the oscillation can vary (i.e. is not truly sinusoidal nor identical between cells), the phase offset of the best sinewave fit can vary and even relative phase differences within a trace are suspect. In most oscillation shapes in our data there is a slightly steeper inclination of the upward slope (see and Fig. S1A
) and a shorter duration of the peak of the STO relative to the trough (see and Fig. S1A
). Because of this, spikes appear to fall in a relatively small phase range of the peak since the actual peak of the STO is shorter than that of the fitted sinewave. Due to the difficulty in fitting sinewave functions to STOs, spikes mapped to the fitted sinewave by our automated analysis software could be considered to be phase-shifted with respect to the actual data when judged by a human: the spikes fall almost exclusively on the rising slope of the fitted sinewave, but start after the trough minimum and extend beyond the peak of the STO in the actual data. In addition, the results from our lab regarding the occurrence of a spike relative to STO phase were generally obtained by fitting a sinewave to the data, but relying on user input for assigning the event to one of eight 45-degree bins, thus potentially introducing a slight bias and explaining the discrepancy between previously reported firing windows and that of our model, at least in part.
In a network setting, our model shows a clear phase-dependency of AP spikelet count in line with findings by Mathy et al. 
when stimulating the entire network of coupled cells. When stimulating only one cell in the network this phase-dependency is largely lost, again in line with the results shown by Mathy et al. 
. Thus, our model not only reaffirms previous findings, but also provides an explanation for seemingly contradicting results. However, there are also differences. Mathy et al. reported a maximum AP spikelet count at ~π radians, which does not match the maximum we found in simulations similar to their experiment (~0.5π). We speculate that this is due to a difference in the mapping of STO phase. Furthermore, their results span the full range of phases of the STO, indicating that in their experiments spikes could be elicited regardless of STO phase.
Calcium currents are the cause of the IO cells' typical spike ADP and low-threshold voltage-dependent calcium ion channels have been shown to be important in the generation of the IO cells' STOs 
. Indeed, with variable somatic low-threshold calcium ion channel expression levels our model shows substantial changes in the STO amplitude and smaller changes in the STO period and in the ADP size. The small change in ADP size was the result of increased dendrosomatic coupling currents at higher calcium ion channel activation levels. Our model predicts that the duration of the ADP and the amount of current flow between the soma and the dendrite are the main determinants of the somatic AP spikelet count.
Since coupling currents between soma and dendrite are a major AP spikelet count determinant, gap-junctional coupling plays a role in establishing the CF burst size. Furthermore, the different CF burst size results between full-network and single-cell stimulation in our simulations also point to an effect of gap junctions on AP spikelet count. The reason for this is that ensemble firing minimizes membrane potential differences between cells, causing less dendrodendritic gap-junctional coupling currents to affect the cells' internal dendrosomatic coupling currents.
Single cells firing due to dendritic stimulation in a more biologically plausible setting with variable low-threshold calcium ion channel expression levels among cells and different coupled cell ensemble sizes show higher average AP spikelet counts and no phase-dependency of the CF burst size at low STO amplitudes. In a certain range of STO amplitudes, there appears to be a relation between STO phase and spikelet count in what might be a coarse coding, but at other STO amplitudes, both larger and smaller, the phase-dependency of climbing fiber burst size shown earlier using in vitro
preparations may be lost. The artificial current injection used in those experiments could impose an oscillation on a cell ensemble and thus create artificial synchrony at moderate STO amplitudes. Under these conditions, our model predicts a correlation between STO phase and AP spikelet count in line with the findings by Mathy et al. 
A quantitative error estimate is required in several computational cerebellar models for learning, but so far these have been hard to explain using IO data due to the low firing rate of IO cells. It has been proposed that variability in spike shape of olivary cells may allow for transmission of more information per event than would otherwise be possible 
. Phase dependency of the CF burst size and somatic AP spikelet count would allow for a coarse, low-resolution encoding of temporal information. Our model predicts that there may be a phase-dependency of climbing fiber burst size, but only in a limited range of STO amplitudes and in coupled cell ensembles of sufficient size.
We provide as an additional hypothesis that IO ensemble synchrony, for which STO amplitude could be used as an indirect measure, modulates the CF burst and in turn allows for online adaptation of learning speeds. Our model predicts that, as synchrony increases, STO amplitude goes up and the average number of AP spikelets goes down. The PF/PC synapse is modulated by CF activity and the size of the CF spike burst may determine the plasticity effect 
. Keeping this in mind, CF burst size could well be an indicator of the state a learning process is in, allowing quick and coarse learning at low ensemble STO amplitudes (i.e. low synchrony) and then more refined learning at higher amplitudes. Since single CF spikes have been shown to cause LTP in PCs rather than LTD 
, the highest STO amplitudes where few AP spikelets occur are conceivably a way of unlearning (preventing the biological equivalent of overfitting data) or converting the direction of learning. A system that has a way of adequately adapting the coarseness with which it learns online can speed up a learning process without sacrificing precision.
It is important to note that simulation results never translate directly to empirical data: our model utilizes ion channel descriptions taken from in vitro preparations from several animal species. It demonstrates principles underlying the generation of olivary STOs and spikes, but such things as the actual number of AP spikelets or the time between two such spikelets may differ from data acquired from an actual cell, much as it may also differ between species. Even so, our model provides valuable insight into how olivary AP spikelet distributions may unfold under different conditions and even how meaningful the CF burst may be in vivo.