Purkinje Cells

We thresholded the identified spatial filter for each Purkinje neuron at 50% of its maximum value before extracting the [Ca²⁺] related fluorescence trace. We then corrected for slow declines of fluorescence emissions as well as more rapid fluctuations in the fluorescence background, which were likely activity-induced. These two effects were separate from the fluctuations in LED illumination power. Slow declines of emissions were due to gradual bleaching of the Ca²⁺ indicator^{9 (link)}. Activity-induced background fluctuations arose from the indicator's non-specific pattern of staining^{4 (link),9 (link),20 (link)}, which labeled not only Purkinje neurons but also other, out of focus neuronal fibers and processes.
To correct for these two effects, we tracked the mean percentage change in fluorescence within all pixels situated outside neurons, denoted Φ(t), as a measure of background fluctuations. Φ(t) was typically within [–5%, +10%]. We corrected each full frame, F(t), by creating a new image, F'(t), where F'(t) = F(t) – Φ(t)*F₀, where F₀ is the time-averaged mean image of stack F(t). Fluorescence fluctuations in areas outside neurons were much reduced within F'(t). This also facilitated detection of Purkinje neurons' Ca²⁺ spikes, since the neuronal areas had likewise been corrected for bleaching and the out of focal plane fluctuations.
We performed algorithmic spike detection on the F'(t) traces by applying a temporal deconvolution with a decaying exponential of 150 ms time constant^{41 (link)}, applying a high-pass filter (8-pole Butterworth; –3 dB cutoff frequency of 8 Hz) and marking as spikes all positive-going threshold crossings at their local maximum. For each video recording, a spike detection threshold was chosen for each neuron so that false positives would occur at a rate <0.05 Hz, which is ∼2.5% −10% of Purkinje neurons' typical Ca²⁺ spike rates and comparable to prior percentages of false positive Ca²⁺ spike detection in these cells^{4 (link),6 (link),20 (link)}. To estimate the rate of false positive detection, we examined 20 fluorescence traces generated from independent sets of randomly chosen pixels. The number of pixels randomly sampled for each trace was set equal to the mean number of pixels within the neurons' spatial filters for that experiment.
The pairwise correlation coefficient for two cells was defined as Pearson's correlation coefficient, the covariance in the activity between the two spike trains divided by the product of their standard deviations. This yielded a correlation coefficient within [-1,1].