Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates , and switch to a phase-dependent mode at high rates.

Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells.

We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell.

It has been shown that the PRC of tonically firing Purkinje Cells is flat at low firing rates , which has profound implications for information processing in the cerebellum.

Here, we propose a novel method to estimate the PRC of single Purkinje cells at various firing rates and use it to unveil the smooth transition between flat and phasic PRC.

The intrinsic electrical activity of Purkinje cells (PCs) exhibits a large repertoire of dynamical behaviors, including spontaneous firing of simple action potentials (APs), bistability of the firing rate , and hysteresis [1—4].

In addition, the extended range of PCs firing rates during behavior suggests that the rate of APs, its sudden transitions, its coherence across PCs, and the AP timing synchronization may contribute to information representation, processing, and downstream relaying.

Unexpectedly, they reported that the PC’s intrinsic firing rate has a profound effect on the response properties: the PRC of PCs firing at low rates displays a flat profile, suggesting that neurons behave like phase-independent inputs integrators; on the other hand, the PRC of PCs firing at high firing rates has a prominent peak, indicating a phase preference similar to coincidence detectors.

Detectability depends on input amplitude and output firing rate , and excitatory inputs are detected more readily than inhibitory.

As before, the postsynaptic firing rate has a large effect on detectability and estimation accuracy with higher rates resulting in faster detection of inputs.

Finally, we find that detection times decrease as ~ c/x2 with increasing input amplitudes, and are shorter for higher post-synaptic firing rates .

We assume that postsynaptic spiking is generated by a Poisson process with a rate determined by a baseline firing rate , the recent history of the neuron’s firing, as well as input produced by presynaptic spikes (see Methods for details).

Thus, in typical experiments only a subset of connections can be detected, with a low amplitude limit depending on recording time and firing rate .

We find that detection time for an input of amplitude x is approximately proportional to 1 / x2 and also depends on firing rates .

When only few synaptic inputs are included in the grouped model the post-spike history accounts for nearly all of the variability in the firing rate (Fig.

2F , where the pre and postsynaptic neurons each have 5Hz firing rates and the amplitude of the synaptic connection is lo, this crossing point occurs around 20s.

Across postsynaptic firing rates r, these times are well approximated by c/ rx2 (Fig.

Although detection time likely depends also on presynaptic firing rates as well as time course of PSCs (not just their amplitude), here, for making the comparison clear, pre-synaptic rates for all inputs were held at 5Hz and PSC kernels had the same time course, differing only in amplitude.

The coupling coefficients accurately reconstruct both excitatory and inhibitory input amplitudes over a broad range, and this reconstruction becomes more accurate with higher postsynaptic firing rates (Fig.

Where the p X 1 vector x is a single observation of the firing rates of p neurons in a time bin of some duration, denotes expectation, and [,4 is the vector of expected firing rates .

firing rates in time bin t, and an independent estimate of the mean firing rates 5c, the sample covariance matrix,

The measured fluorescent traces were deconvolved to reconstruct the firing rates for each neuron: First, the first principal component was subtracted from the raw traces in order to reduce common mode noise related to small cardiovascular movements [60].

Then, the firing rates were estimated using by nonnegative deconvolution [61].

Orientation tuning was computed by fitting the mean firing rates for each direction of mo-1 c eXp (cos(¢ — 9 —|— 7t) — 1)] where b 2 c are the amplitudes of the two respective peaks, w is the tuning width, and 9 is the preferred direction.

The instantaneous firing rates were inferred using sparse nonnegative deconvolution [61] (Fig.

Both models are maximum-entropy models constrained to match the mean firing rates and the covariance matriX [57].

Indeed, there are reports of single neuron integrators in entorhinal corteX with stable firing rates that persist for ten minutes or more [23], which is orders of magnitude longer than the trials modeled here.

For example, if monkeys are trained to memorize the location of a visual stimulus, neurons in lateral intra-parietal cortex (LIP) represent this location as a persistent increase of their firing rate [2,3].

Firing Rate (Hz)

Neurons in this cortical area have broad tuning curves and either monotonically increase or decrease their firing rate as function of the frequency of the vibrotactile stimulus [50].

7.5%) to the firing rates of the input units.

Here we study the formation of such percepts under the assumption that they emerge from a linear readout, i.e., a weighted sum of the neurons’ firing rates .

First, neuron is trial-averaged activity in response to each tested stimulus s is given by the peri-stimulus time histogram (PSTH) or time-varying firing rate , mi(t; s) (Fig.

The CC curve for neuron i, denoted by di(t), measures the difference in firing rate (at each instant in time) between trials where the animal chose c = 1 and trials where it chose c = O—all experimental features (including stimulus value) being fixed.

Synaptic weights are random and balanced, leading to a mean firing rate of 21.8 Hz in the population.

Thus, the mathematical form used in the composite model has a dendritic sigmoid that changes the threshold and maximum firing rate of the somatic sigmoid.

It works by changing the output frequency of the cell from low (or zero) to high firing rates .

We create three abstract models to describe the input-output relationship from tuft and basal excitatory input to firing rate output.