(D) Changes in firing rate induced by membrane voltage fluctuations for low, mid and high regions of the H curves for each model.

With AT 2 2 mV, fluctuation-induced increases in initial spike firing rates are 23 spikes/s and 30 spikes/s under baseline and with increased membrane conductance, respectively (Fig 4Bii—4D).

As a result, the changes in firing rate , rheobase and gain induced by membrane voltage fluctuations correspond more closely to those observed in stellate cells when AT is set to 15 mV (Fig 4D and 4E).

By generating a shallow f- V, a large AT limits the ability for a change in voltage brought about through random fluctuations to increase spike firing rate .

Conversely, when AT is small and the f-Vrelationship is steep, voltage fluctuations can give rise to a large change in spike firing rate (Fig 7D).

We proceeded to measure changes in rheobase and initial firing rate associated Withf-I curves resulting from voltage fluctuations under each of the conductance conditions.

To quantify potential changes in the f-I curve more carefully, we also measured the effects of voltage fluctuations on firing rate within discrete regions of the f-I curve (Fig 1D; low, mid and high).

Previous modeling and experimental work has shown that random voltage fluctuations induce the largest increase in firing rate in the low spike rate region of the f-I curve, near the transition between rest and firing [8—10,19,20,24].

For each cell, we measured the change in firing rate brought about by voltage fluctuations for low, mid and high current input regions relative to the same cell’sf-I curve acquired without fluctuations.

Therefore, higher order terms practically influence weight dynamics only through firing rates , so that by applying the approximation the last term can be obtained.

Each inhibitory neuron receives stronger inputs from one of the output neuron groups and, as a result, shows a higher firing rate for the corresponding external signal.

The input layer shows rate-modulated Poisson firing based on events at the external layer and external noise, which is approximated with the constant firing rate {no}.

We considered the case for information encoded in the correlated activity of input neurons [34,35], and fixed the average firing rate of all input neurons at the constant value UOX (See Table 1 and 2 for the list of variables and parameters).

If the firing rate of input neuron i is of the neuron qiy, then common inputs from the external layer induce a temporal correlation proportional to

To make a clear comparison, in the simulation of random noise, we kept qN = 0 and changed the spontaneous firing rate of the input neurons (no) to modify the noise intensity, whereas in simulation of crosstalk noise we removed random noise (i.e., no 2 0) and changed qN.

In addition, when information is coded by firing rate , homeostatic plasticity is critically important, because STDP itself does not mimic Bienenstock-Cooper-Munro learning [18].

By solving the self-consistency condition (Eq (34) in Methods), the firing rates of inhibitory neurons are approximated as

Here, we used both a reduced firing rate model and numerical simulations of a spiking network model of the striatum to analyze the dynamic balance of spiking activities in D1 and D2 MSNs.

Our analysis and simulations show that the asymmetric connectivity between these neurons gives rise to a decision transition threshold (DTT), as a consequence D1 (D2) neurons have higher firing rate at lower (higher) average cortical firing rates .

These inequalities imply that if the two MSN subpopulations receive the same amount of excitatory input, D2 MSNs will always have a higher firing rate .

In our spiking network simulations this corresponded to a lower mean firing rate of the D1 population compared to the D2 population.

To estimate how much additional excitation would be required for D1 MSNs to have their firing rates exceed over those of D2 MSNs, we systematically varied the drive of cortical inputs to D1 and D2 MSNs and calculated the response firing rates of the two subpopulations, for the firing rate model (Fig 2).

Here we describe the effect of the heterogenous connectivity of D1 and D2 neurons on their mutual interactions using both a reduced firing rate model and numerical simulations of a spiking striatal network model.

We show that the firing rates of both D1 and D2 MSNs change in a non-monotonic manner in response to cortical input rates and correlations.

Correlations in the input can further change the range of cortical inputs for which either D1 or D2 MSNs have the higher firing rate .

Specifically, we evaluated the firing rates of the D1 and D2 MSNs, in response to cortical input rates and input correlations.

We analyzed the effect of factors, such as the mean firing rate and the recording duration, on the detectability of oscillations and their significance, and tested these theoretical results on experimental data recorded in Parkinsonian nonhuman primates.

The generation of each spike within the train is assumed to be dependent on an underlying instantaneous firing rate .

Thus, despite an underlying oscillatory firing rate , in most cases the neuron will skip a large portion of the oscillation cycle or even entire cycles [11].

The most simplistic statistical spike train model assumes that the generation of each spike is dependent solely on the underlying instantaneous firing rate , and is independent of all other previous spikes.

where r0 is the baseline firing rate , 0 g m g 1 is the modulation index, and f0 is the oscillation frequency.

The SNR of these simulated neurons varies linearly as a function of the base firing rate of the neuron (Fig 1H).

As a result, the detection of significant oscillations crossing a specific SNR threshold is not possible for a neuron with a low baseline firing rate (Fig 1E), compared to neurons with higher firing rates (Fig 1F—1G), which have a higher SNR and are therefore identified as oscillatory.

Previous work has demonstrated that both the firing rate of neurons (rate code) and the timing of their stimulus-evoked responses (temporal code) can be used by auditory cortical neurons to represent temporal information.

Neurons not classified as synchronized, non-synchronized, or mixed response, were only included in our analysis (as an atypical response) if they responded to acoustic pulse trains; the criteria for this was a significant vector strength for two neighboring IPIs and/or firing rate significantly above or below (2 o) the spontaneous rate for two neighboring IPIs.

The firing rate at an IPI of 3 ms divided by the maximum firing rate for all IPIs in the range of 35 ms and 75 ms.

Non-synchronized neurons increase their firing rate monotonically with decreasing IPIs over the perceptual range of fusion without exhibiting envelope-locked responses (Fig.

Compared with real neurons, simulated synchronized neurons generally had lower firing rates .

Alternatively, we could use nonparametric models such as Gaussian processes, which have been used to model low-dimensional tuning curves and firing rate maps [36, 37].

The authors also proposed a “nonlinear MID” in which the standard MID estimator is extended by setting the firing rate to be a quadratic function of the form f(kTs+sTC s).

Within the time bin (constrained by the refractory period or firing rate saturation).