Index of papers in PLOS Comp. Biol. that mention

**firing rate**

A gradual increase in membrane resistance is critical to reduced fluctuation-based modulation of input-output responses in an eLlF model | (D) Changes in firing rate induced by membrane voltage fluctuations for low, mid and high regions of the H curves for each model. |

A gradual increase in membrane resistance is critical to reduced fluctuation-based modulation of input-output responses in an eLlF 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). |

A gradual increase in membrane resistance is critical to reduced fluctuation-based modulation of input-output responses in an eLlF model | 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). |

Large AT values reduce modulation of input-output responses through voltage fluctuations by slowing membrane voltage | 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 . |

Large AT values reduce modulation of input-output responses through voltage fluctuations by slowing membrane voltage | 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). |

Manipulation of membrane conductance using dynamic clamp alters voltage trajectories and modulation of input-output responses by voltage fluctuations | 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. |

Stellate cell input-output functions are modulated weakly by membrane voltage fluctuations | 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). |

Stellate cell input-output functions are modulated weakly by membrane voltage fluctuations | 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]. |

Stellate cell input-output functions are modulated weakly by membrane voltage fluctuations | 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. |

firing rate is mentioned in 23 sentences in this paper.

Topics mentioned in this paper:

- input-output (58)
- firing rate (23)
- ANOVA (9)

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

Excitatory and inhibitory STDP cooperatively shape structured lateral connections | 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. |

Model | 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}. |

Model | 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). |

Model | 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 |

Optimal correlation timescale changes depend on the noise source | 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. |

STDP and Bayesian ICA | 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]. |

dev Ma Ma d: g ZLanfv’ VEGA? Z qquv’p — NaWZMa WYZL“ Wig", vi Z qquV/p v,=1 p v’=1 P | By solving the self-consistency condition (Eq (34) in Methods), the firing rates of inhibitory neurons are approximated as |

firing rate is mentioned in 12 sentences in this paper.

Topics mentioned in this paper:

- synaptic weight (44)
- feedforward (14)
- ICA (13)

Abstract | 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. |

Author Summary | 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 . |

D1 MSNs require overall stronger input from cortex than D2 MSNs | 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 . |

D1 MSNs require overall stronger input from cortex than D2 MSNs | In our spiking network simulations this corresponded to a lower mean firing rate of the D1 population compared to the D2 population. |

D1 MSNs require overall stronger input from cortex than D2 MSNs | 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). |

Introduction | 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. |

Introduction | 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. |

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

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

firing rate is mentioned in 89 sentences in this paper.

Topics mentioned in this paper:

- firing rates (89)
- basal ganglia (21)
- feedforward (15)

Abstract | 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. |

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

Introduction | 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]. |

Introduction | 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. |

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

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

Results | 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. |

firing rate is mentioned in 49 sentences in this paper.

Topics mentioned in this paper:

- spike train (54)
- firing rate (49)
- Poisson process (14)

Abstract | 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. |

Abstract | 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. |

Abstract | 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. |

Author Summary | 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. |

Author Summary | 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. |

Introduction | 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]. |

Introduction | 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. |

Introduction | 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. |

firing rate is mentioned in 115 sentences in this paper.

Topics mentioned in this paper:

- firing rate (115)
- computational modeling (5)
- single cell (5)

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

Current-based vs conductance-based synaptic input | As before, the postsynaptic firing rate has a large effect on detectability and estimation accuracy with higher rates resulting in faster detection of inputs. |

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

Detection of artificial EPSCs immersed in fluctuating noise | 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). |

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

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

Prediction of spikes | 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. |

U | 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. |

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

input experiments. | 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. |

input experiments. | 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. |

firing rate is mentioned in 19 sentences in this paper.

Topics mentioned in this paper:

- synaptic inputs (32)
- functional connectivity (26)
- spike trains (19)

Covariance estimation | 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 . |

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

Data processing | 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]. |

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

Data processing | 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 Csparse+latent estimator is most efficient in neural data | The instantaneous firing rates were inferred using sparse nonnegative deconvolution [61] (Fig. |

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

firing rate is mentioned in 7 sentences in this paper.

Topics mentioned in this paper:

Author Summary | 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. |

Data analysis | 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. |

Data analysis | 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. |

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

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

firing rate is mentioned in 5 sentences in this paper.

Topics mentioned in this paper:

- simulated neurons (29)
- computational model (20)
- excitatory input (16)

Association layer | 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. |

Introduction | 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]. |

U | Firing Rate (Hz) |

Vibrotactile discrimination task | 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]. |

Vibrotactile discrimination task | 7.5%) to the firing rates of the input units. |

firing rate is mentioned in 5 sentences in this paper.

Topics mentioned in this paper:

- fixation point (20)
- time step (17)
- learning rule (14)

Abstract | 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 . |

Experimental measures of behavior and neural activities | 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. |

Experimental measures of behavior and neural activities | 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. |

Sensitivity and CC signals as a function of K | Synaptic weights are random and balanced, leading to a mean firing rate of 21.8 Hz in the population. |

firing rate is mentioned in 4 sentences in this paper.

Topics mentioned in this paper:

- spike trains (12)
- experimental data (10)
- decision-making (8)

Identifying high-dimensional subspaces | 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]. |

Relationship to previous work | 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). |

minimum information loss for binary spiking | Within the time bin (constrained by the refractory period or firing rate saturation). |

firing rate is mentioned in 3 sentences in this paper.

Topics mentioned in this paper:

- log-likelihood (30)
- basis functions (20)
- mutual information (14)

A phenomenological model | 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. |

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

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

firing rate is mentioned in 3 sentences in this paper.

Topics mentioned in this paper:

- synaptic input (12)
- action potentials (8)
- current injections (5)