scholarly journals Firing rate distributions in spiking networks with heterogeneous connectivity

2019 ◽  
Author(s):  
Marina Vegué ◽  
Alex Roxin
Keyword(s):  
Experimental Data ◽  
Firing Rate ◽  
Neuronal Activity ◽  
Diffusion Approximation ◽  
Large Amplitude ◽  
Spiking Neurons ◽  
Arbitrary Degree ◽  
Current Form ◽  
Firing Rates ◽  
Spiking Networks

AbstractMeanfield theory for networks of spiking neurons based on the so-called diffusion approximation has been used to calculate certain measures of neuronal activity which can be compared with experimental data. This includes the distribution of firing rates across the network. However, the theory in its current form applies only to networks in which there is relatively little heterogeneity in the number of incoming and outgoing connections per neuron. Here we extend this theory to include networks with arbitrary degree distributions. Furthermore, the theory takes into account correlations in the in-degree and out-degree of neurons, which would arise e.g. in the case of networks with hub-like neurons. Finally, we show that networks with broad and postively correlated degrees can generate a large-amplitude sustained response to transient stimuli which does not occur in more homogeneous networks.

Quantitative Analysis of Abducens Neuron Discharge Dynamics During Saccadic and Slow Eye Movements

1999 ◽  
Vol 82 (5) ◽  
pp. 2612-2632 ◽  
Author(s):  
Pierre A. Sylvestre ◽  
Kathleen E. Cullen
Keyword(s):  
Eye Movements ◽  
Firing Rate ◽  
Eye Movement ◽  
Neuronal Activity ◽  
Smooth Pursuit ◽  
Slow Phase ◽  
Vestibular Nystagmus ◽  
Firing Rates ◽  
Rapid Eye Movements ◽  
Eye Velocity

The mechanics of the eyeball and its surrounding tissues, which together form the oculomotor plant, have been shown to be the same for smooth pursuit and saccadic eye movements. Hence it was postulated that similar signals would be carried by motoneurons during slow and rapid eye movements. In the present study, we directly addressed this proposal by determining which eye movement–based models best describe the discharge dynamics of primate abducens neurons during a variety of eye movement behaviors. We first characterized abducens neuron spike trains, as has been classically done, during fixation and sinusoidal smooth pursuit. We then systematically analyzed the discharge dynamics of abducens neurons during and following saccades, during step-ramp pursuit and during high velocity slow-phase vestibular nystagmus. We found that the commonly utilized first-order description of abducens neuron firing rates (FR = b + kE + rE˙, where FR is firing rate, E and E˙ are eye position and velocity, respectively, and b, k, and r are constants) provided an adequate model of neuronal activity during saccades, smooth pursuit, and slow phase vestibular nystagmus. However, the use of a second-order model, which included an exponentially decaying term or “slide” (FR = b + kE + rE˙ + uË − c[Formula: see text]), notably improved our ability to describe neuronal activity when the eye was moving and also enabled us to model abducens neuron discharges during the postsaccadic interval. We also found that, for a given model, a single set of parameters could not be used to describe neuronal firing rates during both slow and rapid eye movements. Specifically, the eye velocity and position coefficients ( r and k in the above models, respectively) consistently decreased as a function of the mean (and peak) eye velocity that was generated. In contrast, the bias ( b, firing rate when looking straight ahead) invariably increased with eye velocity. Although these trends are likely to reflect, in part, nonlinearities that are intrinsic to the extraocular muscles, we propose that these results can also be explained by considering the time-varying resistance to movement that is generated by the antagonist muscle. We conclude that to create realistic and meaningful models of the neural control of horizontal eye movements, it is essential to consider the activation of the antagonist, as well as agonist motoneuron pools.

scholarly journals Firing rate homeostasis occurs in the absence of neuronal activity-regulated transcription

2019 ◽  
Author(s):  
Kelsey M. Tyssowski ◽  
Katherine C. Letai ◽  
Samuel D. Rendall ◽  
Anastasia Nizhnik ◽  
Jesse M. Gray
Keyword(s):  
Firing Rate ◽  
Neuronal Activity ◽  
Cortical Neurons ◽  
Molecular Mechanisms ◽  
Neuronal Circuits ◽  
Electrode Arrays ◽  
Knock Out ◽  
Firing Rates ◽  
The Face ◽  
Homeostatic Mechanisms

ABSTRACTDespite dynamic inputs, neuronal circuits maintain relatively stable firing rates over long periods. This maintenance of firing rate, or firing rate homeostasis, is likely mediated by homeostatic mechanisms such as synaptic scaling and regulation of intrinsic excitability. Because some of these homeostatic mechanisms depend on transcription of activity-regulated genes, including Arc and Homer1a, we hypothesized that activity-regulated transcription would be required for firing rate homeostasis. Surprisingly, however, we found that cultured mouse cortical neurons grown on multi-electrode arrays homeostatically adapt their firing rates to persistent pharmacological stimulation even when activity-regulated transcription is disrupted. Specifically, we observed firing rate homeostasis Arc knock-out neurons, as well as knock-out neurons lacking activity-regulated transcription factors, AP1 and SRF. Firing rate homeostasis also occurred normally during acute pharmacological blockade of transcription. Thus, firing rate homeostasis in response to increased neuronal activity can occur in the absence of neuronal-activity-regulated transcription.SIGNIFICANCE STATEMENTNeuronal circuits maintain relatively stable firing rates even in the face of dynamic circuit inputs. Understanding the molecular mechanisms that enable this firing rate homeostasis could potentially provide insight into neuronal diseases that present with an imbalance of excitation and inhibition. However, the molecular mechanisms underlying firing rate homeostasis are largely unknown.It has long been hypothesized that firing rate homeostasis relies upon neuronal activity-regulated transcription. For example, a 2012 review (PMID 22685679) proposed it, and a 2014 modeling approach established that transcription could theoretically both measure and control firing rate (PMID 24853940). Surprisingly, despite this prediction, we found that cortical neurons undergo firing rate homeostasis in the absence of activity-regulated transcription, indicating that firing rate homeostasis is controlled by non-transcriptional mechanisms.

Synchrony in Heterogeneous Networks of Spiking Neurons

2000 ◽  
Vol 12 (7) ◽  
pp. 1607-1641 ◽  
Author(s):  
L. Neltner ◽  
D. Hansel ◽  
G. Mato ◽  
C. Meunier
Keyword(s):  
Firing Rate ◽  
Heterogeneous Networks ◽  
Spiking Neurons ◽  
The Other ◽  
Average Firing Rate ◽  
Firing Rates ◽  
Recurrent Excitation ◽  
Asynchronous State ◽  
High Firing ◽  
Inhibitory Networks

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly unstable. We show that at low firing rates, synchrony is more robust in excitatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We introduce a new regime where all inputs, external and internal, are strong and have opposite effects that cancel each other when averaged. In this regime, the robustness of synchrony is strongly enhanced, and robust synchrony can be achieved at a high firing rate in inhibitory networks. On the other hand, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.

Multisecond Periodicities in Basal Ganglia Firing Rates Correlate With Theta Bursts in Transcortical and Hippocampal EEG

2002 ◽  
Vol 87 (2) ◽  
pp. 1118-1122 ◽  
Author(s):  
Kelly A. Allers ◽  
David N. Ruskin ◽  
Debra A. Bergstrom ◽  
Lauren E. Freeman ◽  
Leyla J. Ghazi ◽  
...  
Keyword(s):  
Basal Ganglia ◽  
Firing Rate ◽  
Neuronal Activity ◽  
Field Potentials ◽  
Firing Rates ◽  
Rate Oscillations ◽  
Parietal Cortices ◽  
Hippocampal Eeg ◽  
Wavelet Analyses ◽  
Band Activity

Multisecond oscillations in firing rate with periods in the range of 2–60 s (mean, 20–35 s) are present in 50–90% of spike trains from basal ganglia neurons recorded from locally anesthetized, immobilized rats. To determine whether these periodic oscillations are associated with similar periodicities in cortical activity, transcortical electroencephalographic (EEG) activity was recorded in conjunction with single- or dual-unit neuronal activity in the subthalamic nucleus (STN) or the globus pallidus (GP), and the data were analyzed with spectral and wavelet analyses. Multisecond oscillations in firing rates of 31% of the STN neurons and 46% of the GP neurons with periodicities significantly correlated with bursts of theta (4–7 Hz) activity in transcortical EEG. Further recordings of localized field potentials in the hippocampus and frontal or parietal cortices simultaneously with GP unit activity showed field potentials from the hippocampus, but not from the frontal or parietal cortices, exhibited bursts of theta rhythm that were correlated with GP firing rate oscillations. These results demonstrate a functional connectivity between basal ganglia neuronal activity and theta band activity in the hippocampus.

scholarly journals A deep convolutional visual encoding model of neuronal responses in the LGN

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Eslam Mounier ◽  
Bassem Abdullah ◽  
Hani Mahdi ◽  
Seif Eldawlatly
Keyword(s):  
Firing Rate ◽  
Visual Information ◽  
Visual Stimulation ◽  
Neuronal Population ◽  
Neuronal Firing ◽  
Electrode Arrays ◽  
Deep Convolutional Neural Networks ◽  
Firing Rates ◽  
Spatiotemporal Representation

AbstractThe Lateral Geniculate Nucleus (LGN) represents one of the major processing sites along the visual pathway. Despite its crucial role in processing visual information and its utility as one target for recently developed visual prostheses, it is much less studied compared to the retina and the visual cortex. In this paper, we introduce a deep learning encoder to predict LGN neuronal firing in response to different visual stimulation patterns. The encoder comprises a deep Convolutional Neural Network (CNN) that incorporates visual stimulus spatiotemporal representation in addition to LGN neuronal firing history to predict the response of LGN neurons. Extracellular activity was recorded in vivo using multi-electrode arrays from single units in the LGN in 12 anesthetized rats with a total neuronal population of 150 units. Neural activity was recorded in response to single-pixel, checkerboard and geometrical shapes visual stimulation patterns. Extracted firing rates and the corresponding stimulation patterns were used to train the model. The performance of the model was assessed using different testing data sets and different firing rate windows. An overall mean correlation coefficient between the actual and the predicted firing rates of 0.57 and 0.7 was achieved for the 10 ms and the 50 ms firing rate windows, respectively. Results demonstrate that the model is robust to variability in the spatiotemporal properties of the recorded neurons outperforming other examined models including the state-of-the-art Generalized Linear Model (GLM). The results indicate the potential of deep convolutional neural networks as viable models of LGN firing.

Synaptic Plasticity In Vitro and In Silico: Insights into an Intracellular Signaling Maze

Physiology ◽  
2006 ◽  
Vol 21 (4) ◽  
pp. 289-296 ◽  
Author(s):  
Sriram M. Ajay ◽  
Upinder S. Bhalla
Keyword(s):  
Experimental Data ◽  
Synaptic Plasticity ◽  
Neuronal Activity ◽  
In Silico ◽  
Intracellular Signaling ◽  
Signaling Networks ◽  
Functional Roles ◽  
Current State ◽  
History Of

Synaptic plasticity provides a record of neuronal activity and is a likely basis for memory. The early apparent simplicity of the process of synaptic plasticity has been lost in a flood of experimental data that now implicates some 200 signaling molecules in cellular memory. It is now clear that these signaling networks perform surprisingly sophisticated cellular decisions that weigh factors such as input patterns, location of stimulus, history of activity, and context. Computer models have followed experiments into this maze of molecular detail, often matching closely with their experimental counterparts, but perhaps losing simplicity in the process. Here, we suggest that the merger of models and experiment have begun to restore the earlier simplicity by outlining a few key functional roles for signaling networks in synaptic plasticity. In this review, we discuss the current state of understanding of synaptic plasticity in terms of models and experiments.

Encoding timing and intensity in the ventral cochlear nucleus of the cat

1986 ◽  
Vol 56 (2) ◽  
pp. 261-286 ◽  
Author(s):  
W. S. Rhode ◽  
P. H. Smith
Keyword(s):  
Firing Rate ◽  
Cochlear Nucleus ◽  
Auditory Nerve ◽  
Cell Types ◽  
Nerve Fibers ◽  
Frequency Selectivity ◽  
Firing Rates ◽  
Ventral Cochlear Nucleus ◽  
Auditory Nerve Fibers ◽  
Different Cell Types

Physiological response properties of neurons in the ventral cochlear nucleus have a variety of features that are substantially different from the stereotypical auditory nerve responses that serve as the principal source of activation for these neurons. These emergent features are the result of the varying distribution of auditory nerve inputs on the soma and dendrites of the various cell types within the nucleus; the intrinsic membrane characteristics of the various cell types causing different responses to the same input in different cell types; and secondary excitatory and inhibitory inputs to different cell types. Well-isolated units were recorded with high-impedance glass microelectrodes, both intracellularly and extracellularly. Units were characterized by their temporal response to short tones, rate vs. intensity relation, and response areas. The principal response patterns were onset, chopper, and primary-like. Onset units are characterized by a well-timed first spike in response to tones at the characteristic frequency. For frequencies less than 1 kHz, onset units can entrain to the stimulus frequency with greater precision than their auditory nerve inputs. This implies that onset units receive converging inputs from a number of auditory nerve fibers. Onset units are divided into three subcategories, OC, OL, and OI. OC units have extraordinarily wide dynamic ranges and low-frequency selectivity. Some are capable of sustaining firing rates of 800 spikes/s at high intensities. They have the smallest standard deviation and coefficient of variation of the first spike latency of any cells in the cochlear nuclei. OC units are candidates for encoding intensity. OI and OL units differ from OC units in that they have dynamic ranges and frequency selectivity ranges much like those of auditory nerve fibers. They differ from one another in their steady-state firing rates; OI units fire mainly at the onset of a tone. OI units also differ from OL units in that they prefer frequency sweeps in the low to high direction. Primary-like-with-notch (PLN) units also respond to tones with a well-timed first spike. They differ from onset cells in that the onset peak is not always as precise as the spontaneous rate is higher. A comparison of spontaneous firing rate and saturation firing rate of PLN units with auditory nerve fibers suggest that PLN units receive one to four auditory nerve fiber inputs. Chopper units fire in a sustained regular manner when they are excited by sound.(ABSTRACT TRUNCATED AT 400 WORDS)

Functional Properties of Single Motor Units in the Inferior Head of Human Lateral Pterygoid Muscle: Task Firing Rates

2002 ◽  
Vol 88 (2) ◽  
pp. 751-760 ◽  
Author(s):  
I. Phanachet ◽  
T. Whittle ◽  
K. Wanigaratne ◽  
G. M. Murray
Keyword(s):  
Firing Rate ◽  
Correlation Coefficients ◽  
Motor Units ◽  
Lateral Pterygoid Muscle ◽  
Jaw Movements ◽  
Firing Rates ◽  
Single Motor ◽  
Single Motor Units ◽  
Fine Control ◽  
Contralateral Movement

The precise function of the inferior head of the human lateral pterygoid muscle (IHLP) is unclear. The aim of this study was to clarify the normal function of the IHLP. The hypothesis was that an important function of the IHLP is the generation and fine control of horizontal (i.e., anteroposterior and mediolateral) jaw movements. The activities of 50 single motor units (SMUs) were recorded from IHLP (14 subjects) during two- or three-step contralateral movement ( n = 36) and/or protrusion ( n = 33). Most recording sites were identified by computer tomography. There was a statistically significant overall increase in firing rate as the magnitude of jaw displacement increased between the holding phases (range of increments: 0.3–1.6 mm). The firing rates during the dynamic phases for each unit were significantly greater than those during the previous holding phases but less than those during the subsequent holding phases. For the contralateral step task at the intermediate rate, the cross-correlation coefficients between jaw displacement in the mediolateral axis and the mean firing rate of each unit ranged from r = 0.29 to 0.77; mean ± SD; r = 0.49 ± 0.13 (protrusive step task: r = 0.12–0.74, r = 0.44 ± 0.14 for correlation with anterior–posterior axis). The correlation coefficients at the fast rate during the contralateral step task and the protrusive step task were significantly higher than those at the slow rate. The firing rate change of the SMUs per unit displacement between holding phases was significantly greater for the lower-threshold than for the higher-threshold units during contralateral movement and protrusion. After dividing IHLP into four regions, the SMUs recorded in the superior part exhibited significantly greater mean firing rate changes per unit displacement during protrusion than for the SMUs recorded in the inferior part. Significantly fewer units were related to the protrusive task in the superior–medial part. These data support previously proposed notions of functional heterogeneity within IHLP. The present findings provide further evidence for an involvement of the IHLP in the generation and fine control of horizontal jaw movements.

scholarly journals Multimodal Medullary Neurons and Correlational Linkages of the Respiratory Network

1999 ◽  
Vol 82 (1) ◽  
pp. 188-201 ◽  
Author(s):  
Zhongzeng Li ◽  
Kendall F. Morris ◽  
David M. Baekey ◽  
Roger Shannon ◽  
Bruce G. Lindsey
Keyword(s):  
Firing Rate ◽  
Nucleus Tractus Solitarius ◽  
Motor Pattern ◽  
Sensory Modality ◽  
Spike Trains ◽  
Negative Feedback Regulation ◽  
Firing Rates ◽  
Respiratory Network ◽  
Cross Correlation Analysis ◽  
Stimulation Of

This study addresses the hypothesis that multiple sensory systems, each capable of reflexly altering breathing, jointly influence neurons of the brain stem respiratory network. Carotid chemoreceptors, baroreceptors, and foot pad nociceptors were stimulated sequentially in 33 Dial-urethan–anesthetized or decerebrate vagotomized adult cats. Neuronal impulses were monitored with microelectrode arrays in the rostral and caudal ventral respiratory group (VRG), nucleus tractus solitarius (NTS), and n. raphe obscurus. Efferent phrenic nerve activity was recorded. Spike trains of 889 neurons were analyzed with cycle-triggered histograms and tested for respiratory-modulated firing rates. Responses to stimulus protocols were assessed with peristimulus time and cumulative sum histograms. Cross-correlation analysis was used to test for nonrandom temporal relationships between spike trains. Spike-triggered averages of efferent phrenic activity and antidromic stimulation methods provided evidence for functional associations of bulbar neurons with phrenic motoneurons. Spike train cross-correlograms were calculated for 6,471 pairs of neurons. Significant correlogram features were detected for 425 pairs, including 189 primary central peaks or troughs, 156 offset peaks or troughs, and 80 pairs with multiple peaks and troughs. The results provide evidence that correlational medullary assemblies include neurons with overlapping memberships in groups responsive to different sets of sensory modalities. The data suggest and support several hypotheses concerning cooperative relationships that modulate the respiratory motor pattern. 1) Neurons responsive to a single tested modality promote or limit changes in firing rate of multimodal target neurons. 2) Multimodal neurons contribute to changes in firing rate of neurons responsive to a single tested modality. 3) Multimodal neurons may promote responses during stimulation of one modality and “limit” changes in firing rates during stimulation of another sensory modality. 4) Caudal VRG inspiratory neurons have inhibitory connections that provide negative feedback regulation of inspiratory drive and phase duration.

Identification of Basolateral Amygdala Projection Cells and Interneurons Using Extracellular Recordings

2006 ◽  
Vol 96 (6) ◽  
pp. 3257-3265 ◽  
Author(s):  
Ekaterina Likhtik ◽  
Joe Guillaume Pelletier ◽  
Andrei T. Popescu ◽  
Denis Paré
Keyword(s):  
Firing Rate ◽  
Basolateral Amygdala ◽  
Cell Group ◽  
Small Subset ◽  
Cortical Projection ◽  
Antidromic Activation ◽  
Extracellular Recordings ◽  
Firing Rates ◽  
Cell Groups ◽  
Exact Position

This study tested whether firing rate and spike shape could be used to distinguish projection cells from interneurons in extracellular recordings of basolateral amygdala (BLA) neurons. To this end, we recorded BLA neurons in isoflurane-anesthetized animals with tungsten microelectrodes. Projection cells were identified by antidromic activation from cortical projection sites of the BLA. Although most projection cells fired spontaneously at low rates (<1 Hz), an important subset fired at higher rates (up to 6.8 Hz). In fact, the distribution of firing rates in projection cells and unidentified BLA neurons overlapped extensively, even though the latter cell group presumably contains a higher proportion of interneurons. The only difference between the two distributions was a small subset (5.1%) of unidentified neurons with unusually high firing rates (9–16 Hz). Similarly, distributions of spike durations in both cell groups were indistinguishable, although most of the fast-firing neurons had spike durations at the low end of the distribution. However, we observed that spike durations depended on the exact position of the electrode with respect to the recorded cell, varying by as much as 0.7 ms. Thus neither firing rate nor spike waveform allowed for unequivocal separation of projection cells from interneurons. Nevertheless, we propose the use of two firing rate cutoffs to obtain relatively pure samples of projection cells and interneurons: ≤1 Hz for projection cells and ≥7 Hz for fast-spiking interneurons. Supplemented with spike-duration cutoffs of ≥0.7 ms for projection cells and ≤0.5 ms for interneurons, this approach should keep instances of misclassifications to a minimum.

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