Estimating Network Parameters From Combined Dynamics of Firing Rate and Irregularity of Single Neurons

2011 ◽  
Vol 105 (1) ◽  
pp. 487-500 ◽  
Author(s):  
Kosuke Hamaguchi ◽  
Alexa Riehle ◽  
Nicolas Brunel
Keyword(s):  
Firing Rate ◽  
Network Structure ◽  
Cortical Neurons ◽  
Optimal Parameter ◽  
Inhibitory Neurons ◽  
Local Network ◽  
Excitatory Postsynaptic Potential ◽  
Dimensional Manifold ◽  
Firing Irregularity ◽  
Recurrent Connections

High firing irregularity is a hallmark of cortical neurons in vivo, and modeling studies suggest a balance of excitation and inhibition is necessary to explain this high irregularity. Such a balance must be generated, at least partly, from local interconnected networks of excitatory and inhibitory neurons, but the details of the local network structure are largely unknown. The dynamics of the neural activity depends on the local network structure; this in turn suggests the possibility of estimating network structure from the dynamics of the firing statistics. Here we report a new method to estimate properties of the local cortical network from the instantaneous firing rate and irregularity (CV2) under the assumption that recorded neurons are a part of a randomly connected sparse network. The firing irregularity, measured in monkey motor cortex, exhibits two features; many neurons show relatively stable firing irregularity in time and across different task conditions; the time-averaged CV2 is widely distributed from quasi-regular to irregular (CV2 = 0.3–1.0). For each recorded neuron, we estimate the three parameters of a local network [balance of local excitation-inhibition, number of recurrent connections per neuron, and excitatory postsynaptic potential (EPSP) size] that best describe the dynamics of the measured firing rates and irregularities. Our analysis shows that optimal parameter sets form a two-dimensional manifold in the three-dimensional parameter space that is confined for most of the neurons to the inhibition-dominated region. High irregularity neurons tend to be more strongly connected to the local network, either in terms of larger EPSP and inhibitory PSP size or larger number of recurrent connections, compared with the low irregularity neurons, for a given excitatory/inhibitory balance. Incorporating either synaptic short-term depression or conductance-based synapses leads many low CV2 neurons to move to the excitation-dominated region as well as to an increase of EPSP size.

scholarly journals Estimating Instantaneous Irregularity of Neuronal Firing

2009 ◽  
Vol 21 (7) ◽  
pp. 1931-1951 ◽  
Author(s):  
Takeaki Shimokawa ◽  
Shigeru Shinomoto
Keyword(s):  
Firing Rate ◽  
Cortical Neurons ◽  
Bayesian Method ◽  
Local Variation ◽  
Neuronal Firing ◽  
Empirical Bayesian ◽  
Low Degree ◽  
Firing Irregularity ◽  
Spike Sequence

Cortical neurons in vivo had been regarded as Poisson spike generators that convey no information other than the rate of random firing. Recently, using a metric for analyzing local variation of interspike intervals, researchers have found that individual neurons express specific patterns in generating spikes, which may symbolically be termed regular, random, or bursty, rather invariantly in time. In order to study the dynamics of firing patterns in greater detail, we propose here a Bayesian method for estimating firing irregularity and the firing rate simultaneously for a given spike sequence, and we implement an algorithm that may render the empirical Bayesian estimation practicable for data comprising a large number of spikes. Application of this method to electrophysiological data revealed a subtle correlation between the degree of firing irregularity and the firing rate for individual neurons. Irregularity of firing did not deviate greatly around the low degree of dependence on the firing rate and remained practically unchanged for individual neurons in the cortical areas V1 and MT, whereas it fluctuated greatly in the lateral geniculate nucleus of the thalamus. This indicates the presence and absence of autocontrolling mechanisms for maintaining patterns of firing in the cortex and thalamus, respectively.

Computer Simulation of the Responses of Human Motoneurons to Composite 1A EPSPS: Effects of Background Firing Rate

1997 ◽  
Vol 77 (1) ◽  
pp. 405-420 ◽  
Author(s):  
Kelvin E. Jones ◽  
Parveen Bawa
Keyword(s):  
Computer Simulation ◽  
Firing Rate ◽  
Time Course ◽  
Current Model ◽  
Response Probability ◽  
Muscle Spindles ◽  
Excitatory Postsynaptic Potential ◽  
Biophysical Properties ◽  
Rhythmic Firing ◽  
The Relationship

Jones, Kelvin E. and Parveen Bawa. Computer simulation of the responses of human motoneurons to composite 1A EPSPS: effects of background firing rate. J. Neurophysiol. 77: 405–420, 1997. Two compartmental models of spinal alpha motoneurons were constructed to explore the relationship between background firing rate and response to an excitatory input. The results of these simulations were compared with previous results obtained from human motoneurons and discussed in relation to the current model for repetitively firing human motoneurons. The morphologies and cable parameters of the models were based on two type-identified cat motoneurons previously reported in the literature. Each model included five voltage-dependent channels that were modeled using Hodgkin-Huxley formalism. These included fast Na+ and K+ channels in the initial segment and fast Na+ and K+ channels as well as a slow K+ channel in the soma compartment. The density and rate factors for the slow K+ channel were varied until the models could reproduce single spike AHP parameters for type-identified motoneurons in the cat. Excitatory synaptic conductances were distributed along the equivalent dendrites with the same density described for la synapses from muscle spindles to type-identified cat motoneurons. Simultaneous activation of all synapses on the dendrite resulted in a large compound excitatory postsynaptic potential (EPSP). Brief depolarizing pulses injected into a compartment of the equivalent dendrite resulted in pulse potentials (PPs), which resembled the compound EPSPs. The effects of compound EPSPs and PPs on firing probability of the two motoneuron models were examined during rhythmic firing. Peristimulus time histograms, constructed between the stimulus and the spikes of the model motoneuron, showed excitatory peaks whose integrated time course approximated the time course of the underlying EPSP or PP as has been shown in cat motoneurons. The excitatory peaks were quantified in terms of response probability, and the relationship between background firing rate and response probability was explored. As in real human motoneurons, the models exhibited an inverse relationship between response probability and background firing rate. The biophysical properties responsible for the relationship between response probability and firing rate included the shapes of the membrane voltage trajectories between spikes and nonlinear changes in PP amplitude during the interspike interval at different firing rates. The results from these simulations suggest that the relationship between response probability and background firing rate is an intrinsic feature of motoneurons. The similarity of the results from the models, which were based on the properties of cat motoneurons, and those from human motoneurons suggests that the biophysical properties governing rhythmic firing in human motoneurons are similar to those of the cat.

scholarly journals Intrinsic Dynamics in Neuronal Networks. I. Theory

2000 ◽  
Vol 83 (2) ◽  
pp. 808-827 ◽  
Author(s):  
P. E. Latham ◽  
B. J. Richmond ◽  
P. G. Nelson ◽  
S. Nirenberg
Keyword(s):  
Firing Rate ◽  
Firing Pattern ◽  
Neuronal Networks ◽  
Network Connectivity ◽  
Excitatory Input ◽  
High Rate ◽  
Inhibitory Neurons ◽  
Inhibitory Input ◽  
Dynamic Interactions ◽  
Firing Patterns

Many networks in the mammalian nervous system remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at low rates and rhythmic bursting. How are these firing patterns generated? Specifically, how do dynamic interactions between excitatory and inhibitory neurons produce these firing patterns, and how do networks switch from one firing pattern to the other? We investigated these questions theoretically by examining the intrinsic dynamics of large networks of neurons. Using both a semianalytic model based on mean firing rate dynamics and simulations with large neuronal networks, we found that the dynamics, and thus the firing patterns, are controlled largely by one parameter, the fraction of endogenously active cells. When no endogenously active cells are present, networks are either silent or fire at a high rate; as the number of endogenously active cells increases, there is a transition to bursting; and, with a further increase, there is a second transition to steady firing at a low rate. A secondary role is played by network connectivity, which determines whether activity occurs at a constant mean firing rate or oscillates around that mean. These conclusions require only conventional assumptions: excitatory input to a neuron increases its firing rate, inhibitory input decreases it, and neurons exhibit spike-frequency adaptation. These conclusions also lead to two experimentally testable predictions: 1) isolated networks that fire at low rates must contain endogenously active cells and 2) a reduction in the fraction of endogenously active cells in such networks must lead to bursting.

Effects of 5-HT on thalamocortical synaptic transmission in the developing rat

1994 ◽  
Vol 72 (5) ◽  
pp. 2438-2450 ◽  
Author(s):  
R. W. Rhoades ◽  
C. A. Bennett-Clarke ◽  
M. Y. Shi ◽  
R. D. Mooney
Keyword(s):  
Synaptic Transmission ◽  
Somatosensory Cortex ◽  
Cortical Neurons ◽  
Input Resistance ◽  
Inhibitory Effect ◽  
Primary Somatosensory Cortex ◽  
Excitatory Postsynaptic Potential ◽  
Dependent Manner ◽  
Cortical Cells ◽  
Thalamocortical Axons

1. Recent immunocytochemical and receptor binding data have demonstrated a transient somatotopic patterning of serotonin (5-HT)-immunoreactive fibers in the primary somatosensory cortex of developing rats and a transient expression of 5-HT1B receptors on thalamocortical axons from the ventral posteromedial thalamic nucleus (VPM). 2. These results suggest that 5-HT should strongly modulate thalamocortical synaptic transmission for a limited time during postnatal development. This hypothesis was tested in intracellular recording experiments carried out in thalamocortical slice preparations that included VPM, the thalamic radiations, and the primary somatosensory cortex. Effects of 5-HT and analogues were monitored on membrane potentials and input resistances of cortical neurons and on the amplitude of the synaptic potentials evoked in them by stimulation of VPM. 3. Results obtained from cortical neurons in slices taken from rats during the first 2 wk of life indicated that 5-HT strongly inhibited the VPM-evoked excitatory postsynaptic potential (EPSP) recorded from cortical neurons in a dose-dependent manner. In contrast, 5-HT had no significant effects on membrane potential, input resistance, or depolarizations induced by direct application of glutamic acid to cortical cells. 4. The effects of 5-HT were mimicked by the 5-HT1B receptor agonists 1-[3-(trifluoromethyl)phenyl]-piperazine (TFMPP) and 7-trifluoromethyl-4(4-methyl-1-piperazinyl)-pyrrolo[1,2-a]-quinoxaline maleate and antagonized by the 5-HT1B receptor antagonist (-)-pindolol. The 5-HT1A agonist [(+/-)8-hydroxydipropylaminotetralin HBr] (8-OH-DPAT) had less effect on the VPM-elicited EPSP, and the effects of 5-HT upon this response were generally not antagonized by either 1-(2-methoxyphenyl)-4-[4-(2- phthalimmido)butyl]piperazine HBr (a 5-HT1A antagonist) or ketanserine (a 5-HT2 antagonist) or spiperone (a 5-HT1A and 2 antagonist). 5. The ability of 5-HT to inhibit the VPM-evoked EPSP in cortical neurons was significantly reduced in slices from animals > 2 wk of age. The effectiveness of TFMPP in such animals was even more attenuated than that of 5-HT, and the effectiveness of 8-OH-DPAT was unchanged with age. These results are consistent with the disappearance of 5-HT1B receptors from thalamocortical axons after the second postnatal week and the maintenance of 5-HT1A receptors on some neurons. 6. All of the results obtained in this study are consistent with the conclusion that 5-HT has a profound, but developmentally transient, presynaptic inhibitory effect upon thalamocortical transmission in the rat's somatosensory cortex.

scholarly journals Fast-spiking GABA circuit dynamics in the auditory cortex predict recovery of sensory processing following peripheral nerve damage

eLife ◽  
2017 ◽  
Vol 6 ◽  
Author(s):  
Jennifer Resnik ◽  
Daniel B Polley
Keyword(s):  
Peripheral Nerve ◽  
Auditory Cortex ◽  
Sensory Processing ◽  
Cortical Neurons ◽  
Sensory Nerve ◽  
Intracortical Inhibition ◽  
Nerve Fibers ◽  
Nerve Damage ◽  
Inhibitory Neurons ◽  
Sound Processing

Cortical neurons remap their receptive fields and rescale sensitivity to spared peripheral inputs following sensory nerve damage. To address how these plasticity processes are coordinated over the course of functional recovery, we tracked receptive field reorganization, spontaneous activity, and response gain from individual principal neurons in the adult mouse auditory cortex over a 50-day period surrounding either moderate or massive auditory nerve damage. We related the day-by-day recovery of sound processing to dynamic changes in the strength of intracortical inhibition from parvalbumin-expressing (PV) inhibitory neurons. Whereas the status of brainstem-evoked potentials did not predict the recovery of sensory responses to surviving nerve fibers, homeostatic adjustments in PV-mediated inhibition during the first days following injury could predict the eventual recovery of cortical sound processing weeks later. These findings underscore the potential importance of self-regulated inhibitory dynamics for the restoration of sensory processing in excitatory neurons following peripheral nerve injuries.

scholarly journals Functional selectivity and specific connectivity of inhibitory neurons in primary visual cortex

2018 ◽  
Author(s):  
Petr Znamenskiy ◽  
Mean-Hwan Kim ◽  
Dylan R. Muir ◽  
Maria Florencia Iacaruso ◽  
Sonja B. Hofer ◽  
...  
Keyword(s):  
Visual Cortex ◽  
Primary Visual Cortex ◽  
Pyramidal Cells ◽  
Fine Tuning ◽  
Inhibitory Neurons ◽  
Local Network ◽  
Cortical Circuits ◽  
Sensory Stimuli ◽  
Excitatory Neurons ◽  
Strong Excitation

In the cerebral cortex, the interaction of excitatory and inhibitory synaptic inputs shapes the responses of neurons to sensory stimuli, stabilizes network dynamics1 and improves the efficiency and robustness of the neural code2–4. Excitatory neurons receive inhibitory inputs that track excitation5–8. However, how this co-tuning of excitation and inhibition is achieved by cortical circuits is unclear, since inhibitory interneurons are thought to pool the inputs of nearby excitatory cells and provide them with non-specific inhibition proportional to the activity of the local network9–13. Here we show that although parvalbumin-expressing (PV) inhibitory cells in mouse primary visual cortex make connections with the majority of nearby pyramidal cells, the strength of their synaptic connections is structured according to the similarity of the cells’ responses. Individual PV cells strongly inhibit those pyramidal cells that provide them with strong excitation and share their visual selectivity. This fine-tuning of synaptic weights supports co-tuning of inhibitory and excitatory inputs onto individual pyramidal cells despite dense connectivity between inhibitory and excitatory neurons. Our results indicate that individual PV cells are preferentially integrated into subnetworks of inter-connected, co-tuned pyramidal cells, stabilising their recurrent dynamics. Conversely, weak but dense inhibitory connectivity between subnetworks is sufficient to support competition between them, de-correlating their output. We suggest that the history and structure of correlated firing adjusts the weights of both inhibitory and excitatory connections, supporting stable amplification and selective recruitment of cortical subnetworks.

scholarly journals Risk Aversion and Social Networks

2014 ◽  
Vol 13 (2) ◽  
Author(s):  
Jaromír Kovářík ◽  
Marco J. van der Leij
Keyword(s):  
Risk Aversion ◽  
Undergraduate Students ◽  
Network Structure ◽  
Network Formation ◽  
Empirical Finding ◽  
Local Network ◽  
Network Clustering ◽  
Strongly Correlated ◽  
Social Network Structure ◽  
The One

AbstractThis paper first investigates empirically the relationship between risk aversion and social network structure in a large group of undergraduate students. We find that risk aversion is strongly correlated to local network clustering, that is, the probability that one has a social tie to friends of friends. We then propose a network formation model that generates this empirical finding, suggesting that locally superior information on benefits makes it more attractive for risk averse individuals to link to friends of friends. Finally, we discuss implications of this model. The model generates a positive correlation between local network clustering and benefits, even if benefits are distributed independently ex ante. This provides an alternative explanation of this relationship to the one given by the social capital literature. We also establish a linkage between the uncertainty of the environment and the network structure: risky environments generate more clustered and more unequal networks in terms of connectivity.

scholarly journals Sparse bursts optimize information transmission in a multiplexed neural code

2018 ◽  
Vol 115 (27) ◽  
pp. E6329-E6338 ◽  
Author(s):  
Richard Naud ◽  
Henning Sprekeler
Keyword(s):  
Firing Rate ◽  
Cortical Neurons ◽  
Neural Code ◽  
Spike Timing ◽  
Neural Ensemble ◽  
Multiple Input ◽  
Cortical Hierarchy ◽  
Connectivity Patterns ◽  
Rate Coding

Many cortical neurons combine the information ascending and descending the cortical hierarchy. In the classical view, this information is combined nonlinearly to give rise to a single firing-rate output, which collapses all input streams into one. We analyze the extent to which neurons can simultaneously represent multiple input streams by using a code that distinguishes spike timing patterns at the level of a neural ensemble. Using computational simulations constrained by experimental data, we show that cortical neurons are well suited to generate such multiplexing. Interestingly, this neural code maximizes information for short and sparse bursts, a regime consistent with in vivo recordings. Neurons can also demultiplex this information, using specific connectivity patterns. The anatomy of the adult mammalian cortex suggests that these connectivity patterns are used by the nervous system to maintain sparse bursting and optimal multiplexing. Contrary to firing-rate coding, our findings indicate that the physiology and anatomy of the cortex may be interpreted as optimizing the transmission of multiple independent signals to different targets.

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