Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation

Nesse, William H.; Borisyuk, Alla; Bressloff, Paul C.

doi:10.1007/s10827-008-0114-6

Cited by 8 publications

(19 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, coherent oscillations in one-population spiking neural networks where exhibited by Pham and collaborators [45]. The results obtained by Nesse and collaborators [42] also confirm the presence of noise-induced phenomena in all-to-all coupled networks of leaky integrate-and-fire neurons with filtered noise and slow activity-dependent currents, i.e. noise and spikes are filtered by a second order kernel.…”

Section: Meanmentioning

confidence: 64%

Noise-Induced Behaviors in Neural Mean Field Dynamics

Touboul¹,

Hermann²,

Faugeras³

2012

SIAM J. Appl. Dyn. Syst.

112

View full text Add to dashboard Cite

Abstract. The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belonging to a few types of cell populations and receiving noisy currents. Asymptotic equations as the number of neurons tends to infinity (mean field equations) are rigorously derived based on a probabilistic approach. These equations are implicit on the probability distribution of the solutions which generally makes their direct analysis difficult. However, in our case, the solutions are Gaussian, and their moments satisfy a closed system of nonlinear ordinary differential equations (ODEs), which are much easier to study than the original stochastic network equations, and the statistics of the empirical process uniformly converge towards the solutions of these ODEs. Based on this description, we analytically and numerically study the influence of noise on the collective behaviors, and compare these asymptotic regimes to simulations of the network. We observe that the mean field equations provide an accurate description of the solutions of the network equations for network sizes as small as a few hundreds of neurons. In particular, we observe that the level of noise in the system qualitatively modifies its collective behavior, producing for instance synchronized oscillations of the whole network, desynchronization of oscillating regimes, and stabilization or destabilization of stationary solutions. These results shed a new light on the role of noise in shaping collective dynamics of neurons, and gives us clues for understanding similar phenomena observed in biological networks. Key words. mean field equations, neural mass models, bifurcations, noise, dynamical systems AMS subject classifications. 34C15, 34C23, 60F99, 60B10, 34C25Introduction. The brain is composed of a very large number of neurons interacting in a complex nonlinear fashion and subject to noise. Because of these interactions, stimuli tend to produce coherent global responses, often with high reliability. At the scale of single neurons the presence of noise and nonlinearities often results in highly intricate behaviors. However, at larger scales, neurons form large ensembles that share the same input and are strongly connected, and at these scales, reliable responses to specific stimuli may arise. Such population assemblies (cortical columns or cortical areas) feature a very large number of neurons. Understanding the global behavior of these large-scale neural assemblies has been a focus of many investigations in the past decades. One of the main interests of large-scale modeling is to characterize brain function at the scale most non-invasive imaging techniques operate. Its relevance is also connected to the fact that anatomical data recorded in the cortex reveal its columnar organization at scales ranging from about 50µm to 1mm. These so-called ...

show abstract

Section: Meanmentioning

confidence: 64%

Noise-Induced Behaviors in Neural Mean Field Dynamics

Touboul¹,

Hermann²,

Faugeras³

2012

SIAM J. Appl. Dyn. Syst.

112

View full text Add to dashboard Cite

show abstract

“…The mean rate and variance were gradually increased from F n = 0 to F n = 1 kHz, as suggested by Rodriguez-Molina et al (2007). Similar approaches were also suggested in other studies, e.g., Nesse et al (2008). In the pacemaker-driven simulations we kept all input parameters within the same physiological ranges as before, except that the noise was set at zero and pacemaker features were assigned to the intense neurons.…”

Section: Simulation Modelmentioning

confidence: 87%

“…We kept all model parameters, except the network size, in a constant range in order to have a common point of reference. For small networks created with this setup, parameter ranges were similar to those reported in literature, e.g., Wiedemann and Luthi (2003), Giugliano et al (2004), and Nesse et al (2008). By changing the network size from n = 500 to 5,000 and keeping K max constant, the average number of connections (or "average connection probability") between two randomly chosen neurons was reduced from 1 to 0.1.…”

Section: Network Simulation With Homogeneous Synaptic Strength Distrimentioning

confidence: 99%

“…With similar K max , the probability that two randomly chosen neurons are connected to each other decreases in larger networks. On the one hand, Nesse et al (2008) showed that, in fully connected networks of 500 neurons, increased noise could trigger an abrupt change in network activity from asynchronous to synchronized. On the other hand, Giugliano et al (2004) showed that sparse networks can operate in a more realistic synchronized regime when the strength of synaptic interactions is adjusted.…”

Section: Simulated Datamentioning

confidence: 99%

See 1 more Smart Citation

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

et al. 2011

View full text Add to dashboard Cite

Rhythmic bursting is the most striking behavior of cultured cortical networks and may start in the second week after plating. In this study, we focus on the intervals between spontaneously occurring bursts, and compare experimentally recorded values with model simulations. In the models, we use standard neurons and synapses, with physiologically plausible parameters taken from literature. All networks had a random recurrent architecture with sparsely connected neurons. The number of neurons varied between 500 and 5,000. We find that network models with homogeneous synaptic strengths produce asynchronous spiking or stable regular bursts. The latter, however, are in a range not seen in recordings. By increasing the synaptic strength in a (randomly chosen) subset of neurons, our simulations show interburst intervals (IBIs) that agree better with in vitro experiments. In this regime, called weakly synchronized, the models produce irregular network bursts, which are initiated by neurons with relatively stronger synapses. In some noise-driven networks, a subthreshold, deterministic, input is applied to neurons with strong synapses, to mimic pacemaker network drive. We show that models with such "intrinsically active neurons" (pacemaker-driven models) tend to generate IBIs that are determined by the frequency of the fastest pacemaker and do not resemble experimental data. Alternatively, noise-driven models yield realistic IBIs. Generally, we found that large-scale noise-driven neuronal network models required synaptic strengths with a bimodal distribution to reproduce the experimentally observed IBI range. Our results imply that the results obtained from small network models cannot simply be extrapolated to models of more realistic

show abstract

“…The less used 'pacemaker-driven' approach is based on intrinsically active cells, as described by Latham et al (2000a,b). Recent modeling studies showed that theoretically both the approaches can provide robustness of network bursting behavior in noisedriven (Nesse et al 2008) and pacemaker-driven networks (Vladimirski et al 2008). However, Vladimirski et al (2008) showed that homogeneous noise-driven networks produced fragile rhythmic bursts.…”

Section: Introductionmentioning

confidence: 99%

Network bursts in cortical cultures are best simulated using pacemaker neurons and adaptive synapses

et al. 2010

View full text Add to dashboard Cite

One of the most specific and exhibited features in the electrical activity of dissociated cultured neural networks (NNs) is the phenomenon of synchronized bursts, whose profiles vary widely in shape, width and firing rate. On the way to understanding the organization and behavior of biological NNs, we reproduced those features with random connectivity network models with 5,000 neurons. While the common approach to induce bursting behavior in neuronal network models is noise injection, there is experimental evidence suggesting the existence of pacemaker-like neurons. In our simulations noise did evoke bursts, but with an unrealistically gentle rising slope. We show that a small subset of 'pacemaker' neurons can trigger bursts with a more realistic profile. We found that adding pacemaker-like neurons as well as adaptive synapses yield burst features (shape, width, and height of the main phase) in the same ranges as obtained experimentally. Finally, we demonstrate how changes in network connectivity, transmission delays, and excitatory fraction influence network burst features quantitatively.

show abstract

Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation

Abstract: The publisher regrets that a reference was incorrectly printed for the article, "Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation," by

Cited by 8 publications

References 1 publication

Noise-Induced Behaviors in Neural Mean Field Dynamics

Noise-Induced Behaviors in Neural Mean Field Dynamics

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

Network bursts in cortical cultures are best simulated using pacemaker neurons and adaptive synapses

Contact Info

Product

Resources

About