- Poster presentation
- Open Access
Structured chaos shapes joint spike-response noise entropy in temporally driven balanced networks
BMC Neuroscience volume 15, Article number: P48 (2014)
How variable and noisy is the neural code arising from the joint activity of recurrently connected cells? Isolated neurons are known to respond to fluctuating input currents with reliable spike patterns [1, 2], but variability in stimulus-evoked spike trains is increasingly pronounced in deeper, more recurrently connected brain areas such as cortex . What are the network-level sources of this variability, and how they might constrain spiking features relevant for coding remains an open question.
We focus on spiking model networks with sparse, random connectivity and balanced excitation and inhibition that reproduce the irregular firing that typifies cortical activity. In such models, activity is known to be chaotic, with extremely strong sensitivity of spike outputs on tiny changes in a network’s initial conditions [4–6]. Nevertheless, when subject to temporally fluctuating driving inputs, networks can have chaotic attractors of limited dimension and geometric properties leading to reduced spiking variability at the single-cell level . As recent studies suggest that the impact of noise on network coding cannot be understood by single cell properties alone [8, 9], we study mechanisms underlying the joint activity of entire networks.
We derive a bound for the entropy of joint spike pattern distributions in large spiking model networks in response to a fluctuating temporal signal. The analysis is based on results from random dynamical systems theory and complimented by detailed numerical simulations. We find that despite very weak conditional correlations between neurons, the resulting joint variability of network responses is surprisingly lower than what would be expected by considering only limited statistical neural interactions. Moreover, joint spiking variability is strongly constrained by the level of temporal features of input stimuli.
Bryant H, Segundo J: Spike initiation by trans-membrane current: a white-noise analysis. Journal of Physiology. 1976, 260: 279-314.
Mainen Z, Sejnowski T: Reliability of spike timing in neocortical neurons. Science. 1995, 268 (5216): 1503-1506. 10.1126/science.7770778.
Kara P, Reinagel P, Reid R: Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron. 2000, 27 (3): 635-646. 10.1016/S0896-6273(00)00072-6.
VanVreeswijk C, Sompolinsky H: Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science. 1996, 274 (5293): 1724-10.1126/science.274.5293.1724.
Monteforte M, Wolf F: Dynamical entropy production in spiking neuron networks in the balanced state. Phys Rev Letter. 2010, 105 (26): 268104-
London M, Roth A, Beeren L, Haüsser M, Latham PE: Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature. 2010, 466 (7302): 123-127. 10.1038/nature09086.
Lajoie G, Lin KK, Shea-Brown E: Chaos and reliability in balanced spiking networks with temporal drive. Phys Rev E. 2013, 87 (5): 052901-
Schneidman E, Berry MJ, Segev R, Bialek W: Weak pairwise correlations imply strongly correlated network states in a neural population. Nature. 2006, 440 (7087): 1007-1012. 10.1038/nature04701.
Ecker AS, Berens P, Tolias AS, Bethge M: The effect of noise correlations in populations of diversely tuned neurons. The Journal of Neuroscience. 2011, 31 (40): 14272-14283. 10.1523/JNEUROSCI.2539-11.2011.
The authors thank Fred Wolf, Yu Hu and Kevin K. Lin for helpful insights. This work was supported in part by an NSERC graduate scholarship, an NIH Training Grant from University of Washington’s Center for Computational Neuroscience, the Burroughs Wellcome Fund Scientific Interfaces, the NSF under grant DMS CAREER-1056125 and NSERC Discovery and CIHR operating grants.
About this article
Cite this article
Lajoie, G., Thivierge, J. & Shea-Brown, E. Structured chaos shapes joint spike-response noise entropy in temporally driven balanced networks. BMC Neurosci 15, P48 (2014) doi:10.1186/1471-2202-15-S1-P48
- Spike Train
- Chaotic Attractor
- Network Code
- Dynamical System Theory
- Conditional Correlation