Neuronal avalanches and criticality
Dietmar Plenz
Neural Network Physiology/NIMH (Bethesda, MD, USA)
Neuronal avalanches are spatiotemporal patterns of synchronized activity that occur spontaneously in superficial layers of the mammalian cortex under various experimental conditions. These patterns reflect fast propagation of locally synchronized activity, display a rich spatiotemporal diversity, and recur over several hours. The statistics of pattern sizes is invariant to the choice of spatial scale demonstrating a precise, fractal organization that allows the linking of distant cortical sites. These features suggest an underlying network of neuronal interactions that balances flexible representation with predictable computational outcome, similar to what has been theorized for cell assembly formation. We propose that the avalanche dynamics are a strong candidate for the transient formation of cell assemblies in cortex and discuss various models that provide mechanistic insights, suggesting that they arise in a critical regime.
Critical dynamics in developing cortical networks
Ildiko Vajda, S-S. Poil, Klaus Linkenkaer-Hansen, Arjen van Ooyen
Dept Experimental Neurophysiology, Vrije Universiteit Amsterdam (Amsterdam)
Cultured dissociated neurons develop into densely connected networks, exhibiting reverberating spontaneous activity. Depending on the culture's age, this activity comprises tonic firing, only synchronous network activity or a mixture of two. The persistence of such reverberating activity in these cultures suggests that it is an important intrinsic form of network activity that is prominent even in the absence of wiring of the thalamocortical circuitry.
Theoretical and experimental work shows that in the so-called critical regime of activity, the network is in optimal mode of information processing. Beggs and Plenz (J. of Neurosci., 2003) have introduced an analysis method by which propagation of the so-called avalanche-mode of activity can be quantified and potentially reveal a critical state. By adopting their method we have analyzed the spontaneous activity of dissociated cortical cultures at different ages as well as under application of a cholinergic agonist (carbachol) that is known to disrupt synchronous network activity. First, we wanted to know whether activity propagation in terms of avalanche duration and size is different in cultures of different developmental stages and whether they follow a power-law distribution. We have found that most cultures exhibited a bimodal distribution, older cultures showing a more prominent peak than younger ones. However, when time was binned finely, most cultures showed a power-law distribution of their avalanche sizes and durations. As cultures matured, the estimated exponents approached values that characterize activity in the critical regime. Disrupted network activity by carbachol application resulted in a greater proportion of small and short-lasting avalanches.
We hypothesize that mechanisms of homeostatic plasticity cause cortical cultures to develop into a critical state of network activity. Simulation studies of growing networks point towards these mechanisms (Abbott and Rohrkemper, Prog. Brain Res., in press) and we wish to test this hypothesis experimentally.
Synaptic connectivity underlying long-range temporal correlations
S. Poil1,2, Arjen van Ooyen1, Klaus Linkenkaer-Hansen1
1Dept Experimental Neurophysiology (CNCR), Vrije Universiteit Amsterdam (Amsterdam);
2Niels Bohr Institute (Copenhagen, Denmark)
Oscillations are generated spontaneously in several areas of the brain as neuronal networks transiently form assemblies of synchronously firing cells. The amplitude fluctuations have a complex temporal structure and are characterized by long-range temporal correlations, suggesting that the number and duration of neurons being recruited into synchronized assemblies are highly variable [1]. Non-oscillatory synchronous activity in vitro has been observed to propagate as a critical branching process with a power-law probability distribution of burst sizes also known as "avalanches" [2]. This has raised the possibility that a "critical" functional connectivity of cortical networks is underlying the large variability in bursts of oscillatory activity. We aim to develop a computational model of neuronal network oscillations that allow us to investigate the possible links between branching processes in networks, spatial propagation of oscillatory activity and power-law temporal correlations in ongoing oscillations.
[1] Linkenkaer-Hansen et al, J Neurosci 21:1370-1377, 2001.
[2] Beggs JM, Plenz D, J Neurosci 23:11167-11177, 2003.
Dynamical synapses give rise to the critical neural networks
Anna Levina1, J. Michael Herrmann2, Theo Geisel2,3
1Uni. Goettingen (Goettingen, Germany);
2Bernstein Center for Computational Neuroscience (Goettingen, Germany);
3Max Planck Institute for Dynamics and Self-Organization (Goettingen, Germany)
We investigate the effect of dynamical synapses on the dynamics of spiking neural networks. We find that activity-dependent synaptic depression causes the mean synaptic strengths to approach a critical value for a certain range of interaction parameters, while outside of this range other dynamical behaviors are prevalent.
Deriving analytical expressions for the average coupling strengths and inter-spike intervals, we demonstrate that networks with dynamical synapses exhibit critical avalanche dynamics for a wide range of interaction parameters. Extended numerical simulations indicate the validity of the analytical solution. We prove that in the thermodynamical limit the network becomes critical for all coupling parameters.
Structural homeostatic plasticity and critical network dynamics
Markus Butz1, Florentin Woergoetter1, Arjen van Ooyen2
1Bernstein Center Computational Neuroscience (Goettingen, Germany);
2CNCR, Vrije Universiteit Amsterdam (Amsterdam)
Structure and function are mutually depending in biological neural networks and their development realizes learning processes. In contrast to artificial neural networks, biological neural networks therefore have to fulfill certain boundary criteria i.e. keeping their activity within a physiologically adequate range. This is achieved by compensatory changes of the neurons' connectivity spectra. Latest imaging techniques reveal a permanent activity-dependent remodelling of spines and axons that contribute to the homeostasis of the whole network. We have developed a neural network model to study structural homeostatic plasticity in terms of synaptic rewiring by axon and spine turnover. It is to be observed, how structural processes interfere with the functional dynamics of the model network and if criticality is obtained by local synaptic adaptation rules.