Scientific Understanding of Consciousness
Chaos in Neuronal Networks
Science 6 December 1996: Vol. 274. no. 5293, pp. 1724 - 1726
Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity
C. van Vreeswijk and H. Sompolinsky
Racah Institute of Physics and Center for Neural Computation, Hebrew University, Jerusalem, 91904 Israel.
Neurons in the cortex of behaving animals show temporally irregular spiking patterns. The origin of this irregularity and its implications for neural processing are unknown. The hypothesis that the temporal variability in the firing of a neuron results from an approximate balance between its excitatory and inhibitory inputs was investigated theoretically. Such a balance emerges naturally in large networks of excitatory and inhibitory neuronal populations that are sparsely connected by relatively strong synapses. The resulting state is characterized by strongly chaotic dynamics, even when the external inputs to the network are constant in time. Such a network exhibits a linear response, despite the highly nonlinear dynamics of single neurons, and reacts to changing external stimuli on time scales much smaller than the integration time constant of a single neuron.
Recent theoretical and experimental studies have focused on the source of the temporally irregular firing patterns of neurons in cortex, as exemplified by their Poisson-like histograms of interspike intervals. Understanding the origin of this irregularity has important implications for elucidating the temporal components of the neuronal code in cortex. In experiments performed in vitro, cortical slices showed regular firing patterns when stimulated by a constant current, indicating that the irregular firing of neurons in the intact brain is due to strong temporal fluctuations in their synaptic inputs; however, the origin of the fluctuations of the synaptic inputs is not yet known. Furthermore, because a neuron in cortex makes thousands of synaptic contacts with other neurons, the fluctuations in the total synaptic input to a cell is expected to be relatively small even when individual synaptic inputs are strongly fluctuating. It was recently proposed that the timing of the firing of cells in cortex is sensitive to the relatively small fluctuations in their total synaptic input because the excitatory inputs are largely canceled by the inhibitory ones. This intriguing hypothesis raises several questions about (i) the origin of the irregularity of individual synaptic inputs, (ii) the fine-tuning of synaptic constants required to ensure the balance between the total excitatory and inhibitory currents, and (iii) the functional benefits of generating synaptic currents that cancel each other. Several studies have investigated the balance hypothesis in network models, but whether a balance between excitation and inhibition can emerge without fine-tuning of the network parameters remained an open question.
Cortical neurons and circuits are much more complex than the simple network we have studied here, but the mechanism proposed here can also account for the irregular spike trains observed in cortical cells. Indeed, the simplicity of our model suggests that irregular spiking is an emergent network property that does not necessarily depend on intricate cellular mechanisms. Other aspects of balanced networks such as broad, skewed rate distributions and fast tracking are expected to hold also for more realistic models. The linear response of population activities will also hold provided that synaptic inputs are summed approximately linearly. Finally, the predicted chaotic activity of the balanced networks puts constraints on the use of precise temporal patterns of firing as neural codes.
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