The Emergence of Up and Down States in Cortical Networks

The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.

[1]  P. Jung,et al.  Colored Noise in Dynamical Systems , 2007 .

[2]  R. Nicoll,et al.  Long-term potentiation--a decade of progress? , 1999, Science.

[3]  D. Ferster,et al.  Synchronous Membrane Potential Fluctuations in Neurons of the Cat Visual Cortex , 1999, Neuron.

[4]  Boris S. Gutkin,et al.  Turning On and Off with Excitation: The Role of Spike-Timing Asynchrony and Synchrony in Sustained Neural Activity , 2001, Journal of Computational Neuroscience.

[5]  Alex M. Thomson More Than Just Frequency Detectors? , 1997, Science.

[6]  C. Wilson,et al.  Spontaneous firing patterns and axonal projections of single corticostriatal neurons in the rat medial agranular cortex. , 1994, Journal of neurophysiology.

[7]  David Holcman,et al.  Modeling the Spontaneous Activity of the Auditory Cortex , 2005, Journal of Computational Neuroscience.

[8]  Charles J. Wilson,et al.  Effect of subthreshold up and down states on the whisker-evoked response in somatosensory cortex. , 2004, Journal of neurophysiology.

[9]  A. Grinvald,et al.  Spontaneously emerging cortical representations of visual attributes , 2003, Nature.

[10]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. , 2003, Journal of neurophysiology.

[11]  H. Markram,et al.  Redistribution of synaptic efficacy between neocortical pyramidal neurons , 1996, Nature.

[12]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[13]  Charles J. Wilson,et al.  Spontaneous subthreshold membrane potential fluctuations and action potential variability of rat corticostriatal and striatal neurons in vivo. , 1997, Journal of neurophysiology.

[14]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

[15]  Henry Markram,et al.  Neural Networks with Dynamic Synapses , 1998, Neural Computation.

[16]  M Steriade,et al.  Intracellular analysis of relations between the slow (< 1 Hz) neocortical oscillation and other sleep rhythms of the electroencephalogram , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[17]  Ad Aertsen,et al.  Synaptic integration in rat frontal cortex shaped by network activity. , 2005, Journal of neurophysiology.

[18]  J. A. Kuznecov Elements of applied bifurcation theory , 1998 .

[19]  R. Yuste,et al.  Attractor dynamics of network UP states in the neocortex , 2003, Nature.

[20]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of rhythmic recurrent activity in neocortex , 2000, Nature Neuroscience.

[21]  D. McCormick,et al.  Turning on and off recurrent balanced cortical activity , 2003, Nature.

[22]  M. Carandini,et al.  Stimulus dependence of two-state fluctuations of membrane potential in cat visual cortex , 2000, Nature Neuroscience.

[23]  L. Abbott,et al.  Synaptic Depression and Cortical Gain Control , 1997, Science.

[24]  H. Markram,et al.  The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[25]  D. Ferster,et al.  The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. , 2000, Science.

[26]  Zeev Schuss,et al.  Theory and Applications of Stochastic Differential Equations , 1980 .

[27]  Misha Tsodyks,et al.  Computation by Ensemble Synchronization in Recurrent Networks with Synaptic Depression , 2002, Journal of Computational Neuroscience.

[28]  J. Deuchars,et al.  Temporal and spatial properties of local circuits in neocortex , 1994, Trends in Neurosciences.

[29]  Bernard J. Matkowsky,et al.  A direct approach to the exit problem , 1990 .

[30]  A. Grinvald,et al.  Interaction of sensory responses with spontaneous depolarization in layer 2/3 barrel cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[31]  R. Nicoll,et al.  Hippocampal Long-Term Potentiation Preserves the Fidelity of Postsynaptic Responses to Presynaptic Bursts , 1999, The Journal of Neuroscience.