A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.

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Simple model of spiking neurons

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

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Dynamical Systems in Neuroscience

The organization of behavior: A neuropsychological theory

We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks.

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Which model to use for cortical spiking neurons

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

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Neurophysiological and Computational Principles of Cortical Rhythms in Cognition

http://www.izhikevich.org/publications/tinsu.pdf

Bursts as a unit of neural information: selective communication via resonance

What is the functional significance of generating a burst of spikes, as opposed to a single spike? A dominant point of view is that bursts are needed to increase the reliability of communication between neurons. Here, we discuss the alternative, but complementary, hypothesis: bursts with specific resonant interspike frequencies are more likely to cause a postsynaptic cell to fire than are bursts with higher or lower frequencies. Such a frequency preference might occur at the level of individual synapses because of the interplay between short-term synaptic depression and facilitation, or at the postsynaptic cell level because of subthreshold membrane potential oscillations and resonance. As a result, the same burst could resonate for some synapses or cells and not resonate for others, depending on their natural resonance frequencies. This observation suggests that, in addition to increasing reliability of synaptic transmission, bursts of action potentials might provide effective mechanisms for selective communication between neurons.

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Bursts as a unit of neural information: selective communication via

We demonstrate that the BCM learning rule follows directly from STDP when pre- and postsynaptic neurons fire uncorrelated or weakly correlated Poisson spike trains, and only nearest-neighbor spike interactions are taken into account.

Relating STDP to BCM

Spike-timing dependent plasticity (STDP) offers a powerful means of forming and modifying neural circuits. Experimental and theoretical studies have demonstrated its potential usefulness for functions as varied as cortical map development, sharpening of sensory receptive fields, working memory, and associative learning. Even so, it is unlikely that STDP works alone. Unless changes in synaptic strength are coordinated across multiple synapses and with other neuronal properties, it is difficult to maintain the stability and functionality of neural circuits. Moreover, there are certain features of early postnatal development (e.g., rapid changes in sensory input) that threaten neural circuit stability in ways that STDP may not be well placed to counter. These considerations have led researchers to investigate additional types of plasticity, complementary to STDP, that may serve to constrain synaptic weights and/or neuronal firing. These are collectively known as “homeostatic plasticity” and include schemes that control the total synaptic strength of a neuron, that modulate its intrinsic excitability as a function of average activity, or that make the ability of synapses to undergo Hebbian modification depend upon their history of use. In this article, we will review the experimental evidence for homeostatic forms of plasticity and consider how they might interact with STDP during development and learning & memory.

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Homeostatic plasticity and STDP: keeping a neuron's cool in a fluctuating world

The study of experience-dependent plasticity has been dominated by questions of how Hebbian plasticity mechanisms act during learning and development. This is unsurprising as Hebbian plasticity constitutes the most fully developed and influential model of how information is stored in neural circuits and how neural circuitry can develop without extensive genetic instructions. Yet Hebbian plasticity may not be sufficient for understanding either learning or development: the dramatic changes in synapse number and strength that can be produced by this kind of plasticity tend to threaten the stability of neural circuits. Recent work has suggested that, in addition to Hebbian plasticity, homeostatic regulatory mechanisms are active in a variety of preparations. These mechanisms alter both the synaptic connections between neurons and the intrinsic electrical properties of individual neurons, in such a way as to maintain some constancy in neuronal properties despite the changes wrought by Hebbian mechanisms. Here we review the evidence for homeostatic plasticity in the central nervous system, with special emphasis on results from cortical preparations.

Niraj S. Desai

Papers

Bursts as a unit of neural information: selective communication via resonance

Bursts as a unit of neural information: selective communication via

Relating STDP to BCM

Homeostatic plasticity and STDP: keeping a neuron's cool in a fluctuating world

Homeostatic plasticity in the CNS: synaptic and intrinsic forms