Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons
TL;DR: It is proved that the existence of limit cycle dynamics in response to one class of stimuli implies theexistence of multiple stable states and hysteresis in responseTo this work, coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons.
About: This article is published in Biophysical Journal.The article was published on 1972-01-01 and is currently open access. It has received 3355 citations till now. The article focuses on the topics: Wilson–Cowan model & Limit cycle.
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Book•
01 Oct 2006
TL;DR: 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, providing a link between the two disciplines.
Abstract: 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
3,683 citations
Book•
01 Jan 2001
TL;DR: This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory.
Abstract: Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory The book is divided into three parts Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of neurons Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics Part III analyzes the role of plasticity in development and learning An appendix covers the mathematical methods used, and exercises are available on the book's Web site
3,441 citations
TL;DR: The mammalian visual system is endowed with a nearly infinite capacity for the recognition of patterns and objects, but to have acquired this capability the visual system must have solved what is a fundamentally combinatorial prob lem.
Abstract: The mammalian visual system is endowed with a nearly infinite capacity for the recognition of patterns and objects. To have acquired this capability the visual system must have solved what is a fundamentally combinatorial prob lem. Any given image consists of a collection of features, consisting of local contrast borders of luminance and wavelength, distributed across the visual field. For one to detect and recognize an object within a scene, the features comprising the object must be identified and segregated from those comprising other objects. This problem is inherently difficult to solve because of the combinatorial nature of visual images. To appreciate this point, consider a simple local feature such as a small vertically oriented line segment placed within a fixed location of the visual field. When combined with other line segments, this feature can form a nearly infinite number of geometrical objects. Any one of these objects may coexist with an equally large number of other
3,198 citations
Book•
15 Aug 2002TL;DR: A comparison of single and two-dimensional neuron models for spiking neuron models and models of Synaptic Plasticity shows that the former are superior to the latter, while the latter are better suited to population models.
Abstract: Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.
2,814 citations
TL;DR: The cellular and synaptic mechanisms underlying gamma oscillations are reviewed and empirical questions and controversial conceptual issues are outlined, finding that gamma-band rhythmogenesis is inextricably tied to perisomatic inhibition.
Abstract: Gamma rhythms are commonly observed in many brain regions during both waking and sleep states, yet their functions and mechanisms remain a matter of debate. Here we review the cellular and synaptic mechanisms underlying gamma oscillations and outline empirical questions and controversial conceptual issues. Our main points are as follows: First, gamma-band rhythmogenesis is inextricably tied to perisomatic inhibition. Second, gamma oscillations are short-lived and typically emerge from the coordinated interaction of excitation and inhibition, which can be detected as local field potentials. Third, gamma rhythm typically concurs with irregular firing of single neurons, and the network frequency of gamma oscillations varies extensively depending on the underlying mechanism. To document gamma oscillations, efforts should be made to distinguish them from mere increases of gamma-band power and/or increased spiking activity. Fourth, the magnitude of gamma oscillation is modulated by slower rhythms. Such cross-frequency coupling may serve to couple active patches of cortical circuits. Because of their ubiquitous nature and strong correlation with the "operational modes" of local circuits, gamma oscillations continue to provide important clues about neuronal population dynamics in health and disease.
2,168 citations
Cites background from "Excitatory and Inhibitory Interacti..."
...In most E-I models, there is no need for I-I connections (Wilson & Cowan 1972, Whittington et al. 2000, Borgers & Kopell 2003, Brunel & Wang 2003, Geisler et al. 2005)....
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...The earliest model of gamma oscillations is based on the reciprocal connections between pools of excitatory pyramidal (E) and inhibitory (I) neurons (Wilson & Cowan 1972, Freeman 1975, Leung 1982, Ermentrout & Kopell 1998, Borgers & Kopell 2003, Brunel & Wang 2003, Geisler et al. 2005)....
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References
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1,948 citations
Book•
01 Jan 1964
TL;DR: This chapter discusses the development of ideas on the synapse, the ionic mechanism generating the inhibitory postsynaptic potential, and the trophic and plastic properties of synapses.
Abstract: I. The development of ideas on the synapse.- II. Structural features of chemically transmitting synapses.- III. Physiological properties of chemically transmitting synapses in the resting state.- IV. Excitatory postsynaptic responses to presynaptic impulses.- V. Excitatory transmitter substances.- VI. The release of transmitter by presynaptic impulses.- VII. The generation of impulses by the excitatory postsynaptic potential and the endplate potential.- VIII. The presynaptic terminals of chemically transmitting synapses.- IX. Excitatory synapses operating by electrical transmission.- X. The postsynaptic electrical events produced by chemically transmitting inhibitory synapses.- XI. The ionic mechanism generating the inhibitory postsynaptic potential.- XII. Inhibitory transmitter substances.- XIII. Pathways responsible for postsynaptic inhibitory action.- XIV. Inhibitory synapses operating by electrical transmission.- XV. Presynaptic inhibition.- XVI. The trophic and plastic properties of synapses.- Epilogue.- References.
654 citations
"Excitatory and Inhibitory Interacti..." refers background or methods in this paper
...This is usually not the case, for physiological studies show a to be around 4 msec and r around 1-2 msec (Eccles, 1964)....
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...7 The assumption that the influence of one neuron upon all others is either exclusively excitatory or exclusively inhibitory is known as Dale's law (Eccles, 1964)....
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...Among such systems are the thalamus (Andersen and Eccles, 1962) and the olfactory bulb and cortex (Freeman, 1967, 1968 a, b). Further examples are given in MacKay (1970). Such oscillations typically show periods of 25-40 msec or more....
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...…subpopulations explicitly, and this requires the use of the two variables E(t) and I(t) to characterize the state of the population.7 The assumption that the influence of one neuron upon all others is either exclusively excitatory or exclusively inhibitory is known as Dale's law (Eccles, 1964)....
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