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

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

Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems

The authors present a unified account of 2 neural systems concerned with the development and expression of adaptive behaviors: a mesencephalic dopamine system for reinforcement learning and a “generic” error-processing system associated with the anterior cingulate cortex The existence of the error-processing system has been inferred from the error-related negativity (ERN), a component of the event-related brain potential elicited when human participants commit errors in reaction-time tasks The authors propose that the ERN is generated when a negative reinforcement learning signal is conveyed to the anterior cingulate cortex via the mesencephalic dopamine system and that this signal is used by the anterior cingulate cortex to modify performance on the task at hand They provide support for this proposal using both computational modeling and psychophysiological experimentation

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The neural basis of human error processing: Reinforcement learning, dopamine, and the error-related negativity.

The moment-to-moment processing of information by the nervous system involves the propagation and interaction of electrical and chemical signals that are distributed in space and time. Biologically realistic modeling is needed to test hypotheses about the mechanisms that govern these signals and how nervous system function emerges from the operation of these mechanisms. The NEURON simulation program provides a powerful and flexible environment for implementing such models of individual neurons and small networks of neurons. It is particularly useful when membrane potential is nonuniform and membrane currents are complex. We present the basic ideas that would help informed users make the most efficient use of NEURON.

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The NEURON simulation environment

In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through creation of new classes for linear and nonlinear solvers, enhancements to the vector class, and the creation of modern Fortran interfaces that leverage interoperability features of the Fortran 2003 standard. The vast majority of this work has been performed "behind-the-scenes," with minimal changes to the user interface and no reduction in solver capabilities or performance. However, these changes now allow advanced users to create highly customized solvers that exploit their problem structure, enabling SUNDIALS use on extreme-scale, heterogeneous computational architectures.

Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers.

Assuming no previous knowledge of computer programming or numerical methods, The NEURON Book provides practical advice on how to get the most out of the NEURON software program. Although written primarily for neuroscientists, teachers and students, readers with a background in the physical sciences or mathematics and some knowledge about brain cells and circuits, will also find it helpful. Covering details of NEURON's inner workings, and practical considerations specifying anatomical and biophysical properties to be represented in models, this book uses a problem-solving approach that includes many examples to challenge readers.

https://www.neuron.yale.edu/ftp/ted/book/neuronbookflyer.pdf

The NEURON Book

NEURON is a simulation environment for models of individual neurons and networks of neurons that are closely linked to experimental data. NEURON provides tools for conveniently constructing, exercising, and managing models, so that special expertise in numerical methods or programming is not required for its productive use. This article describes two tools that address the problem of how to achieve computational efficiency and accuracy.

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Neuron: A Tool for Neuroscientists

Wider dissemination and testing of computational models are crucial to the field of computational neuroscience. Databases are being developed to meet this need. ModelDB is a web-accessible database for convenient entry, retrieval, and running of published models on different platforms. This article provides a guide to entering a new model into ModelDB.

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ModelDB: A Database to Support Computational Neuroscience.

γ-aminobutyric acid-mediated (GABAergic) inhibition plays a critical role in shaping neuronal activity in the neocortex. Numerous experimental investigations have examined perisomatic inhibitory synapses, which control action potential output from pyramidal neurons. However, most inhibitory synapses in the neocortex are formed onto pyramidal cell dendrites, where theoretical studies suggest they may focally regulate cellular activity. The precision of GABAergic control over dendritic electrical and biochemical signaling is unknown. By using cell type-specific optical stimulation in combination with two-photon calcium (Ca(2+)) imaging, we show that somatostatin-expressing interneurons exert compartmentalized control over postsynaptic Ca(2+) signals within individual dendritic spines. This highly focal inhibitory action is mediated by a subset of GABAergic synapses that directly target spine heads. GABAergic inhibition thus participates in localized control of dendritic electrical and biochemical signaling.

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Nicholas T. Carnevale

Papers

The NEURON simulation environment

The NEURON Book

Neuron: A Tool for Neuroscientists

ModelDB: A Database to Support Computational Neuroscience.

Compartmentalization of GABAergic Inhibition by Dendritic Spines