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.

The input–output transform performed by mitral cells, the principal projection neurons of the olfactory bulb, is one of the key factors in understanding olfaction. We used combined calcium and voltage imaging from the same neuron and computer modeling to investigate signal processing in the mitral cells, focusing on the glomerular dendritic tuft. The main finding was that the dendritic tuft functions as a single electrical compartment for subthreshold signals within the range of amplitudes detectable by voltage-sensitive dye recording. These evoked EPSPs had uniform characteristics throughout the glomerular tuft. The Ca2+ transients associated with spatially uniform subthreshold synaptic potentials were comparable but not equal in amplitude in all regions. The average range of normalized amplitudes of the EPSP-driven Ca2+ signals from different locations on dendritic branches in the glomerular tuft was relatively narrow and appeared to be independent of the dendritic surface-to-volume ratio. The computer simulations constrained by the imaging data indicated that a synchronized activation of ∼100 synapses randomly distributed on tuft branches was sufficient to generate spatially homogenous EPSPs. This number of activated synapses is consistent with the data from anatomical studies. Furthermore, voltage attenuation of the EPSP along the primary dendrite at physiological temperature was weak compared with other cell types. In the model, weak attenuation of the EPSP along the primary dendrite could be accounted for by passive electrical properties of the mitral cell.

https://www.jneurosci.org/content/jneuro/28/15/4057.full.pdf

Functional Structure of the Mitral Cell Dendritic Tuft in the Rat Olfactory Bulb

Precision in neuron names is increasingly needed. We are entering a new era in which classical anatomical criteria are only the beginning toward defining the identity of a neuron as carried in its name. New criteria include patterns of gene expression, membrane properties of channels and receptors, pharmacology of neurotransmitters and neuropeptides, physiological properties of impulse firing, and state-dependent variations in expression of characteristic genes and proteins. These gene and functional properties are increasingly defining neuron types and subtypes. Clarity will therefore be enhanced by conveying as much as possible the genes and properties in the neuron name. Using a tested format of parent-child relations for the region and subregion for naming a neuron, we show how the format can be extended so that these additional properties can become an explicit part of a neuron’s identity and name, or archived in a linked properties database. Based on the mouse, examples are provided for neurons in several brain regions as proof of principle, with extension to the complexities of neuron names in the cerebral cortex. The format has dual advantages, of ensuring order in archiving the hundreds of neuron types across all brain regions, as well as facilitating investigation of a given neuron type or given gene or property in the context of all its properties. In particular, we show how the format is extensible to the variety of neuron types and subtypes being revealed by RNA-seq and optogenetics. As current research reveals increasingly complex properties, the proposed approach can facilitate a consensus that goes beyond traditional neuron types.

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Neuron Names: A Gene- and Property-Based Name Format, With Special Reference to Cortical Neurons

The spatial distribution and time course of electrical signals in neurons have important theoretical and practical consequences. Because it is difficult to infer how neuronal form affects electrical signaling, we have developed a quantitative yet intuitive approach to the analysis of electrotonus. This approach transforms the architecture of the cell from anatomical to electrotonic space, using the logarithm of voltage attenuation as the distance metric. We describe the theory behind this approach and illustrate its use.

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The Electrotonic Transformation: a Tool for Relating Neuronal Form to Function

The last few decades have seen the emergence of computational neuroscience as a mature field where researchers are interested in modeling complex and large neuronal systems and require access to high performance computing machines and associated cyber infrastructure to manage computational workflow and data. The neuronal simulation tools, used in this research field, are also implemented for parallel computers and suitable for high performance computing machines. But using these tools on complex high performance computing machines remains a challenge because of issues with acquiring computer time on these machines located at national supercomputer centers, dealing with complex user interface of these machines, dealing with data management and retrieval. The Neuroscience Gateway is being developed to alleviate and/or hide these barriers to entry for computational neuroscientists. It hides or eliminates, from the point of view of the users, all the administrative and technical barriers and makes parallel neuronal simulation tools easily available and accessible on complex high performance computing machines. It handles the running of jobs and data management and retrieval. This paper shares the early experiences in bringing up this gateway and describes the software architecture it is based on, how it is implemented, and how users can use this for computational neuroscience research using high performance computing at the back end. We also look at parallel scaling of some publicly available neuronal models and analyze the recent usage data of the neuroscience gateway.

Nicholas T. Carnevale

Papers

Functional Structure of the Mitral Cell Dendritic Tuft in the Rat Olfactory Bulb

Neuron Names: A Gene- and Property-Based Name Format, With Special Reference to Cortical Neurons

The Electrotonic Transformation: a Tool for Relating Neuronal Form to Function

Early experiences in developing and managing the neuroscience gateway

Computer modeling methods for neurons