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Principles of Computational Modelling in Neuroscience Hardcover – 30 Jun 2011
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'Here at last is a book that is aware of my problem, as an experimental neuroscientist, in understanding the maths … I expect it to be as mind expanding as my involvement with its authors was over the years. I only wish I had had the whole book sooner - then my students and post-docs would have been able to understand what I was trying to say and been able to derive the critical tests of the ideas that only the rigor of the mathematical formulation of them could have generated.' Gordon W. Arbuthnott, Okinawa Institute of Science and Technology
'This is a wonderful, clear and compelling text on mathematically-minded computational modelling in neuroscience. It is beautifully aimed at those engaged in capturing quantitatively, and thus simulating, complex neural phenomena at multiple spatial and temporal scales, from intracellular calcium dynamics and stochastic ion channels, through compartmental modelling, all the way to aspects of development. It takes particular care to define the processes, potential outputs and even some pitfalls of modelling; and can be recommended for containing the key lessons and pointers for people seeking to build their own computational models. By eschewing issues of coding and information processing, it largely hews to concrete biological data, and it nicely avoids sacrificing depth for breadth. It is very suitably pitched as a Master's level text, and its two appendices, on mathematical methods and software resources, will rapidly become dog-eared.' Peter Dayan, University College London
'Principles of Computational Modelling in Neuroscience sets a new standard of clarity and insight in explaining biophysical models of neurons. This provides a firm foundation for network models of brain function and brain development. I plan to use this textbook in my course on computational neurobiology.' Terrence Sejnowski, Salk Institute for Biological Studies and University of California, San Diego
This book is for neuroscientists at all levels and for people from the informational and physical sciences who want to develop computational models of the neuron and neural circuits. It presents the principles of computational neuroscience in a clear and coherent manner, and addresses practical issues that arise in modelling projects.See all Product description
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The book is intended for postgraduates and researchers in the field of experimental and computational neuroscience. Readers are assumed to have basic knowledge of the multidisciplinary fields of physical sciences, computer science and engineering, and neuroscience. Organization of chapters is structured well evolving from the lowest component level to the highest system and network level. A detailed chapter-by-chapter summary of the book follows.
The first and introductory chapter defines computational modeling and presents a synopsis of the succeeding chapters of the book. The authors define the term computational model as "Hodgkin and Huxley's simulation of the propagation of a nerve impulse (action potential) along an axon." Remaining chapters address the questions regarding the following: "deciding what type of model to use; at what level to model; what aspects of the system to model; and how to deal with parameters that have not or cannot be measured experimentally."
Chapters 2 and 3 lay the basic foundation needed for modeling. The former models the neural membrane as an electrical circuit made up of resistances and capacitance (RC circuit) with ionic currents generating membrane potential across the membrane conductance (inverse of resistance), which is defined by Nernst equation. Chapter 3 introduces the concept of action potential as the signal propagating in the neural network and the dynamics of depolarization and repolarization of the membrane. Hodgkin-Huxley (HH) model of active membrane properties with propagating action potential lays the foundation for modern modeling methodologies of the nervous system. Hodgkin and Huxley invented the voltage clamping technique "to produce the experimental data required to construct a set of mathematical equations representing the movement of independent gating particles across the membrane thought to control the opening and closing of sodium and potassium channels."
In Chapter 4 neuron with complex dendric and axonal morphology is modeled by treating the neuron as consisting of multiple compartments each comprising the basic HH model interconnected by a resistor. In constructing the models, one has to choose values for capacitance, membrane and axial resistances, and ion channel conductances, which may produce errors during validation. Procedures for error handling are discussed. Although Chapter 4 mainly focuses on compartments comprising passive channels; i.e., with membrane capacitance and resistance being constant, the concept of active ion channels in which the conductance varies in each compartment is introduced. HH model is extended to deal with the simple situation with a single channel parameter that is different for each compartment.
Chapter 5 introduces the presence of individual ion channels, each with its own gating particles. There are two types of gated channels, the voltage gated channel with potassium and sodium ions that was developed for the HH model and a second one gated by ligands, such as calcium. The authors describe the channel structures and functions including primary and auxiliary subunits and homogeneous and heterogeneous types. A third type of current parameter, gating current, is introduced and illustrated with an example of A-type current. The concept of a stimulus now producing signaling stream is explained. Control of A-type current produced two types of neurons, type I and type II with different firing patterns. These neurons fired with a delayed reaction to the stimulus. Further, the former produces a gradual increase in frequency of signaling stream beyond the threshold level, called the spiking threshold, and the latter produces a quantum jump and non-linear dependency with the stimulus current. The HH model was extended to handle these cases as well as thermodynamic models. Mathematical treatment of Markov models is presented that handles stochastic treatment of kinetic ion channels for both voltage-gated and ligand gated channels.
In Chapters 6 and 7 the authors address how to develop models for specific applications. Chapter 6 deals with intracellular ionic signaling in which signaling pathways act as a second messenger. Mathematical modeling of binding reactions between molecules reaction-diffusion system in the cell cytoplasm is presented. Various modeling schemes for diffusion, buffering, and synaptic plasticity that cause LTP and LTD, based on temporal and spatial evolving conditions as well as stochastic processes, are treated. Chapter 7 deals with the inputs and outputs of neurons looking at presynaptic receptors and postsynaptic neurotransmitters. The models range from empirical models of voltage waveforms to more detailed kinetic and complex stochastic models including vesicle recycling and release. Models of LTP and LTD that attempt to map the functional relationship between presynaptic and postsynaptic activities are presented.
Chapters 8 and 9 are devoted to integrating the models developed in the previous chapters into modeling of the neuron and network of neurons respectively. In modeling the neuron, there is innumerable number of computational models for each component of the neuron. The challenge is to simplify the model and thus reduce the computational resource needed to a manageable level in integrating the nurite and synoptic interface models. Several examples of reducing the number of compartments are sited and a detailed treatment of Pinskey-Rinzel two-compartment model is presented. Even the single compartment HH models with four state variables have been reduced to two by choosing the voltage and one of the three gating variables and examples of these are referenced. Among the various schemes of signaling, a basic integrate-and-fire scheme is chosen for Type I neurons and a mathematical model is developed for the number of spikes per second as a function of injected current and multiple synaptic inputs. Examples of Type II neurons include Stein model and Izkevich model. Alternatives to integrate-and-fire model discussed are the spike-response model, which is the impulse response and rate-based models that are based on the average firing rate.
Once again, the approach in Chapter 9 is how to construct the neural network model of neurons and synapses with appropriate simplifications. The selection process includes consideration of level of details to model the neuron, communication between neurons, scaling the number of neurons in the system, positioning the neurons in space, variability in cell properties, and extracellular field potentials, among other criteria. The authors discuss the associative network with feedforward and recurrent forms and the consequential Hebbian plasticity, wherein memories are encoded in synaptic strengths. Examples of models are presented for complex networks of spiking neurons, conductance-based neuronal network, and large-scale model of thalamocortical systems such as Blue Brain project. Of greater complexity is modeling of the network comprising the basal ganglia, like the one in which deep brain stimulation is performed by placing electrode in basal ganglia for therapeutic treatment of Parkinson's disease.
Although the physiology and morphology is not based on HH model, and hence not addressed as a modeling problem, Chapter 10 describes the development aspects of the nervous system for completeness of computational modeling. Such computational modeling is done by constructing special purpose simulators such as NEURON and GENENSIS. Modeling work in the development of nerve cell morphology, cell physiology, cell patterning, patterns of ocular dominance, and connection between nerve cell and muscle, and retinotopic maps are presented.
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