Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 A tour of the NEURON simulation environment
- 2 The modeling perspective
- 3 Expressing conceptual models in mathematical terms
- 4 Essentials of numerical methods for neural modeling
- 5 Representing neurons with a digital computer
- 6 How to build and use models of individual cells
- 7 How to control simulations
- 8 How to initialize simulations
- 9 How to expand NEURON's library of mechanisms
- 10 Synaptic transmission and artificial spiking cells
- 11 Modeling networks
- 12 hoc, NEURON's interpreter
- 13 Object-oriented programming
- 14 How to modify NEURON itself
- Appendix A1 Mathematical analysis of IntFire4
- Appendix A2 NEURON's built-in editor
- Epilogue
- Index
3 - Expressing conceptual models in mathematical terms
Published online by Cambridge University Press: 01 September 2010
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 A tour of the NEURON simulation environment
- 2 The modeling perspective
- 3 Expressing conceptual models in mathematical terms
- 4 Essentials of numerical methods for neural modeling
- 5 Representing neurons with a digital computer
- 6 How to build and use models of individual cells
- 7 How to control simulations
- 8 How to initialize simulations
- 9 How to expand NEURON's library of mechanisms
- 10 Synaptic transmission and artificial spiking cells
- 11 Modeling networks
- 12 hoc, NEURON's interpreter
- 13 Object-oriented programming
- 14 How to modify NEURON itself
- Appendix A1 Mathematical analysis of IntFire4
- Appendix A2 NEURON's built-in editor
- Epilogue
- Index
Summary
But this critical act is not always unattended with the saddest and most fatal casualties.
Computational neuronal modeling usually focuses on voltage and current in excitable cells, but it is often necessary to represent other processes such as chemical reactions, diffusion, and the behavior of electronic instrumentation. These phenomena seem quite different from each other, and each has evolved its own distinct “notational shorthand.” As these specialized notations have particular advantages for addressing domain-specific problems, NEURON has provisions that allow users to employ each of them as appropriate (see Chapter 9). Apparent differences notwithstanding, there are fundamental parallels among these notations that can be exploited at the computational level: all are equivalent to sets of algebraic and differential equations. In this chapter, we will explore these parallels by examining the mathematical representations of chemical reactions, electrical circuits, and cables.
Chemical reactions
A natural first step in thinking about voltage-dependent or ligand-gated channel models or elaborate cartoons of dynamic processes is to express them with chemical reaction notation (i.e. kinetic schemes) (Fig. 3.1). Kinetic schemes focus attention on conservation of material (in a closed set of reactions, material is neither created or destroyed) and flow of material from one state to another.
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- Chapter
- Information
- The NEURON Book , pp. 36 - 54Publisher: Cambridge University PressPrint publication year: 2006