Much of the flexibility of NEURON is due to its use of a built-in interpreter, called hoc (pronounced “hoak”), for defining the anatomical and biophysical properties of models of neurons and neuronal networks, controlling simulations, and creating a graphical user interface. In this chapter we present a survey of hoc and how it is used in NEURON. Readers who seek the most up-to-date list of hoc keywords and documentation of syntax are referred to the online Programmer's Reference (see link at http://www.neuron.yale.edu/neuron/docs/docs.html). This can also be downloaded as a pkzip archive for convenient offline viewing with any WWW browser. The standard distribution for MSWindows includes a copy of the Programmer's Reference which is current as of the date of the NEURON executable that it accompanies (see the “Documentation” item in the NEURON program group).

NEURON's hoc is based on the floating point calculator by the same name that was developed by Kernighan and Pike (1984).

Finally: It was stated at the outset, that this system would not be here, and at once, perfected. You cannot but plainly see that I have kept my word. But I now leave my cetological system standing thus unfinished, even as the great Cathedral of Cologne was left, with the crane still standing upon the top of the uncompleted tower. For small erections may be finished by their first architects; grand ones, true ones, ever leave the copestone to posterity. God keep me from ever completing anything. This whole book is but a draught–nay, but the draught of a draught. Oh Time, Strength, Cash, and Patience!

Information processing in the nervous system involves the spread and interaction of electrical and chemical signals within and between neurons and glia. From the perspective of the experimentalist working at the level of cells and networks, these signals are continuous variables. They are described by the diffusion equation and the closely related cable equation (Rall 1977; Crank 1979), in which potential (voltage, concentration) and flux (current, movement of solute) are smooth functions of time and space. But everything in a digital computer is inherently discontinuous: memory addresses, data, and instructions are all specified in terms of finite sequences of 0s and 1s, and there are finite limits on the precision with which numbers can be represented. Thus there is no direct parallel between the continuous world of biology and what exists in digital computers, so special effort is required to implement digital computer models of biological neural systems. The aim of this chapter is to show how the NEURON simulation environment makes it easier to bridge this gap.

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.

Who should read this book?

This book is about how to use the NEURON simulation environment to construct and apply empirically based models of neurons and neural networks. It is written primarily for neuroscience investigators, teachers, and students, but readers with a background in the physical sciences or mathematics who have some knowledge about brain cells and circuits and are interested in computational modeling will also find it helpful. The emphasis is on the most productive use of NEURON as a means for testing hypotheses that are founded on experimental observations, and for exploring ideas that may lead to the design of new experiments. Therefore the book uses a problem-solving approach, with many working examples that readers can try for themselves.

What this book is, and is not, about

Formulating a conceptual model is an attempt to capture the essential features that underlie some particular function. This necessarily involves simplification and abstraction of real-world complexities. Even so, one may not necessarily understand all implications of the conceptual model. To evaluate a conceptual model it is often necessary to devise a hypothesis or test in which the behavior of the model is compared against a prediction.

Many people are already comfortable with their own text editor and will find it most convenient to load text files into hoc with the xopen () or load_file() command. However, NEURON has a built-in editor that is closely related, if not identical, to MicroEMACS (http://uemacs.tripod.com/), and which we will simply call “emacs.” In this era of richly menued, GUI-based editing software, NEURON's tiny emacs editor is definitely showing its age, and no one would ever confuse it with the much more powerful EMACS that has Lisp-like syntax (Cameron and Rosenblatt 1991). Nonetheless, it is quite capable and has the advantage of having the same “look and feel” on all platforms.

Like EMACS, emacs is a command-driven editor with modes and multiple buffers. What does this mean? Being “command-driven” means that there are no menus or buttons to click on with a mouse. Instead, special keystrokes, like the “keyboard shortcuts” in other editors, are used as commands to the editor. Having “modes” implies that some of these commands change how emacs responds to what you type, like the way many editors can be switched between “insert” and “replace” mode. The notion of “buffers” may seem strange, but if you have ever used any kind of editor or word processing software, then you have almost certainly worked with buffers even if you didn't realize it.

NEURON's extensive library of functions and graphical tools has been developed with an eye to providing those features that are most widely applicable in empirically based neural modeling. Since they are necessarily rather generic, it is sometimes desirable to change these features or add new ones in order to meet the special needs of individual projects. This is particularly important where the graphical user interface (GUI) is concerned, given the well-established role of the GUI in enhancing software utility. Here we show how to create new GUI tools and add new functions to NEURON.

A word about graphics terminology

Computer graphics literature is full of technical jargon, of which we will use only the most minute part. Think of a scene as being like a sheet of paper that has its own coordinate system (scene coordinates), and a view as a rectangular area on that sheet.

NEURON was initially developed to handle models of individual cells or parts of cells, in which complex membrane properties and extended geometry play important roles (Hines 1989; 1993; 1995). However, as the research interests of experimental and theoretical neuroscientists evolved, NEURON has been revised to meet their changing needs. Since the early 1990s it has been used to model networks of biological neurons (e.g. Destexhe et al. 1993; Lytton et al. 1997; Sohal et al. 2000). This work stimulated the development of powerful strategies that increase the convenience and efficiency of creating, managing, and exercising such models (Destexhe et al. 1994; Lytton 1996; Hines and Carnevale 2000). Increasing research activity on networks of spiking neurons (e.g. Riecke et al. 1997; Maass and Bishop 1999) prompted further enhancements to NEURON, such as inclusion of an event delivery system and development of the NetCon (network connection) class (see Chapter 10).

Consequently, since the latter 1990s, NEURON has been capable of efficient simulations of networks that may include biophysical neuron models and/or artificial spiking neurons.

In most cases, initialization basically means the assignment of values at time t = 0 for membrane potential, gating states, and ionic concentrations at every spatial position in the model. A model is properly initialized when clicking on the Init & Run button produces exactly the same results, regardless of previous simulation history. Of course we assume that model parameters have not changed between runs, and that any random number generator has been re-initialized with the same seed so that it produces the same sequence of “random” numbers. Models described by kinetic schemes require that each of the reactant states be initialized to some concentration. If linear circuits are involved, initial values must be assigned to voltages across capacitors and the internal states of operational amplifiers. For networks and other models that use the event delivery system, initialization also includes specifying which events are in transit to their destinations at time 0 (i.e. events generated, at least conceptually, at t ≤ 0 for delivery at t ≥ 0).

In NEURON, a cell model is a set of differential equations. Network models consist of cell models and the connections between them. Some forms of communication between cells, e.g. graded synapses, gap junctions, and ephaptic interactions, require more or less complete representations of the underlying biophysical mechanisms. In these cases, coupling between cells is achieved by adding terms that refer to one cell's variables into equations that belong to a different cell. The first part of this chapter describes the POINTER syntax that makes this possible in NEURON.

The same approach can be used for detailed mechanistic models of spike-triggered transmission, which entails spike initiation and propagation to the presynaptic terminal, transmitter release, ligand–receptor interactions on the postsynaptic cell, and somatodendritic integration. However, it is far more efficient to use the widespread practice of treating spike propagation from the trigger zone to the synapse as a delayed logical event. The second part of this chapter tells how the NetCon (network connection) class supports this event-based style of communication.

In the last part of this chapter, we use event-based communication to simplify the representations of neurons themselves, creating highly efficient implementations of artificial spiking cells; for example, integrate and fire “neurons.”

Object orientation is in many ways a natural style of programming whose techniques are reinvented constantly by every programer (Coplien 1992). Object notation consolidates these techniques, so that much of the tedious programming necessary to use them is automatically handled by the interpreter. An object can be thought of as an abstract data type that is very useful in separating the idea of what a thing does from the details of the way it goes about doing it. Support for objects in hoc came late to NEURON, after the notion of cable sections, and as a consequence there are several types of variables (e.g. sections, mechanisms, range variables) that are clearly treated as objects from a conceptual point of view but grew up without a uniform syntax.

In hoc, an object is a collection of functions, procedures, and data, where the data defines the state of the object. There is just enough extra syntax in hoc to support a subset of the object-oriented programming paradigm: specifically, it supports information hiding and polymorphism, but not inheritance. Yet this subset is sufficient to greatly increase the user's ability to maintain conceptual control of complex programs.

In Chapter 2 we remarked that a conceptual model is an absolute prerequisite for the scientific application of computational modeling. But if a computational model is to be a fair test of our conceptual model, we must take special care to establish a direct correspondence between concept and implementation. To this end, the research use of NEURON involves all of these steps:

1. Implement a computational model of the biological system

2. Instrument the model

3. Set up controls for running simulations

4. Save the model with instrumentation and run controls

5. Run simulation experiments

6. Analyze results

These steps are often applied iteratively. We first encountered them in Chapter 1, and we will return to each of them repeatedly in the remainder of this book.

Graphical user interface vs. hoc code: which to use, and when?

At the core of NEURON is an interpreter which is based on the hoc programming language (Kernighan and Pike 1984).

Neuronal function involves the interaction of electrical and chemical signals that are distributed in time and space. The mechanisms that generate these signals and regulate their interactions are marked by a wide diversity of properties, differing across neuronal cell class, developmental stage, and species (e.g. Chapter 7 in (Johnston and Wu 1995); also see (McCormick 1998)). To be useful in research, a simulation environment must provide a flexible and powerful means for incorporating new biophysical mechanisms in models. It must also help the user remain focused on the model instead of programming.

Such a means is provided to NEURON by NMODL, a high level language that was originally implemented for NEURON by Michael Hines and later extended by him and Upinder Bhalla to generate code suitable for linking with GENESIS (Wilson and Bower 1989).

Modeling and understanding

Modeling can have many uses, but its principal benefit is to improve understanding. The chief question that it addresses is whether what is known about a system can account for the behavior of the system. An indispensable step in modeling is to postulate a conceptual model that expresses what we know, or think we know, about a system, while omitting unnecessary details. This requires considerable judgment and is always vulnerable to hindsight and revision, but it is important to keep things as simple as possible. The choice of what to include and what to leave out depends strongly on the hypothesis that we are studying. The issue of how to make such decisions is outside the primary focus of this book, although from time to time we may return to it briefly.

The task of building a computational model should only begin after a conceptual model has been proposed. In building a computational model we struggle to establish a match between the conceptual model and its computational representation, always asking the question: would the conceptual model behave like the simulation? If not, where are the errors? If so, how can we use NEURON to help understand why the conceptual model implies that behavior?

Introducing NEURON

NEURON is a simulation environment for models of individual neurons and networks of neurons that are closely linked to experimental data.