Neuroscience-Net - Theoretical Neuroscience Article #10013

<body bgcolor="#FFFFFF"> <div align="left"><table border="3"> <tr> <td><font size="4"><strong><img src="images/h_theo1.gif" width="312" height="51"></strong></font></td> </tr> </table> </div><table border="0"> <tr> <td valign="top"><a name="top">© Neuroscience-Net<br> Volume 2, Article #10013 </a></td> <td align="right" width="500"><a name="top">Received June 12, 1997<br> Accepted for Publication July 29, 1997<br> Published August 25, 1997<br> </a></td> </tr> </table> <p align="left"><a href="http://www.neuroscience.com/theoretical_neuroscience.html"><font size="4"><strong><img src="images/b_back.gif" border="0" width="76" height="37"></strong></font></a></p> <p align="center"><font size="4"><strong>A Library for the Compartmental Simulation of Neurons</strong></font></p> <p align="left"><font size="3">J. Strout, Department of Neuroscience, University of California, San Diego</font></p> <p><font size="2">Send correspondence to:</font></p> <p><font size="2">J. Strout<br> Department of Neuroscience,<br> University of California, San Diego<br> La Jolla, CA 92093-0608 (USA)<br> </font><a href="mailto:jstrout@ucsd.edu"><font size="2">jstrout@ucsd.edu</font></a></p> <blockquote> <p><font size="2"><strong>KEY WORDS:</strong> </font><font size="3">neural simulation, compartmental modeling, C++, class library</font></p> </blockquote> <hr> <p align="left"><font size="6">Abstract<br> </font><font size="3">(Neuroscience-Net, Volume 2, Article #10013; August 25, 1997)</font></p> <p align="left"><font size="3">A programming library ("CONICAL") is presented which assists in the construction of compartmental models of neurons. The library consists of approximately 20 classes in the C++ programming language. Standard input and output are used, and the code has been co-developed under several operating systems, to ensure maximum portability. The library is non-monolithic, i.e. portions of it may be used as needed without the entire library present. Complex classes were derived from simpler ones in several steps to provide flexible opportunities for customization; and as a C++ library, the simulation code may be readily embedded in larger applications. Documentation, including introductory material and examples, is provided in hypertext format and can be viewed with any tables-capable World-Wide Web browser. Classes provided include cylindrical compartments, passive and active ion channels, and synapses, including one based on Markov kinetic models. Performance of the library was compared to the Genesis and Neuron neural simulators on a simple action potential simulation. The CONICAL program required less user-written code and much less memory than the equivalent Genesis script, and ran more than twice as fast; it was also significantly faster and more memory-efficient than the comparable Neuron script. CONICAL provides an alternative simulation environment which may be useful when portability, extensibility, or efficiency is needed, especially on personal computers or single-processor workstations.</font></p> <p align="center"><a name="top"><font size="4"><strong>A Library for the Compartmental Simulation of Neurons</strong></font></a></p> <p align="left"><font size="3">J. Strout, Department of Neuroscience, University of California, San Diego</font></p> <p><font size="2">Send correspondence to:</font></p> <p><font size="2">J. Strout<br> Department of Neuroscience,<br> University of California, San Diego<br> La Jolla, CA 92093-0608 (USA)<br> </font><a href="mailto:jstrout@ucsd.edu"><font size="2">jstrout@ucsd.edu</font></a></p> <blockquote> <p><font size="2"><strong>KEY WORDS:</strong></font><font size="3"> neural simulation, compartmental modeling, C++, class library</font></p> </blockquote> <hr> <ul> <li><a href="TN00013_ab.html" target="_parent">Abstract</a></li> <li><a href="#intro">Introduction</a></li> <li><a href="#Methods">Materials and Methods</a></li> <li><a href="#results">Results</a></li> <li><a href="#discuss">Discussion</a></li> <li><a href="#acknow">Acknowledgments</a></li> <li><a href="#references">References</a></li> <li><a href="#figures">Figures and Legends</a></li> </ul> <p align="left"><a name="intro"><font size="6"><strong>Introduction</strong></font></a></p> <p align="left"><font size="3">Biologically detailed simulations of neurons and neural networks are typically based on compartmental modeling; that is, each cell is divided into many isopotential compartments, joined by conductances, and activated via simulated ion channels and current injectors. Compartmental models are often built using dedicated Unix-based simulation packages, e.g. Genesis (Wilson et al., 1989) or Neuron (Hines 1989). Each such package has its own interpreted scripting language, in which users define the components and running parameters of their simulations. In the hands of an experienced user with access to a compatible computer system, these modeling packages are powerful research tools. However, they do suffer several drawbacks for other users: they can be difficult to learn; they are not easy to modify, extend, and integrate with other software; and they are generally not portable to operating systems other than Unix or MS-DOS.</font></p> <p align="left"><font size="3">When existing software is not suitable, it may be necessary to write custom software. However, a significant fraction of the time spent in developing a simulation in a general programming language is consumed by writing, testing, and debugging core data structures and algorithms, even though these rarely change for a particular simulation. This extra cost may be avoided by using an existing library of code which handles these lower-level issues, freeing the user to concentrate on the unique aspects of the desired simulation.</font></p> <p align="left"><font size="3">Most modern code libraries make use of object-oriented programming techniques, which offer important advantages over procedural libraries. First, a set of object classes presents a cleaner, simpler interface to its user. Details of implementation are hidden (a property known as encapsulation); and all classes derived from a common base inherit the properties of that base class. Thus, by understanding a handful of base classes, one can grasp the general behavior of any object in the library. Second, algorithms and data structures are tied together; instead of calling a function and passing it some data, an object's method is called directly from the object reference itself; this reduces the frequency of programming errors and makes the dependencies between the data and algorithms more clear. Third, if the object is a specialized type (i.e. of a derived class), the appropriate code for that type will be automatically invoked. This is a very powerful feature, as it allows new class behavior to be invoked without changing existing classes.</font></p> <p align="left"><font size="3">A number of object-oriented languages are currently available on a wide variety of platforms, for example, C++, Smalltalk, and Python. Of these, C++ has a number of desirable features. It is strongly typed, which means that many mistakes (such as trying to square a string) are caught as soon as the program is compiled, rather than at run time or not at all. C++ is becoming increasingly common in both business and scientific programming; as a result, a wide variety of educational resources, class libraries, and compilers are available. As an extension of C, many programmers will already be comfortable with its syntax, even if they have never used C++. Finally, it tends to be efficient in both speed and memory usage (especially as compared to interpreted languages such as Python), and allows the programmer to use both high-level or low-level constructs as required. One drawback to C++ is the somewhat cryptic syntax inherited from the C programming language, e.g., the use of "&&" for "and". Given the widespread use of C and C++, this is apparently a minor inconvenience.</font></p> <p align="left"><font size="3">Based on these considerations, a C++ class library was created. CONICAL, the Computational Neuroscience Class Library, is a hierarchy of classes in the C++ programming language. It is intended to provide all the common functionality needed in compartmental simulations, while remaining efficient and simple to understand. The library may be used in whole or in part as needed, and each object class is designed to be readily extended or modified through the standard inheritance mechanism. CONICAL has been co-developed and tested with Unix, DOS, and MacOS compilers, and makes use of only standard functions and calls, ensuring maximum portability among various platforms and compilers. The result is a flexible, efficient alternative to existing packages for compartmental modeling.</font></p> <p align="left"><font size="3">CONICAL provides classes to simulate isopotential compartments, which may include a variety of passive or active ion channels, and which can be joined electrically or via synapses. It is suited to a variety of levels of simulation, from single neurons reconstructed in great detail, to large networks of more reduced model neurons. In addition to this basic functionality, CONICAL includes classes to simulate direct current injection, and to simplify the recording of data. Although it is primarily intended for low-level compartmental modeling, the library also includes an integrate-and-fire compartment type which can greatly reduce the computation needed for large multi-cell simulations. Integrate-and-fire compartments can be freely intermixed with standard compartments, allowing (for example) one to combine a detailed dendritic model with a simplified axon.</font></p> <p align="left"><font size="3">All files and documentation are available via the CONICAL World Wide Web site (</font><a href="http://www-acs.ucsd.edu/~jstrout/conical/"><font size="3">http://www-acs.ucsd.edu/~jstrout/conical/</font></a><font size="3">). This includes introductory material, a class reference, example programs and results, and application notes.</font></p> <p align="left"> </p> <p align="left"><a name="Methods"><font size="6"><strong>Methods</strong></font></a></p> <p align="left"><font size="3">CONICAL was developed using common C++ syntax, conforming to the emerging ANSI standard (Koenig, 1995). Constructs which are frequently troublesome, i.e. templates and exceptions, were avoided. File names are restricted to eight letters, and do not depend on case sensitivity, so that they may be used without change on any operating system.</font></p> <p align="left"><font size="3">Since the ANSI C++ standard has not yet solidified (Koenig, 1995), various compilers often differ in their implementation of subtle details. For example, some compilers allow you to access a variable declared in a "for" statement from outside the loop, while others consider this an error. To make the code as portable as possible, it was necessary to co-develop the code under a variety of systems (i.e. operating systems and compilers). Troublesome constructs were quickly found in this way, and replaced with code which compiled cleanly on all systems. At the time of this writing, the library has been compiled and tested under four systems:</font></p> <ul> <li><p align="left"><font size="3">(1) gcc 2.7.2 running under IRIX 5.3 on a Silicon Graphics Crimson workstation</font></p> </li> <li><p align="left"><font size="3">(2) gcc 2.7.2 running under SunOS 4.1.3 on a Sun Microsystems Sparc 10 workstation</font></p> </li> <li><p align="left"><font size="3">(3) Borland Turbo C++ 3.0 running under MS-DOS 6.0 on a Datel 386 PC</font></p> </li> <li><p align="left"><font size="3">(4) Metrowerks CodeWarrior 8.0 running under MacOS 7.5.3 on an Apple Macintosh 8500</font></p> </li> </ul> <p align="left"><font size="3">Test programs compile without modification on all four systems, and produce identical output. Given the diverse nature of these systems, it is likely that the library would compile without change on most C++ compilers which adhere to the emerging ANSI standard.</font></p> <p align="left"><font size="3">Compartmental modeling is a well-known technique (e.g. Segev et al., 1989). Briefly, a neuron is represented by one or more isopotential compartments. Each compartment consists of a resistance and capacitance across the cell membrane, a resistive connection to neighboring compartments, and possibly a number of active conductances which represent voltage- or ligand-gated ion channels. In addition, each membrane resistance is placed in series with a voltage source which results from the relative concentrations of charged ions inside and outside the cell. </font><a href="images/mms06971.gif" target="_top"><img src="images/mms06971_T.gif" align="top" border="1" width="72" height="74"></a> <font size="3">(See </font><a href="images/mms06971.gif" target="_top"><font size="3">Figure 1</font></a><font size="3">.)</font></p> <p align="left"><font size="3">The connected network of voltage sources, conductances, and capacitance effects produces a system of differential equations. For the general case (i.e., compartments with active channels and which may be connected in loops), the equations must be solved numerically. CONICAL uses the exponential Euler integration method, which is optimized for equations of this form (MacGregor 1987), and which produces a reasonable combination of speed and accuracy.</font></p> <p align="left"><font size="3">CONICAL consists of approximately twenty classes arranged in an inheritance tree, as shown in </font><a href="images/mms06972.gif" target="_top"><img src="images/mms06972_T.gif" border="1" width="72" height="32"></a> <a href="images/mms06972.gif" target="_top"><font size="3">Figure 2</font></a><font size="3">. The tree has four roots, that is, four classes which have no base class. The Stepper class forms a base of any object which requires periodic updates; this includes compartments and active channels, among others. Stepper objects can be attached to a Stepmaster object, which streamlines the updating of multiple objects. CONICAL's one global variable, gStepmaster, is of this type; by default, newly created Steppers are attached to this object.</font></p> <p align="left"><font size="3">Classes VSource and VSink represent any voltage source or sink, respectively. Either may be used alone, for example, as a constant voltage source. They are combined in the Compartment class, which is a voltage source and sink, as well as a Stepper. On each tick of the simulation clock, a compartment updates its voltage by exponential Euler integration, taking into account membrane resistance and capacitance. Each compartment may also store an axial conductance, though this is not used by the compartment itself; rather, this variable is used to set the intercompartment conductance when compartments are joined together. Membrane parameters for a generic compartment must be assigned with actual values, and no physical dimensions are stored. For most purposes, it is easier to use the Cylinder class, which automatically computes the absolute resistances and capacitance from cylinder dimensions plus membrane specific resistance, specific capacitance, and specific axial resistance. Cylinder has one derived class: Spiker, an "integrate-and-fire" compartment, which can generate simplified action potentials with a much coarser time scale, and without active ion channels.</font></p> <p align="left"><font size="3">Current flows into any voltage source via an object of the Current class. This class may be instantiated directly to create a passive ion channel or "leak" current, that is, one with a fixed reversal potential. Several lines of derived classes extend this basic functionality. The Injector class implements an ideal current source, i.e. one that delivers constant current regardless of the potential of the voltage sink to which it is connected. The Link class connects a voltage source to a voltage sink; the amount of current flowing to the sink depends on the relative potential of the two. This is the class commonly used to connect compartments together (though for a two-way connection, a pair of links must be used). Typically, the conductance of a Link is set to the average of the axial conductances of the compartments it joins. To economically implement conduction delays, one may substitute a Delay link, which uses the voltage of the source at some time in the past, rather than the present voltage.</font></p> <p align="left"><font size="3">Ion channels whose conductance varies with time are derived from the Channel class, which is itself a type of current. Real ion channels respond to a wide variety of variables, such as ligands, voltages, and so on; this diversity is reflected by the variety of classes derived from the basic Channel class. One type of channel is the synapse, which sets its conductance as a function of the concentration of neurotransmitter in the synaptic cleft. The basic synapse models this concentration as simply a square pulse, initiated when the voltage of the presynaptic compartment exceeds a threshold. Specialized synapses include AlphaSyn, which implements a simple alpha-function response, and MarkovSyn, a more flexible synapse whose kinetics can be defined in the form of a Markov kinetic model. The other major type of channel is the Hodgkin-Huxley-form ion channel, a flexible base class for any channel with one or two gating variables (Hodgkin & Huxley, 1952). Derived from this is ChanStd (standard channel), which allows the voltage dependency and kinetics to be specified with the standard equation forms and parameters typically used to describe active ion channels (e.g., Migliore et al., 1995). This class is derived from Channel in several steps, allowing its behavior to be efficiently overridden at any point; for example, one could create a channel which uses Hodgkin-Huxley gating variables, but adjusts these variables by a look-up table, by overriding ChanHH and implementing only the "UpdateM" and "UpdateH" methods.</font></p> <p align="left"><font size="3">As a C++ class library, CONICAL requires no functions for input and output; standard C++ constructs can be used instead. One optional output class (StepStream) is included, which simplifies the recording of tabular data at each step of the simulation.</font></p> <p align="left"><font size="3">Typical usage of CONICAL proceeds as follows. A small main program is written to create the simulation objects and link them together. These will normally include a Cylinder compartment, joined by Links to its neighbors, and each containing one or more active channels (usually ChanStd). For a multi-cell simulation, additional cells are created in the same manner, which may be joined by synapses (e.g., MarkovSyn) or gap junctions (Link or Delay). In the simplest case, model parameters are hardcoded into the main program; in this case, changing a parameter means recompiling only the main program, not the rest of the library. For more flexibility, parameters may be entered by the user or read from a file using the standard C++ input/output capability. Once the simulation has been set up, a short main loop is begun. This loop makes one call to the library ("gStepMaster.StepAll(dt)") to simultaneously update all the simulation components, generates any output of interest, and repeats until done. The size of the time-step is specified in the call to "StepAll", and may be adjusted between steps to dynamically balance speed against accuracy.</font></p> <p align="left"><font size="3">To embed compartmental modeling in a larger software application, such as an educational demonstration or graphical network builder, one would simply link the CONICAL classes into the project. Objects would be created in response to the user's commands, and the graphical display could be continuously updated as the simulation proceeds. Though such a program has not yet been attempted, CONICAL was designed with such applications in mind. To reduce the possibility of conflicts with existing software frameworks, CONICAL defines only a single global variable and fewer than five global functions (depending on the modules included). In addition, since CONICAL does not require any other C++ libraries (except the standard input/output classes), use of CONICAL does not dictate a particular implementation of such classes as strings or containers.</font></p> <p align="left"> </p> <p align="left"><a name="results"><font size="6"><strong>Results</strong></font></a></p> <p align="left"><font size="3">Preliminary performance benchmarks have been performed comparing a small CONICAL program to the equivalent Genesis script and a similar Neuron script. Each program created a single compartment with standard Hodgkin-Huxley ion channels. A constant current was injected, resulting in a train of action potentials. The simulation ran for 100 to 1000 ms of simulation time, with a constant time step of 0.1 ms. The code used for the 100 ms version is available on the CONICAL web site as example program 4.</font></p> <p align="left"><font size="3">The performance results are shown in </font><a href="images/mms06973.gif" target="_top"><img src="images/mms06973_T.gif" border="1" width="72" height="69"></a> <a href="images/mms06973.gif" target="_top"><font size="3">Figure 3</font></a><font size="3">. The CONICAL program required less user-written code as the Genesis script, needed slightly more than one-tenth as much memory, and ran the simulation more than twice as fast, at all simulation times used. The Neuron script was not strictly equivalent, since it is impossible to set most of the Hodgkin-Huxley ion channel parameters from within the scripting language; as a result, the CONICAL program contained slightly more code. However, it still ran significantly faster and required less memory than the Neuron script. CONICAL's efficiency is probably due partly due to compilation of the code, as compared to interpretation, and partly due to linking only those components that are needed. For more complex simulations, the advantages of CONICAL over Genesis and Neuron might be attenuated. Further benchmarks are planned to elucidate the relationship between simulation size and runtime efficiency.</font></p> <p align="left"> </p> <p align="left"><a name="discuss"><font size="6"><strong>Discussion</strong></font></a></p> <p align="left"><font size="3">CONICAL is intended to compliment existing simulation packages. It is particularly suited to users who are already familiar with C or C++, or who need the extra efficiency or portability not available with larger simulators. Its modularity allows users to take as much or as little as they need for a particular application. With the library tending to the low-level details of integration, data structure maintenance, and so on, the user is freed to program in an exploratory manner, quickly trying out simulation ideas.</font></p> <p align="left"><font size="3">CONICAL currently has two major limitations. First, it requires a C++ compiler if it is to be used alone. For some classroom settings, that may not be practical; a graphical (or script-based) simulator front-end might be appropriate in that situation. Second, CONICAL currently provides no graphing capability; the user must supply some graphing or data analysis software. While this is readily available on any platform, it might be more convenient to have graphs generated directly from a CONICAL main program. It also lacks some of the advanced features found in other simulation packages; for example, it does not currently read files generated by cell-tracing software. Despite these drawbacks, it is suggested that CONICAL fills an important niche in our array of neural simulation tools.</font></p> <p align="left"> </p> <p align="left"><a name="acknow"><font size="6"><strong>Acknowledgements</strong></font></a></p> <p align="left"><font size="3">The author would like to acknowledge S. Young and M. Ellisman for helpful comments on the manuscript, and M. Wong for technical assistance with the Neuron software. This research was supported in part by an NSF Graduate Fellowship.</font></p> <p align="left"> </p> <p align="left"><a name="references"><font size="6"><strong>References</strong></font></a></p> <p align="left"><font size="3">Hines, M. (1989). A program for simulation of nerve equations with branching geometries. International Journal of Biomedical Computing, 24, 33-68.</font></p> <p align="left"><font size="3">Hodgkin, A.L., and Huxley, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.), 117, 500-544.</font></p> <p align="left"><font size="3">Koenig, A.(ed) (1995). ISO/ANSI C++ Draft. At URL <</font><a href="http://www.cygnus.com/misc/wp/"><font size="3">http://www.cygnus.com/misc/wp/</font></a><font size="3">> on 3 December 1996.</font></p> <p align="left"><font size="3">Migliore, M., Cook, E. P., Jaffe, D. B., Turner, D. A., and Johnston, D. (1995). Computer simulations of morphologically reconstructed CA3 hippocampal neurons. J. Neurophysiol., 73, 1157-1168.</font></p> <p align="left"><font size="3">Segev, I., Fleshman, J. W., and Burke, R. E. (1989). Compartmental models of complex neurons. In Koch, C. & Segev, I. (eds), Methods in Neuronal Modeling: From Synapses to Networks. The MIT Press, Cambridge, pp.63-96.</font></p> <p align="left"><font size="3">Wilson, M.A., Bhalla, U.S., Uhley, J.D., and Bower, J.M. (1989). GENESIS: a system for simulating neural networks. In D. Touretzky (ed), Advances in Neural Information Processing Systems . Morgan Kaufman, San Mateo, pp. 485-492.</font></p> <p align="left"> </p> <p align="left"><a name="figures"><font size="6"><strong>Figure Legends</strong></font></a></p> <div align="left"><table border="0" cellpadding="2"> <tr> <td valign="top"><a href="images/mms06971.gif" target="_top"><img src="images/mms06971_T.gif" border="1" width="72" height="74"></a></td> <td><p align="left"><a href="images/mms06971.gif" target="_top"><font size="3">Figure 1</font></a><font size="3"> -- Overview of compartmental modeling. In (a), a branching section of dendrite has been divided into seven cylindrical compartments. Each is connected to its neighbors via bidirectional links. In the CONICAL library, these objects would be implemented with the Cylinder and Link class, respectively. (b) shows an equivalent electric circuit for one compartment. Links to neighboring compartments (left) are resistors; the cell membrane includes a capacitance, a resistor and membrane potential, and variable resistors which correspond to active channels (left to right).</font></p> </td> </tr> <tr> <td valign="top"><a href="images/mms06972.gif" target="_top"><img src="images/mms06972_T.gif" border="1" width="72" height="32"></a></td> <td><p align="left"><a href="images/mms06972.gif" target="_top"><font size="3">Figure 2</font></a><font size="3"> -- Inheritance diagram for the CONICAL library. Each line indicates that the class on the right is derived from the class on the left; a derived class implements all the functionality of its base class, and extends it with additional capabilities. Note that Compartment, Delay, and MarkovSyn each derive from several classes.</font></p> </td> </tr> <tr> <td valign="top"><a href="images/mms06973.gif" target="_top"><img src="images/mms06973_T.gif" border="1" width="72" height="69"></a></td> <td><a href="images/mms06973.gif" target="_top"><font size="3">Figure 3</font></a><font size="3"> -- A CONICAL program is compared to the equivalent Genesis and Neuron scripts on several measures: (a) kilobytes of memory used at run time; (b) lines of user-written code, excluding comments; (c) CPU time required as a function of simulation time. Tests were run on a Sparc 10 workstation under SunOS 4.1.3. The amount of code (b) for the Neuron script is not strictly comparable to the others, since several parameters of the model could not be set from within the scripting language.</font></td> </tr> </table> </div><p align="center"> </p> <div align="center"><center><table border="0"> <tr> <td align="center"><a href="http://www.neuroscience.com/theoretical_neuroscience.html" target="_top"><img src="images/b_back.gif" alt="Back" border="0" width="76" height="37"></a> </td> <td align="center"><a href="#top" target="_top"><img src="images/b_top.gif" alt="Top" border="0" width="76" height="37"></a> </td> <td><a href="newbody.html"><img src="images/b_body.gif" alt="Body" border="0" width="76" height="37"></a> </td> </tr> <tr> <td><a href="http://www.neuroscience.com/articles.html" target="_top"><img src="images/b_ita1.gif" alt="Index to Articles" border="0" width="179" height="54"></a> </td> <td><a href="http://www.neuroscience.com/newart.html" target="_top"><img src="images/b_naw.gif" alt="New Articles This Week" border="0" width="179" height="54"></a> </td> <td><a href="http://www.neuroscience.com/index.html" target="_top"><img src="images/b_home1.gif" alt="Return Home" border="0" width="179" height="54"></a></td> </tr> </table> </center></div> </body>