Translating network models to parallel hardware in NEURON.

The increasing complexity of network models poses a growing computational burden. At the same time, computational neuroscientists are finding it easier to access parallel hardware, such as multiprocessor personal computers, workstation clusters, and massively parallel supercomputers. The practical question is how to move a working network model from a single processor to parallel hardware. Here we show how to make this transition for models implemented with NEURON, in such a way that the final result will run and produce numerically identical results on either serial or parallel hardware. This allows users to develop and debug models on readily available local resources, then run their code without modification on a parallel supercomputer.

Model structure analysis in NEURON : toward interoperability among neural simulators.

One of the more important recent additions to the NEURON simulation environment is a tool called ModelView, which simplifies the task of understanding exactly what biological attributes are represented in a computational model. Here, we illustrate how ModelView contributes to the understanding of models and discuss its utility as a neuroinformatics tool for analyzing models in online databases and as a means for facilitating interoperability among simulators in computational neuroscience.

Amphotericin B-induced myelopathy.

Two patients with coccidioidal meningitis experienced transient neurologic deficits shortly after receiving intrathecal injections of amphotericin B. Continuation of treatment eventually led to a severe flaccid paraparesis with a thoracic sensory level in one patient, and a partial Brown-Séquard's syndrome in the other. Myelography was normal in both, with no evidence of arachnoiditis. Autopsy findings in the first patient showed a focal area of necrosis in the left half of the spinal cord consistent with the patient's clinical findings during life. The distribution of the lesion corresponded to the area supplied by a central sulcal artery. Amphotericin B may exert a direct toxic effect on the spinal cord or its vascular supply when given intrathecally.

NEURON: a tool for neuroscientists.

NEURON is a simulation environment for models of individual neurons and networks of neurons that are closely linked to experimental data. NEURON provides tools for conveniently constructing, exercising, and managing models, so that special expertise in numerical methods or programming is not required for its productive use. This article describes two tools that address the problem of how to achieve computational efficiency and accuracy.

Numerical analysis of electrotonus in multicompartmental neuron models.

Advances in anatomical and biophysical techniques have produced a wealth of data from certain classes of mammalian central neurons. In order to evaluate quantitatively these data and the hypotheses of neuronal function to which they lead, we have developed LADDER, a computer program for simulating neuronal electrotonus under current- or voltage-clamp conditions. This program models a neuron as an unbranched series of isopotential compartments composed of resistive and capacitive elements, i.e., a ladder network. Synaptic inputs are represented by realistic time-varying conductance changes. LADDER solves the set of simultaneous linear differential equations that describe this model by numerical integration in the time domain. Several tests confirmed the accuracy of LADDER's calculations. Simulated responses to current pulses were quantitatively similar to the charging transients that have been reported in hippocampal CA3 pyramidal neurons. These digital simulations also agreed closely with previously reported results from an analog neuronal model. In addition, transfer of synaptic charge in the model neuron, under both current- and voltage-clamp conditions, equalled theoretical predictions from two-port analyses of linear electrotonus. To illustrate the application of LADDER, we present the results of simulations involving the spread of voltage and current arising from various synaptic inputs.

Kinetics of diffusion in a spherical cell. I. No solute buffering.

Realistic neuron models that involve effects of concentration changes of second messengers on ion channels must include processes such as diffusion and solute buffering. These processes, which span a wide range of spatial and temporal scales, may impose a severe computational burden. In this paper and its companion, we examine the kinetics of diffusion and present methods for stimulating it accurately and efficiency. The problem of calcium diffusion in a spherical cell is used as a device to demonstrate the practical application of our analysis. However, the scope of these papers is not limited to this problem. The same analysis that we apply and concerns that we raise are germane to the spread of any second messenger, and can be adapted to other geometries. The focus of this paper is the simplest case: diffusion in the absence of solute buffering. This analysis also applies whenever buffering is so fast that it is instantaneous compared to diffusion, or so slow that concentration gradients have dissipated before substantial buffering takes place. The second paper investigates the more difficult situation where diffusion and buffering occur at comparable rates. In the absence of buffering, concentration changes produced by diffusion can be fit by an infinite series of exponential terms. We show how to design a model with N + 1 compartments that fits the N slowest terms of this series exactly in a shell just inside the cell membrane.

Kinetics of diffusion in a spherical cell. II. Solute buffering included.

This paper on diffusion kinetics in neurons presents an analysis of diffusion in the presence of solute buffering. Computational rather than theoretical methods are usually necessary since buffering generally precludes an analytical solution to the diffusion equations. As in the companion paper, our methods are illustrated in the context of calcium diffusion in a spherical cell. However, the same methods can be applied to the spread of any second messenger and other geometries. Analytical or computational predictions of the time course of diffusion and buffering may help guide further experiments and simulations. For example, simulations of calcium diffusion in a model of the bullfrog sympathetic ganglion cell show that buffering at depths greater than 5-6 microns is almost instantaneous compared to diffusion from sources at the cell membrane. Since buffering complicates the design of multicompartmental models, we demonstrate that a few compartments designed on the basis of diffusion alone (Carnevale and Rosenthal, 1992) may be a satisfactory framework for a model that includes bimolecular buffering. An analytical solution may be possible if the buffering reaction can be linearized. We describe a method for linearizing bimolecular saturating buffering, i.e., approximating it by a unimolecular non-saturating process that immobilizes solute. The analytical solution for the linearized reactive diffusion problem fits a non-linear model of calcium movement in the bullfrog sympathetic ganglion cell quite well after a few milliseconds.

Neuron simulations with SABER.

Computational models can provide critical tests of hypotheses of neuronal function. These models are essential for dealing with the complications of time- and voltage-dependent (active) ionic conductances. Commercial circuit analysis programs have been useful tools for this work. We report our experience modelling biophysically realistic membrane properties with SABER (Analogy, Inc.), a new general purpose simulator. SABER allows construction of models with arbitrary membrane properties. This is a major advantage over similar programs (e.g. SPICE), which are limited to a predefined library of electronic components. The empirically determined equations that describe rate constants, ionic conductances, currents, and concentration shifts can be translated directly into model elements ('templates') written in C-like code. We describe the development of SABER models that simulate a synapse and an action potential.

Two reciprocating current components underlying slow oscillations in Aplysia bursting neurons.

The mechanisms of the slow oscillatory potential in burst firing neurons in the abdominal ganglion of Aplysia californica (L3-L6 and R15) were studied using voltage clamp methods, including a novel tract and hold technique. The steady-state negative resistance characteristic (NRC) of these neurons is attributed to the activation of a moderately fast, persistent, inward current over a range of membrane potential below spike threshold. This inward current is quite sensitive to changes in external sodium concentration (Na)0 and insensitive to potassium (K)0. By contrast, the portion of the I-V curve below the NRC range is insensitive to (Na)0, but highly sensitive to (K)0. The results of 'track and store' voltage clamping show that there are actually two reciprocating currents whose combined action produces the slow oscillation. In addition to the inward current, there is a slow outward current which develops during the depolarized (burst) phase. The slow outward current can also be evoked, and more completely examined, with prolonged depolarizing voltage commands. The extremely slow decay of this current (tau approximately 45 sec) appears to be the factor underlying the slow, ramplike depolarization of Vm during the interburst interval. This slow outward current is insensitive to changes of (Na)0, but changes with (K)0 in a manner consistent with the Nerst equation. We conclude that the burst-inducing slow oscillations are generated as follows: a moderately fast inward sodium dependent current (INa) produces a regenerative depolarization, and this in turn, produces a much slower outward potassium current (IS) which hyperpolarizes the cell. The cycle is completed when IS has decayed sufficiently to allow Vm to depolarize enough to reactivate INa. We have used a quantitative version of this model to determine the time courses of gNa and gK throughout the oscillation, and to explain why different portions of the oscillatory cycle display 'graded' or 'all-or-none' behavior.

Integration of data obtained at fixed intervals.

This article discusses the design and implementation of a program well suited to integrating experimental or simulated data obtained at fixed intervals. The program uses Simpson's method and produces substantially better accuracy than trapezoidal rule integration at little extra computational cost. It accepts command line specification of integration parameters (step size and/or number) and source files. Multiple source files and integration parameters can be specified at runtime. Output can be displayed on the console or redirected to an ASCII file.

Digitizing graphic data.

Using a digitizing pad instead of a ruler and calipers accelerates and increases the accuracy of graphic data analysis. Factors important in choosing and using such a pad are discussed in this article. A program is presented which facilitates use of the Houston Instruments HiPad DT11, a digitizing pad which is particularly well suited to neurophysiological applications.

The NEURON simulation environment.

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.

Expanding NEURON's repertoire of mechanisms with NMODL.

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 rich diversity of properties that precludes a "one size fits all" approach to modeling. This article presents a summary of how the model description language NMODL enables the neuronal simulation environment NEURON to accommodate these differences.

Passive normalization of synaptic integration influenced by dendritic architecture.

We examined how biophysical properties and neuronal morphology affect the propagation of individual postsynaptic potentials (PSPs) from synaptic inputs to the soma. This analysis is based on evidence that individual synaptic activations do not reduce local driving force significantly in most central neurons, so each synapse acts approximately as a current source. Therefore the spread of PSPs throughout a dendritic tree can be described in terms of transfer impedance (Z(c)), which reflects how a current applied at one location affects membrane potential at other locations. We addressed this topic through four lines of study and uncovered new implications of neuronal morphology for synaptic integration. First, Z(c) was considered in terms of two-port theory and contrasted with dendrosomatic voltage transfer. Second, equivalent cylinder models were used to compare the spatial profiles of Z(c) and dendrosomatic voltage transfer. These simulations showed that Z(c) is less affected by dendritic location than voltage transfer is. Third, compartmental models based on morphological reconstructions of five different neuron types were used to calculate Z(c), input impedance (Z(N)), and voltage transfer throughout the dendritic tree. For all neurons, there was no significant variation of Z(c) with location within higher-order dendrites. Furthermore, Z(c) was relatively independent of synaptic location throughout the entire cell in three of the five neuron types (CA3 interneurons, CA3 pyramidal neurons, and dentate granule cells). This was quite unlike Z(N), which increased with distance from the soma and was responsible for a parallel decrease of voltage transfer. Fourth, simulations of fast excitatory PSPs (EPSPs) were consistent with the analysis of Z(c); peak EPSP amplitude varied <20% in the same three neuron types, a phenomenon that we call "passive synaptic normalization" to underscore the fact that it does not require active currents. We conclude that the presence of a long primary dendrite, as in CA1 or neocortical pyramidal cells, favors substantial location-dependent variability of somatic PSP amplitude. In neurons that lack long primary dendrites, however, PSP amplitude at the soma will be much less dependent on synaptic location.

Comparisons between Active Properties of Distal Dendritic Branches and Spines: Implications for Neuronal Computations.

The specific contributions of distal dendrites to the computational properties of cortical neurons are little understood and are completely ignored in most network simulations of higher brain functions. Compartmental models, based on realistic estimates of morphology and physiology, provide a means for exploring these contributions. We have pursued analysis of a model of synaptic integration in a distal dendrite bearing four spines, using a new general-purpose simulation program called SABER. We have analyzed this model under the assumption that the dendrite contains sites of impulse-generating membrane, and we have compared its responses to synaptic activation with the case of impulse-generating membrane located instead in the spine heads, as previously reported. Both types of models generate basic logic operations, such as AND, OR, and AND-NOT gates. Active spine heads require lower excitatory synaptic conductances, but active branch segments lead to larger responses in the soma. The transients recorded near the soma give no evidence of their origin in either active branch or active spines, indicating that the interpretation of experimental recordings with regard to sites of distal active responses must be viewed with caution. The results suggest the hypothesis that a hierarchy of logic operations is virtually inherent in the branching structure of dendritic trees of cortical pyramidal neurons. Inclusion of these properties in representations of cortical neurons would greatly enhance the computational power of neural networks aimed at simulating higher brain functions.

Comparative electrotonic analysis of three classes of rat hippocampal neurons.

We present a comparative analysis of electrotonus in the three classes of principal neurons in rat hippocampus: pyramidal cells of the CA1 and CA3c fields of the hippocampus proper, and granule cells of the dentate gyrus. This analysis used the electrotonic transform, which combines anatomic and biophysical data to map neuronal anatomy into electrotonic space, where physical distance between points is replaced by the logarithm of voltage attenuation (log A). The transforms were rendered as "neuromorphic figures" by redrawing the cell with branch lengths proportional to log A along each branch. We also used plots of log A versus anatomic distance from the soma; these reveal features that are otherwise less apparent and facilitate comparisons between dendritic fields of different cells. Transforms were always larger for voltage spreading toward the soma (V(in)) than away from it (V(out)). Most of the electrotonic length in V(out) transforms was along proximal large diameter branches where signal loss for somatofugal voltage spread is greatest. In V(in) transforms, more of the length was in thin distal branches, indicating a steep voltage gradient for signals propagating toward the soma. All transforms lengthened substantially with increasing frequency. CA1 neurons were electrotonically significantly larger than CA3c neurons. Their V(out) transforms displayed one primary apical dendrite, which bifurcated in some cases, whereas CA3c cell transforms exhibited multiple apical branches. In both cell classes, basilar dendrite V(out) transforms were small, indicating that somatic potentials reached their distal ends with little attenuation. However, for somatopetal voltage spread, attenuation along the basilar and apical dendrites was comparable, so the V(in) transforms of these dendritic fields were nearly equal in extent. Granule cells were physically and electrotonically most compact. Their V(out) transforms at 0 Hz were very small, indicating near isopotentiality at DC and low frequencies. These transforms resembled those of the basilar dendrites of CA1 and CA3c pyramidal cells. This raises the possibility of similar functional or computational roles for these dendritic fields. Interpreting the anatomic distribution of thorny excrescences on CA3 pyramidal neurons with this approach indicates that synaptic currents generated by some mossy fiber inputs may be recorded accurately by a somatic patch clamp, providing that strict criteria on their time course are satisfied. Similar accuracy may not be achievable in somatic recordings of Schaffer collateral synapses onto CA1 pyramidal cells in light of the anatomic and biophysical properties of these neurons and the spatial distribution of synapses.

Electrotonic architecture of hippocampal CA1 pyramidal neurons based on three-dimensional reconstructions.

1. The spread of electrical signals in pyramidal neurons from the CA1 field of rat hippocampus was investigated through multicompartmental modeling based on three-dimensional morphometric reconstructions of four of these cells. These models were used to dissect the electrotonic architecture of these neurons, and to evaluate the equivalent cylinder approach that this laboratory and others have previously applied to them. Robustness of results was verified by the use of wide ranges of values of specific membrane resistance (Rm) and cytoplasmic resistivity. 2. The anatomy exhibited extreme departures from a key assumption of the equivalent cylinder model, the so-called "3/2 power law." 3. The compartmental models showed that the frequency distribution of steady-state electrotonic distances between the soma and the dendritic terminations was multimodal, with a large range and a sizeable coefficient of variation. This violated another central assumption of the equivalent cylinder model, namely, that all terminations are electronically equidistant from the soma. This finding, which was observed both for "centrifugal" (away from the soma) and "centripetal" (toward the soma) spread of electrical signals, indicates that the concept of an equivalent electrotonic length for the whole dendritic tree is not appropriate for these neurons. 4. The multiple peaks in the electrotonic distance distributions, whether for centrifugal or centripetal voltage transfer, were clearly related to the laminar organization of synaptic afferents in the CA1 region. 5. The results in the three preceding paragraphs reveal how little of the electrotonic architecture of these neurons is captured by a simple equivalent cylinder model. The multicompartmental model is more appropriate for exploring synaptic signaling and transient events in CA1 pyramidal neurons. 6. There was significant attenuation of synaptic potential, current, and charge as they spread from the dendritic tree to the soma. Charge suffered the least and voltage suffered the most attenuation. Attenuation depended weakly on Rm and strongly on synaptic location. Delay of time to peak was more distorted for voltage than for current and was more affected by Rm. 7. Adequate space clamp is not possible for most of the synapses on these cells. Application of a somatic voltage clamp had no significant effect on voltage transients in the subsynaptic membrane. 8. The possible existence of steep voltage gradients within the dendritic tree is consistent with the idea that there can be some degree of local processing and that different regions of the neuron may function semiautonomously. These spatial gradients are potentially relevant to synaptic plasticity in the hippocampus, and they also suggest caution in interpreting some neurophysiological results.