Simulation of intrinsic bursting in CA3 hippocampal neurons

Biophysical Model: A Promising Method in the Study of the Mechanism of Propofol: A Narrative Review

The physiological and neuroregulatory mechanism of propofol is largely based on very limited knowledge. It is one of the important puzzling issues in anesthesiology and is of great value in both scientific and clinical fields. It is acknowledged that neural networks which are comprised of a number of neural circuits might be involved in the anesthetic mechanism. However, the mechanism of this hypothesis needs to be further elucidated. With the progress of artificial intelligence, it is more likely to solve this problem through using artificial neural networks to perform temporal waveform data analysis and to construct biophysical computational models. This review focuses on current knowledge regarding the anesthetic mechanism of propofol, an intravenous general anesthetic, by constructing biophysical computational models.

Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits

Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.

How glutamatergic synapse loss affects the firing rhythm of DG-CA3 model related with Alzheimer's disease

As well known that synapse loss is a significant pathological feature of Alzheimer's disease (AD), meanwhile, the hippocampus is one of brain regions to be first affected in the early stage of AD. Thus, this work employs a comprehensive DG-CA3 network model of the hippocampus so as to explore the neuronal correlation between glutamatergic synapse loss and abnormal firing rhythm associated with AD from the perspective of neurocomputation. The neuropathological condition of glutamatergic synapse loss caused by the reduction of Shank3 protein in AD patients is imitated by decreasing glutamatergic excitatory synapse strength between different neurons. By means of power spectral analysis and dynamics technique, the numerical results reveal that excitability of pyramidal neuron as well as oriens lacunosum-moleculare (O-LM) cell in CA3 region is strongly degraded by the decrease of NMDA or AMPA-type glutamatergic excitatory synapse strength. Moreover, the relative power together with the peak of relative power density within alpha band is also diminished by decreasing glutamatergic synapse strength. These findings accord with the electrophysiological experiment of EEG that there is a decrease of alpha rhythm for AD patients, on the same time, they could highlight the significance of glutamatergic synapse loss in the pathogenesis of AD.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Emergence of global synchronization in directed excitatory networks of type I neurons

The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.

A multiple timescales approach to bridging spiking- and population-level dynamics

A rigorous bridge between spiking-level and macroscopic quantities is an on-going and well-developed story for asynchronously firing neurons, but focus has shifted to include neural populations exhibiting varying synchronous dynamics. Recent literature has used the Ott-Antonsen ansatz (2008) to great effect, allowing a rigorous derivation of an order parameter for large oscillator populations. The ansatz has been successfully applied using several models including networks of Kuramoto oscillators, theta models, and integrate-and-fire neurons, along with many types of network topologies. In the present study, we take a converse approach: given the mean field dynamics of slow synapses, we predict the synchronization properties of finite neural populations. The slow synapse assumption is amenable to averaging theory and the method of multiple timescales. Our proposed theory applies to two heterogeneous populations of N excitatory n-dimensional and N inhibitory m-dimensional oscillators with homogeneous synaptic weights. We then demonstrate our theory using two examples. In the first example, we take a network of excitatory and inhibitory theta neurons and consider the case with and without heterogeneous inputs. In the second example, we use Traub models with calcium for the excitatory neurons and Wang-Buzsáki models for the inhibitory neurons. We accurately predict phase drift and phase locking in each example even when the slow synapses exhibit non-trivial mean-field dynamics.

Computational model of brain-stem circuit for state-dependent control of hypoglossal motoneurons

In patients with obstructive sleep apnea (OSA), the pharyngeal muscles become relaxed during sleep, which leads to a partial or complete closure of upper airway. Experimental studies suggest that withdrawal of noradrenergic and serotonergic drives importantly contributes to depression of hypoglossal motoneurons and, therefore, may contribute to OSA pathophysiology; however, specific cellular and synaptic mechanisms remain unknown. In this new study, we developed a biophysical network model to test the hypothesis that, to explain experimental observations, the neuronal network for monoaminergic control of excitability of hypoglossal motoneurons needs to include excitatory and inhibitory perihypoglossal interneurons that mediate noradrenergic and serotonergic drives to hypoglossal motoneurons. In the model, the state-dependent activation of the hypoglossal motoneurons was in qualitative agreement with in vivo data during simulated rapid eye movement (REM) and non-REM sleep. The model was applied to test the mechanisms of action of noradrenergic and serotonergic drugs during REM sleep as observed in vivo. We conclude that the proposed minimal neuronal circuit is sufficient to explain in vivo data and supports the hypothesis that perihypoglossal interneurons may mediate state-dependent monoaminergic drive to hypoglossal motoneurons. The population of the hypothesized perihypoglossal interneurons may serve as novel targets for pharmacological treatment of OSA. NEW & NOTEWORTHY In vivo studies suggest that during rapid eye movement sleep, withdrawal of noradrenergic and serotonergic drives critically contributes to depression of hypoglossal motoneurons (HMs), which innervate the tongue muscles. By means of a biophysical model, which is consistent with a broad range of empirical data, we demonstrate that the neuronal network controlling the excitability of HMs needs to include excitatory and inhibitory interneurons that mediate noradrenergic and serotonergic drives to HMs.

Linking dynamics of the inhibitory network to the input structure

Networks of inhibitory interneurons are found in many distinct classes of biological systems. Inhibitory interneurons govern the dynamics of principal cells and are likely to be critically involved in the coding of information. In this theoretical study, we describe the dynamics of a generic inhibitory network in terms of low-dimensional, simplified rate models. We study the relationship between the structure of external input applied to the network and the patterns of activity arising in response to that stimulation. We found that even a minimal inhibitory network can generate a great diversity of spatio-temporal patterning including complex bursting regimes with non-trivial ratios of burst firing. Despite the complexity of these dynamics, the network's response patterns can be predicted from the rankings of the magnitudes of external inputs to the inhibitory neurons. This type of invariant dynamics is robust to noise and stable in densely connected networks with strong inhibitory coupling. Our study predicts that the response dynamics generated by an inhibitory network may provide critical insights about the temporal structure of the sensory input it receives.

Inferring Neuronal Dynamics from Calcium Imaging Data Using Biophysical Models and Bayesian Inference

Calcium imaging has been used as a promising technique to monitor the dynamic activity of neuronal populations. However, the calcium trace is temporally smeared which restricts the extraction of quantities of interest such as spike trains of individual neurons. To address this issue, spike reconstruction algorithms have been introduced. One limitation of such reconstructions is that the underlying models are not informed about the biophysics of spike and burst generations. Such existing prior knowledge might be useful for constraining the possible solutions of spikes. Here we describe, in a novel Bayesian approach, how principled knowledge about neuronal dynamics can be employed to infer biophysical variables and parameters from fluorescence traces. By using both synthetic and in vitro recorded fluorescence traces, we demonstrate that the new approach is able to reconstruct different repetitive spiking and/or bursting patterns with accurate single spike resolution. Furthermore, we show that the high inference precision of the new approach is preserved even if the fluorescence trace is rather noisy or if the fluorescence transients show slow rise kinetics lasting several hundred milliseconds, and inhomogeneous rise and decay times. In addition, we discuss the use of the new approach for inferring parameter changes, e.g. due to a pharmacological intervention, as well as for inferring complex characteristics of immature neuronal circuits.

Calcium imaging of single neurons enables the indirect observation of neuronal dynamics, for example action potential firing. In contrast to the precise timing of spike trains, the calcium trace is temporally rather smeared and measured as a fluorescence trace. Consequently, several methods have been proposed to reconstruct spikes from calcium imaging data. However, a common feature of these methods is that they are not based on the biophysics of how neurons fire spikes and bursts. We propose to introduce well-established biophysical models to create a direct link between neuronal dynamics, e.g. the membrane potential, and fluorescence traces. Using both synthetic and experimental data, we show that this approach not only provides a robust and accurate spike reconstruction but also a reliable inference about the biophysically relevant parameters and variables. This enables novel ways of analyzing calcium imaging experiments in terms of the underlying biophysical quantities.

Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells

Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.

A MODEL OF HIPPOCAMPAL MEMORY BASED ON AN ADAPTIVE LEARNING RULE OF SYNAPSES

We constructed a neural network of the hippocampus and proposed an adaptive learning rule of synapses to simulate the storing and retrieving processes of memory in the hippocampus by a mechanism of resonance. The hippocampus network consists of CA1, CA3 and DG, in particular, CA1 is a storage of memory, which receives inputs from both EC through perforant path (PP) and CA3 through Schaffer collaterals (SC). The stimulated results showed that the memory trace was unable to be encoded in CA1 when only a single subthreshold signal from EC or CA3 was inputted, of which the main reason might be lack of the resonance of the two signals. We calculated signal-to-noise ratio (SNR) of the network, and found it reached a peak value at appropriate SC connection strength, indicating that a typical stochastic resonance phenomenon appeared in PP signal detection. The inputs from EC and CA3 were able to enhance the memory representation in CA1, although still incomplete. We used a learning rule to modify synaptic weights by which the network could learn an external pattern. The hippocampus network tended to be stable after sufficient evolution. Some CA1 neurons show synchronized firings which are used to represent memory and are clearer than observed memory traces before learning. The model and results provide a good guidance to our understanding of the mechanism of the hippocampus memory.

The layer-oriented approach to declarative languages for biological modeling

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.

Sparse gamma rhythms arising through clustering in adapting neuronal networks

Gamma rhythms (30-100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons.

A multi-compartment model for interneurons in the dorsal lateral geniculate nucleus

GABAergic interneurons (INs) in the dorsal lateral geniculate nucleus (dLGN) shape the information flow from retina to cortex, presumably by controlling the number of visually evoked spikes in geniculate thalamocortical (TC) neurons, and refining their receptive field. The INs exhibit a rich variety of firing patterns: Depolarizing current injections to the soma may induce tonic firing, periodic bursting or an initial burst followed by tonic spiking, sometimes with prominent spike-time adaptation. When released from hyperpolarization, some INs elicit rebound bursts, while others return more passively to the resting potential. A full mechanistic understanding that explains the function of the dLGN on the basis of neuronal morphology, physiology and circuitry is currently lacking. One way to approach such an understanding is by developing a detailed mathematical model of the involved cells and their interactions. Limitations of the previous models for the INs of the dLGN region prevent an accurate representation of the conceptual framework needed to understand the computational properties of this region. We here present a detailed compartmental model of INs using, for the first time, a morphological reconstruction and a set of active dendritic conductances constrained by experimental somatic recordings from INs under several different current-clamp conditions. The model makes a number of experimentally testable predictions about the role of specific mechanisms for the firing properties observed in these neurons. In addition to accounting for the significant features of all experimental traces, it quantitatively reproduces the experimental recordings of the action-potential- firing frequency as a function of injected current. We show how and why relative differences in conductance values, rather than differences in ion channel composition, could account for the distinct differences between the responses observed in two different neurons, suggesting that INs may be individually tuned to optimize network operation under different input conditions.

Neural mass activity, bifurcations, and epilepsy

In this letter, we propose a general framework for studying neural mass models defined by ordinary differential equations. By studying the bifurcations of the solutions to these equations and their sensitivity to noise, we establish an important relation, similar to a dictionary, between their behaviors and normal and pathological, especially epileptic, cortical patterns of activity. We then apply this framework to the analysis of two models that feature most phenomena of interest, the Jansen and Rit model, and the slightly more complex model recently proposed by Wendling and Chauvel. This model-based approach allows us to test various neurophysiological hypotheses on the origin of pathological cortical behaviors and investigate the effect of medication. We also study the effects of the stochastic nature of the inputs, which gives us clues about the origins of such important phenomena as interictal spikes, interictal bursts, and fast onset activity that are of particular relevance in epilepsy.

Enhancement of information transmission of sub-threshold signals applied to distal positions of dendritic trees in hippocampal CA1 neuron models with stochastic resonance

Stochastic resonance (SR) has been shown to enhance the signal-to-noise ratio and detection of low level signals in neurons. It is not yet clear how this effect of SR plays an important role in the information processing of neural networks. The objective of this article is to test the hypothesis that information transmission can be enhanced with SR when sub-threshold signals are applied to distal positions of the dendrites of hippocampal CA1 neuron models. In the computer simulation, random sub-threshold signals were presented repeatedly to a distal position of the main apical branch, while the homogeneous Poisson shot noise was applied as a background noise to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the mutual information and information rate of the spike trains were estimated. The simulation results obtained showed a typical resonance curve of SR, and that as the activity (intensity) of sub-threshold signals increased, the maximum value of the information rate tended to increased and eventually SR disappeared. It is concluded that SR can play a key role in enhancing the information transmission of sub-threshold stimuli applied to distal positions on the dendritic trees.

Stochastic resonance can enhance information transmission of supra-threshold neural signals

Stochastic resonance (SR) has been shown to improve detection of sub-threshold signals with additive uncor-related background noise, not only in a single hippocampal CA1 neuron model, but in a population of hippocampal CA1 neuron models (Array-Enhanced Stochastic Resonance; AESR). However, most of the information in the CNS is transmitted through supra-threshold signals and the effect of stochastic resonance in neurons on these signals is unknown. Therefore, we investigate through computer simulations whether information transmission of supra-threshold input signal can be improved by uncorrelated noise in a population of hippocampal CA1 neuron models by supra-threshold stochastic resonance (SSR). The mutual information was estimated as an index of information transmission via total and noise entropies from the inter-spike interval (ISI) histograms of the spike trains generated by gathering each of spike trains in a population of hippocampal CA1 neuron models at N = 1, 2, 4, 10, 20 and 50. It was shown that the mutual information was maximized at a specific amplitude of uncorrelated noise, i.e., a typical curve of SR was observed when the number of neurons was greater than 10 with SSR. However, SSR did not affect the information transfer with a small number of neurons. In conclusion, SSR may play an important role in processing information such as memory formation in a population of hippocampal neurons.

Enhancement of information transmission with stochastic resonance in hippocampal CA1 neuron network

Stochastic resonance (SR) has been shown to improve the detection of subthreshold neural signals in uncorrelated noise. It is yet unclear if and how interactions within a population of neurons can improve information processing in neural networks. In this paper, we investigate the effect of the number of neurons on information transmission in an array of hippocampal CA1 neuron models, i.e., array-enhanced SR (AESR). In computer simulations, the sub-threshold synaptic current (signal) generated by a filtered homogeneous Poisson process was applied to a distal position in each of the apical dendrites, while the background synaptic currents (uncorrelated noise) were presented to a proximal or middle point in each of the dendrites. The transmembrane potentials were recorded at one of the somas in the array of CA1 neuron models, in order to find spike firings and likewise to estimate the total and noise entropies calculated from those spike firing times. The results show that the information rate estimated at the population of the CA1 neuron models is maximized at a specific amplitude of uncorrelated noise, implying AESR. The results further show that the maximum information rate is increased as the number of neurons is increased. It is concluded that AESR can be an important role in information processing is neural systems and that the AESR is modulated by the number of neurons within the network.

Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar Golgi cells

The Golgi cells have been recently shown to beat regularly in vitro (Forti et al., 2006. J. Physiol. 574, 711–729). Four main currents were shown to be involved, namely a persistent sodium current (I_Na-p), an h current (I_h), an SK-type calcium-dependent potassium current (I_K-AHP), and a slow M-like potassium current (I_K-slow). These ionic currents could take part, together with others, also to different aspects of neuronal excitability like responses to depolarizing and hyperpolarizing current injection. However, the ionic mechanisms and their interactions remained largely hypothetical. In this work, we have investigated the mechanisms of Golgi cell excitability by developing a computational model. The model predicts that pacemaking is sustained by subthreshold oscillations tightly coupled to spikes. I_Na-p and I_K-slow emerged as the critical determinants of oscillations. I_h also played a role by setting the oscillatory mechanism into the appropriate membrane potential range. I_K-AHP, though taking part to the oscillation, appeared primarily involved in regulating the ISI following spikes. The combination with other currents, in particular a resurgent sodium current (I_Na-r) and an A-current (I_K-A), allowed a precise regulation of response frequency and delay. These results provide a coherent reconstruction of the ionic mechanisms determining Golgi cell intrinsic electroresponsiveness and suggests important implications for cerebellar signal processing, which will be fully developed in a companion paper (Solinas et al., 2008. Front. Neurosci. 2:4).

Neuronal firing sensitivity to morphologic and active membrane parameters

Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

Homeostasis is a process that allows a system to maintain a certain level of output over a long time, even though the inputs controlling the output are changing. Recently, studies of neurons and neuronal networks have shown that the “active” parameters that describe the movement of ions across the cell membrane contribute to homeostasis, since these parameters can be combined in different ways to maintain a specific output. There is also evidence that the physical shape (“morphology”) of the neuron may play a role in homeostasis, but this possibility has not been explored in computational models. We have developed a method that uses sensitivity analysis to evaluate how different kinds of parameters, like active and morphologic ones, affect model output. Across a multi-dimensional parameter space, we identified both local and global trends in parameter sensitivities that indicate regions where different parameters, even morphologic ones, contribute strongly to homeostasis. Significantly, the authors used sensitivities to predict which parameters should change, and by how much, to compensate for changes in another parameter to restore normal function. These predictions may prove important to neuronal aging, disease, and trauma research, but the method can be used to analyze any computational model.

Enhancement of information transmission with stochastic resonance in hippocampal CA1 neuron models: effects of noise input location

Stochastic resonance (SR) has been shown to enhance the signal to noise ratio or detection of signals in neurons. It is not yet clear how this effect of SR on the signal to noise ratio affects signal processing in neural networks. In this paper, we investigate the effects of the location of background noise input on information transmission in a hippocampal CA1 neuron model. In the computer simulation, random sub-threshold spike trains (signal) generated by a filtered homogeneous Poisson process were presented repeatedly to the middle point of the main apical branch, while the homogeneous Poisson shot noise (background noise) was applied to a location of the dendrite in the hippocampal CA1 model consisting of the soma with a sodium, a calcium, and five potassium channels. The location of the background noise input was varied along the dendrites to investigate the effects of background noise input location on information transmission. The computer simulation results show that the information rate reached a maximum value for an optimal amplitude of the background noise amplitude. It is also shown that this optimal amplitude of the background noise is independent of the distance between the soma and the noise input location. The results also show that the location of the background noise input does not significantly affect the maximum values of the information rates generated by stochastic resonance.

Enhancement of information transmission with stochastic resonance in hippocampal CA1 neuron models

Stochastic resonance (SR) has been shown to enhance the signal to noise ratio or detection of signals in neurons. It is not yet clear how this effect of SR on the signal to noise ratio affects signal processing in neural networks. In this paper, we test the hypothesis that SR can improve information transmission in the hippocampus. From spike firing times recorded at the soma, the inter spike intervals were generated and then "total" and "noise" entropies were estimated to obtain the mutual information and information rate of the spike trains. The results show that the information rate reached a maximum value at a specific amplitude of the background noise, implying that the stochastic resonance can improve the information transmission in the CA1 neuron model. Furthermore, the results also show that the effect of stochastic resonance tended to decrease as the intensity of the random sub-threshold spike trains (signal) (more than 20 l/s) approached to that of the background noise (100 l/s). In conclusion, the computation results that the stochastic resonance can improve information processing in the hippocampal CA1 neuron model in which the intensity of the random sub-threshold spike trains was set at 5-20 l/s.

Information transmission in hippocampal CA1 neuron models in the presence of poisson shot noise: the case of periodic sub-threshold spike trains

This article presents an analysis of the information transmission of periodic sub-threshold spike trains in a hippocampal CA1 neuron model in the presence of a homogeneous Poisson shot noise. In the computer simulation, periodic sub-threshold spike trains were presented repeatedly to the midpoint of the main apical branch, while the homogeneous Poisson shot noise was applied to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the inter spike intervals were generated and then the probability, p(T), of the inter-spike interval histogram corresponding to the spike interval, r, of the periodic input spike trains was estimated to obtain an index of information transmission. In the present article, it is shown that at a specific amplitude of the homogeneous Poisson shot noise, p(T) was found to be maximized, as well as the possibility to encode the periodic sub-threshold spike trains became greater. It was implied that setting the amplitude of the homogeneous Poisson shot noise to the specific values which maximize the information transmission might contribute to efficiently encoding the periodic sub-threshold spike trains by utilizing the stochastic resonance.

Dynamic behaviors in directed networks

Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the Watts-Strogatz undirected network and then change undirected edges to directed arcs with a given probability, still preserving the connectivity of the network. A generalized clustering coefficient for directed networks is defined and used to investigate the interplay between the synchronization behavior and underlying structural properties of directed networks. We observe that the directedness of complex networks plays an important role in emerging dynamical behaviors, which is also confirmed by a numerical study of the sociological game theoretic voter model on directed networks.

Fast odor learning improves reliability of odor responses in the locust antennal lobe

Recordings in the locust antennal lobe (AL) reveal activity-dependent, stimulus-specific changes in projection neuron (PN) and local neuron response patterns over repeated odor trials. During the first few trials, PN response intensity decreases, while spike time precision increases, and coherent oscillations, absent at first, quickly emerge. We examined this "fast odor learning" with a realistic computational model of the AL. Activity-dependent facilitation of AL inhibitory synapses was sufficient to simulate physiological recordings of fast learning. In addition, in experiments with noisy inputs, a network including synaptic facilitation of both inhibition and excitation responded with reliable spatiotemporal patterns from trial to trial despite the noise. A network lacking fast plasticity, however, responded with patterns that varied across trials, reflecting the input variability. Thus, our study suggests that fast olfactory learning results from stimulus-specific, activity-dependent synaptic facilitation and may improve the signal-to-noise ratio for repeatedly encountered odor stimuli.

Computational models of epileptiform activity in single neurons

A series of original computational models written in NEURON of increasing physiological and morphological complexity were developed to determine the dominant causes of epileptiform behavior. Current injections to a model hippocampal pyramidal neuron consisting of three compartments produced the sustained depolarizations (SD) and simple paroxysmal depolarizing shifts (PDS) characteristic of ictal and interictal behavior in a cell, respectively. Our results indicate that SDs are the result of the semi-saturation of Na+, Ca2+ and K+ active channels, particularly the CaN, with regular Na+/K+ spikes riding atop a saturated depolarization; PDS rides on a similar semi-saturated depolarization whose shape depends more heavily on interactions between low-threshold voltage-gated Ca2+ channels (CaT) and Ca(2+)-dependent K+ channels. Our results reflect and predict recent physiological data, and we report here a cellular basis of epilepsy whose mechanisms reside mainly in the membrane channels, and not in specific morphology or network interactions, advancing a possible resolution to the cellular/network debate over the etiology of epileptiform activity.

Intrinsic and circuit properties favor coincidence detection for decoding oscillatory input

In the insect olfactory system the antennal lobe generates oscillatory synchronization of its output as a framework for coincidence detection by its target, the mushroom body (MB). The intrinsic neurons of the MB (Kenyon cells, KCs) are thus a good model system in which to investigate the functional relevance of oscillations and neural synchronization. We combine electrophysiological and modeling approaches to examine how intrinsic and circuit properties might contribute to the preference of KCs for coincident input and how their decoding of olfactory information is affected by the absence of oscillatory synchronization in their input. We show that voltage-dependent subthreshold properties of KCs bring about a supralinear summation of their inputs, favoring responses to coincident EPSPs. Abolishing oscillatory synchronization weakens the preference of KCs for coincident input and causes a large reduction in their odor specificity. Finally, we find that a decoding strategy that is based on coincidence detection enhances both noise tolerance and input discriminability by KCs.

A computer model of neural processes observed in the cat motor cortex during performance of an operant movement

This report describes a computer model of a "column" in the cat motor cortex. The model includes two layers of two-segment pyramidal neurons with two groups of inhibitory interneurons in each layer, which selectively control the somatic and dendritic segments of the pyramidal cells. In this model, neurons include active sodium, calcium, and several types of potassium currents. Excitatory connections between neurons are of the AMPA and NMDA types, while collateral connections between neurons of the upper layer are mainly of the NMDA type; connections between neurons in the lower layer are of the AMPA type. All inhibitory connections are of the GABA(A) type. The model reproduces the main neuronal processes seen in the cat motor cortex during performance of an operant movement. Pyramidal neurons of the upper layer generate primary and secondary responses to external stimuli. As in real experiments, secondary NMDA-dependent responses appear when GABA(A) inhibition is weakened and disappear when stimulation is increased; these properties of secondary responses are only reproduced when NMDA receptors are located in the terminals of collateral connections. Using only rapid NMDA-independent connections, neurons in the lower layer generate a slow bell-shaped wave of excitation (a "motor command"), which is formed by sequential activation of neurons with dendritic trees of different sizes.

Connection topology dependence of synchronization of neural assemblies on class 1 and 2 excitability

Two main classes of excitable neurons are analyzed in terms of connection topology and strength of the coupling in a network of neurons. In both cases, we measure the degree of synchronization and responsiveness of the neural assembly. Class 2 excitability presents a fast wave-like propagation of the activity pattern, strong frequency dependence on the connection topology and a good level of synchronization regardless of the topology. On the other hand, class 1 excitability shows a strong dependence of the wave propagation speed and the synchronization degree on the connection topology, in addition no frequency adaptation is observed. We conclude that both types of neural excitability endow the neural assembly with very different dynamical properties. Although, for simplicity reasons, no inhibition has been included in our study, the emergent properties described in this paper may help to determine the class of excitability underlying a neural assembly.

Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron

Although spike-frequency adaptation is a commonly observed property of neurons, its functional implications are still poorly understood. In this work, using a leaky integrate-and-fire neural model that includes a Ca2+-activated K+ current (IAHP), we develop a quantitative theory of adaptation temporal dynamics and compare our results with recent in vivo intracellular recordings from pyramidal cells in the cat visual cortex. Experimentally testable relations between the degree and the time constant of spike-frequency adaptation are predicted. We also contrast the IAHP model with an alternative adaptation model based on a dynamical firing threshold. Possible roles of adaptation in temporal computation are explored, as a a time-delayed neuronal self-inhibition mechanism. Our results include the following: (1) given the same firing rate, the variability of interspike intervals (ISIs) is either reduced or enhanced by adaptation, depending on whether the IAHP dynamics is fast or slow compared with the mean ISI in the output spike train; (2) when the inputs are Poisson-distributed (uncorrelated), adaptation generates temporal anticorrelation between ISIs, we suggest that measurement of this negative correlation provides a probe to assess the strength of IAHP in vivo; (3) the forward masking effect produced by the slow dynamics of IAHP is nonlinear and effective at selecting the strongest input among competing sources of input signals.

Complexity of spatiotemporal activity of a neural network model which depends on the degree of synchronization

Spatiotemporal activity of a hippocampal CA3 model and its dynamic features were investigated. The CA3 model consists of 256 pyramidal cells and 25 inhibitory interneurons. Each pyramidal cell is a single-compartment model which was reduced from the 19-compartment cable model of the CA3 pyramidal cell developed by [Traub et al. (1991)]. Each interneuron is a model which causes tonic responses to constant depolarizing currents. The hippocampal model spontaneously causes four kinds of rhythms, A-D, which depend on the degree of synchronization of neuronal activity. The rhythm A (about 2Hz) which occurs in a range of strong mutual excitation is spatially coherent, though epileptiform bursts of pyramidal cells propagate from one end of the network to the other in a short period of time. The rhythm B (about 3Hz) occurs in an intermediate range of the strength of mutual excitation; synchronization of bursts is incomplete and the spatiotemporal pattern is complex. When the mutual excitation is relatively weak, the rhythm C (about 6Hz) occurs. Burst propagation is not uniform in direction, and the spatiotemporal activity is irregular. The rhythm D (10-35Hz) occurs in a range of weak mutual excitation when the recurrent inhibition is relatively strong. In this parameter region, pyramidal cells do not cause bursting discharges but irregular beating discharges. The hippocampal model causes phase-lockings and irregular responses to periodic synaptic stimulation depending on its own rhythmic activity and stimulus parameters. Bursting discharges of pyramidal cells are well synchronized in phase-locked responses. Several irregular responses of the rhythms A and B are evidently chaotic; each one-dimensional strobomap of chaotic responses is a non-invertible function with an unstable fixed point. Attractors reconstructed from chaotic responses demonstrate the stretching and folding mechanism.

Single-neuron modeling of LSO unit responses

We investigated, using a computational model, the biophysical correlates of measured discharge patterns of lateral superior olive (LSO) neuron responses to monaural and binaural stimuli. The model's geometry was based on morphological data, and static electric properties of the model agree with available intracellular responses to hyperpolarizing current pulses. Inhibitory synapses were located on the soma and excitatory ones on the dendrites, which were modeled as passive cables. The active properties of the model were adjusted to agree with statistical measures derived from extracellular recordings. Calcium-dependent potassium channels supplemented the usual Hodgkin-Huxley characterization for the soma to produce observed serial interspike interval dependence characteristics. Intracellular calcium concentration is controlled by voltage- and calcium-dependent potassium channels and by calcium diffusion and homeostatic mechanisms. By adjusting the density of the calcium-dependent potassium channels, we could span the observed range of transient response patterns found in different LSO neurons. Inputs from the two ears were modeled as Poisson processes to describe the responses to tone-burst stimuli. Transient and sustained responses to monaural and binaural tone-burst stimuli over a wide range of stimulus conditions could be well described by varying only the model's inputs. As found in recordings, model responses having similar discharge rates but different binaural stimulus combinations exhibited differences in interval statistics.

Calcium coding and adaptive temporal computation in cortical pyramidal neurons

In this work, we present a quantitative theory of temporal spike-frequency adaptation in cortical pyramidal cells. Our model pyramidal neuron has two-compartments (a "soma" and a "dendrite") with a voltage-gated Ca2+ conductance (gCa) and a Ca2+-dependent K+ conductance (gAHP) located at the dendrite or at both compartments. Its frequency-current relations are comparable with data from cortical pyramidal cells, and the properties of spike-evoked intracellular [Ca2+] transients are matched with recent dendritic [Ca2+] imaging measurements. Spike-frequency adaptation in response to a current pulse is characterized by an adaptation time constant tauadap and percentage adaptation of spike frequency Fadap [% (peak - steady state)/peak]. We show how tauadap and Fadap can be derived in terms of the biophysical parameters of the neural membrane and [Ca2+] dynamics. Two simple, experimentally testable, relations between tauadap and Fadap are predicted. The dependence of tauadap and Fadap on current pulse intensity, electrotonic coupling between the two compartments, gAHP as well the [Ca2+] decay time constant tauCa, is assessed quantitatively. In addition, we demonstrate that the intracellular [Ca2+] signal can encode the instantaneous neuronal firing rate and that the conductance-based model can be reduced to a simple calcium-model of neuronal activity that faithfully predicts the neuronal firing output even when the input varies relatively rapidly in time (tens to hundreds of milliseconds). Extensive simulations have been carried out for the model neuron with random excitatory synaptic inputs mimicked by a Poisson process. Our findings include 1) the instantaneous firing frequency (averaged over trials) shows strong adaptation similar to the case with current pulses; 2) when the gAHP is blocked, the dendritic gCa could produce a hysteresis phenomenon where the neuron is driven to switch randomly between a quiescent state and a repetitive firing state. The firing pattern is very irregular with a large coefficient of variation of the interspike intervals (ISI CV > 1). The ISI distribution shows a long tail but is not bimodal. 3) By contrast, in an intrinsically bursting regime (with different parameter values), the model neuron displays a random temporal mixture of single action potentials and brief bursts of spikes. Its ISI distribution is often bimodal and its power spectrum has a peak. 4) The spike-adapting current IAHP, as delayed inhibition through intracellular Ca2+ accumulation, generates a "forward masking" effect, where a masking input dramatically reduces or completely suppresses the neuronal response to a subsequent test input. When two inputs are presented repetitively in time, this mechanism greatly enhances the ratio of the responses to the stronger and weaker inputs, fulfilling a cellular form of lateral inhibition in time. 5) The [Ca2+]-dependent IAHP provides a mechanism by which the neuron unceasingly adapts to the stochastic synaptic inputs, even in the stationary state following the input onset. This creates strong negative correlations between output ISIs in a frequency-dependent manner, while the Poisson input is totally uncorrelated in time. Possible functional implications of these results are discussed.

Modalities of distortion of physiological voltage signals by patch-clamp amplifiers: a modeling study

An extensive evaluation of the possible alterations affecting physiological voltage signals recorded with patch-clamp amplifiers (PCAs) working in the current-clamp (CC) mode was carried out by following a modeling approach. The PCA output voltage and current signals obtained during CC recordings performed under simplified experimental conditions were exploited to determine the equations describing the generation of error currents and voltage distortions by PCAs. The functions thus obtained were used to construct models of PCAs working in the CC mode, which were coupled to numerical simulations of neuronal bioelectrical behavior; this allowed us to evaluate the effects of the same PCAs on different physiological membrane-voltage events. The models revealed that rapid signals such as fast action potentials are preferentially affected, whereas slower events, such as low-threshold spikes, are less altered. Prominent effects of model PCAs on fast action potentials were alterations of their amplitude, duration, depolarization and repolarization speeds, and, most notably, the generation of spurious afterhyperpolarizations. Processes like regular firing and burst firing could also be altered, under particular conditions, by the model PCAs. When a cell consisting of more than one single intracellular compartment was considered, the model PCAs distorted fast equalization transients. Furthermore, the effects of different experimental and cellular parameters (series resistance, cell capacitance, temperature) on PCA-generated artifacts were analyzed. Finally, the simulations indicated that no off-line correction based on manipulations of the error-current signals returned by the PCAs can be successfully performed in the attempt to recover unperturbed voltage signals, because of alterations of the overall current flowing through the cell-PCA system.

Evaluation of simplified compartmental models of reconstructed neocortical neurons for use in large-scale simulations of biological neural networks

The electrotonic properties of the complex arborizations of neurons can be simulated by creating compartmental models based on the morphology of real neurons. These models can be very detailed with thousands of individual compartments and active channels. Large numbers of these models can be linked together into biologically realistic, large-scale neural networks with which to obtain a better understanding of the interactions among real neurons. However, the use of detailed compartmental models in such large networks is hindered by long computation times. Methods exist to reduce the complex morphology of detailed compartmental models to simpler reconstructions that retain many of the electrotonic properties of the original model yet are computationally efficient. However, little work exists that evaluates the limitations and performance of such reduced models with realistic active conductances modeled in both the soma and the dendrites to ensure that they are appropriate for use in biologically realistic network models. We have created detailed and reduced models of reconstructed dye-filled neurons from rat somatosensory neocortex and evaluated the ability of the reduced models to faithfully reproduce the input-output functions of the more detailed models. We find that the reduced models are not capable of perfectly reproducing the exact output of the detailed models using identical parameters. However, if the parameters are adjusted the reduced models are certainly capable of providing input-output patterns that are well within an acceptable range of known neural activity. The limitations and the benefits of such models are discussed.

Sensory gating in a computer model of the CA3 neural network of the hippocampus

We have developed a unique computer model of the CA3 region of the hippocampus that simulates the P50 auditory evoked potential response to repeated stimuli in order to study the neuronal circuits involved in a sensory processing deficit associated with schizophrenia. Our computer model of the CA3 hippocampal network includes recurrent activation from within the CA3 region as well as input from the entorhinal cortex and the medial septal nucleus. We used the model to help us determine if the cortical and septal inputs to the CA3 hippocampus alone are responsible for the gating of auditory evoked activity, or if the strong recurrent activity within the CA3 region contributes to this phenomenon. The model suggests that the medial septal input is critical for normal gating; however, to a large extent the activity of the medial septal input can be replaced by simulated stimulation of the hippocampal neurons by a nicotinic agonist. The model is thus consistent with experimental data that show that nicotine restores gating of the N40 evoked potential in fimbria-fornix lesioned rats and of the P50 evoked potential in schizophrenic patients.

Idiotypic regulation of B cell differentiation

We study the equilibrium properties of idiotypically interacting B cell clones in the case where only the differentiation of B cells is affected by idiotypic interactions. Furthermore, we assume that clones may recognize and be stimulated by self antigen in the same fashion as by anti-antibodies. For idiotypically interacting pairs of non-autoreactive clones we observe three qualitatively different dynamical regimes. In the first regime, at small antibody production an antibody-free fixed point, the virgin state, is the only attractor of the system. For intermediate antibody production, a symmetric activated state replaces the virgin state as the only attractor of the system. For large antibody production, finally, the symmetric activated state gives way to two asymmetric activated states where one clone suppresses the other clone. If one or both clones in the pair are autoreactive there is no virgin state. However, we still observe the switch from an almost symmetric activated state to two asymmetric activated states. The two asymmetric activated states at high antibody production have profoundly different implications for a self antigen which is recognized by one of the clones of the pair. In the attractor characterized by high autoantibody concentration the self antigen is attacked vigorously by the immune system while in the opposite steady state the tiny amount of autoantibody hardly affects the self antigen. Accordingly, we call the first state the autoimmune state and the second the tolerant state. In the tolerant state the autoreactive clone is down-regulated by its anti-idiotype providing an efficient mechanism to prevent an autoimmune reaction. However, the antibody production required to achieve this anti-idiotypic control of autoantibodies is rather large.

Electrotonic coupling between two CA3 hippocampal pyramidal neurons: a distributed cable model with somatic gap-junction

A model of a pair of electrotonically coupled CA3 hippocampal pyramidal neurons is presented. Each neuron is represented by a tapered equivalent cable attached to an isopotential soma. The synaptic potential in a neuron soma is determined as a consequence of electrical coupling to another soma that receives a synaptic input on its dendritic tree. Estimates of the coupling resistances, soma input resistances and soma-to-dendritic tree conductance ratio show that a substantial current may arise in a neuron as a consequence of synaptic activity in a neuron coupled to it. The small increase in decay time due to coupling in the model indicates that actual coupling is between more than just pairs of neurons.

Action potential propagation and propagation block by GABA in rat posterior pituitary nerve terminals

1. A theoretical model was developed to investigate action potential propagation in posterior pituitary nerve terminals. This model was then used to evaluate the efficacy of depolarizing and shunting GABA responses on action potential propagation. 2. Experimental data obtained from the posterior pituitary with patch clamp techniques were used to derive empirical expressions for the voltage and time dependence of the nerve terminal Na+ and K+ channels. The essential structure employed here was based on anatomical and cable data from the posterior pituitary, and consisted of a long cylindrical axon (diameter, 0.5 mm) with a large spherical swelling (diameter, 4-21 mm) in the middle. 3. In the absence of an inhibitory conductance, simulated action potentials propagated with high fidelity through the nerve terminal. Swellings could block propagation, but only when sizes exceeded those observed in the posterior pituitary. Adding axonal branches reduced the critical size only slightly. These results suggested that action potentials invade the entire posterior pituitary nerve terminal in the absence of inhibition or depression. 4. The addition of inhibitory conductance to a swelling caused simulated action potentials to fail at the swelling. Depolarizing inhibitory conductances were 1.6 times more effective than shunting inhibitory conductances in blocking propagation. 5. Inhibitory conductances within the range of experimentally observed magnitudes and localized to swellings in the observed range of sizes were too weak to block simulated action potentials. However, twofold enhancement of GABA responses by neurosteroid resulted in currents strong enough to block propagation in realistic swelling sizes. 6. GABA could block simulated propagation without neurosteroid enhancement provided that GABA was present throughout a region in the order of a few hundred micrometres. For this widespread inhibition depolarizing conductance was 2.2 times more effective than shunting conductance. 7. These results imply two modes of propagation block, one resulting from highly localized release of inhibitory transmitter under conditions potentiating GABA responses, and the other resulting from widespread release of GABA in the absence of receptor potentiation. 8. The Na+ channels of the posterior pituitary nerve terminal have a unique voltage dependence that allows small depolarizations to inactivate without causing activation. The voltage dependence of this Na+ channel may serve as a specialized adaptation that facilitates in allowing small depolarizing conductances to block action potential propagation.

Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression

A spatial-temporal model for the description of electroencephalographic (EEG) data is introduced that combines smooth reconstruction in the spatial domain and autoregressive representation in the time domain. Its spatial aspect is formulated in a general framework that covers interpolation, smoothing, and regression. Contrary to the multivariate time series models used for EEG analysis up to date, the introduced model provides a smooth spatial reconstruction of the EEG cross-spectrum, keeping the condition of nonnegative definiteness. As an instance of practical importance, the case in which the spatial reconstruction is based on spherical splines is developed in detail. Illustrative examples are presented that show the flexibility of the model to describe both normal and abnormal EEG data.

Information Processing in Dendritic Trees

This review considers the input-output behavior of neurons with dendritic trees, with an emphasis on questions of information processing. The parts of this review are (1) a brief history of ideas about dendritic trees, (2) a review of the complex electrophysiology of dendritic neurons, (3) an overview of conceptual tools used in dendritic modeling studies, including the cable equation and compartmental modeling techniques, and (4) a review of modeling studies that have addressed various issues relevant to dendritic information processing.

Modelling the cerebellar Purkinje cell: experiments in computo

Detailed compartmental models of neurons are useful tools for investigating neuronal properties and mechanisms that are not accessible to experimental procedures. If a rigorous approach is used in building the model, simulation studies can be as valuable as laboratory experimentation. As such, modelling becomes an additional method for exploring the function of neurons and nervous systems. As an example, a complex compartmental model with active dendritic membrane of a Purkinje cell is described. The response properties of the model to parallel fiber inputs were investigated. The model fired simple spikes in patterns comparable with those recorded from Purkinje cells in vivo. Synchronous activation of only 20 granule cell inputs was sufficient to generate a measurable response in simulated peri-stimulus histograms. This sensitivity to small excitatory inputs was caused by P-type Ca2+ channels in the dendritic membrane. Such P channels may also be present in the spine heads. Simulations suggest, however, that Ca2+ channels in spine heads cannot be activated by single parallel fiber inputs.

Analysis of the propagation of disinhibition-induced after-discharges along the guinea-pig hippocampal slice in vitro

1. A model has been proposed of picrotoxin-induced hippocampal in vitro after-discharges; it depends critically upon alpha-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid (AMPA) and N-methyl-D-aspartate (NMDA) receptors in the recurrent excitatory connections between pyramidal neurones, and upon the ability of pyramidal neurones to generate bursts at about 10 Hz when their dendrites are sufficiently depolarized. 2. We study here the question of whether this model can account for spatial--as well as temporal--aspects of after-discharges in guinea-pig hippocampal slices. For example, can the model explain the propagation along a transverse slice of the initial burst and the secondary bursts at about the same velocity, approximately 0.10-0.20 m s-1? Under what conditions might the secondary bursts exhibit a different spatial pattern to the initial burst, as we now show can occur in longitudinal slices? To examine these questions, we increased the number of cells in our model from 100 to 8000 (in a 20 x 400 array), arranging the excitatory synaptic connections in a spatially restricted fashion, with an average extent of 1.0 mm (as suggested experimentally). 3. Our model suggests that both AMPA and NMDA receptors contribute to the propagation pattern and velocity of the initial and the secondary bursts in an after-discharge. 4. When unitary AMPA and NMDA conductances are in the range where the primary burst lasts for 100-200 ms, and there are three or four secondary bursts, then both primary and secondary bursts propagate near to the experimentally observed velocity for transverse slices. In the model, however, secondary bursts propagate at somewhat slower velocities than the initial burst. 5. The mechanisms of propagation are different for the initial and for the secondary bursts: propagation of the primary burst depends upon the initiation of electrogenesis in 'resting' dendrites by AMPA and NMDA inputs that are rapidly increasing in time. Propagation of secondary bursts depends upon the timing of calcium spikes in depolarized dendrites with slowly varying NMDA inputs; the timing of calcium spikes can be influenced by a 'wave' of AMPA input, but calcium spikes--we predict--should occur even without the AMPA input, once the after-discharge has been initiated. The blockade of firing in an intermediate region of the disinhibited slice is predicted to have different effects on the primary burst and on secondary bursts distal to the region of blockade.(ABSTRACT TRUNCATED AT 400 WORDS)