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Nancy Kopell

Publications and source records attributed to Nancy Kopell.

At least 19 recordsLinked to original sources
PubMed2006

The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells.

Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the "canard structure," in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking ("canard explosion") is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models.

Action Potentials↗
PubMed2006

Network architecture, receptive fields, and neuromodulation: computational and functional implications of cholinergic modulation in primary auditory cortex.

Two fundamental issues in auditory cortical processing are the relative importance of thalamocortical versus intracortical circuits in shaping response properties in primary auditory cortex (ACx), and how the effects of neuromodulators on these circuits affect dynamic changes in network and receptive field properties that enhance signal processing and adaptive behavior. To investigate these issues, we developed a computational model of layers III and IV (LIII/IV) of AI, constrained by anatomical and physiological data. We focus on how the local and global cortical architecture shape receptive fields (RFs) of cortical cells and on how different well-established cholinergic effects on the cortical network reshape frequency-tuning properties of cells in ACx. We identify key thalamocortical and intracortical circuits that strongly affect tuning curves of model cortical neurons and are also sensitive to cholinergic modulation. We then study how differential cholinergic modulation of network parameters change the tuning properties of our model cells and propose two different mechanisms: one intracortical (involving muscarinic receptors) and one thalamocortical (involving nicotinic receptors), which may be involved in rapid plasticity in ACx, as recently reported in a study by Fritz and coworkers.

Acoustic Stimulation↗
PubMed2006

Oscillations and slow patterning in the antennal lobe.

Odor presentation generates both fast oscillations and slow patterning in the spiking activity of the projection neurons (PNs) in the antennal lobe (AL) of locusts, moths and bees. Experimental results indicate that the oscillations are the result of the interaction between the PNs and the inhibitory local neurons (LNs) in the AL; e.g., blocking inhibition by application of GABA-receptor antagonists abolishes these oscillations. The slow patterning, on the other hand, was shown to be somewhat resistant to such blockage. In a H-H model, we reproduce both the oscillations and the slow patterning. As previously suggested, the oscillations are the result of the interaction between the PNs and LNs. We suggest that calcium and calcium-dependent potassium channels (found in PNs of bees and moths) are sufficient to account for the slow patterning resistant to the application of GABA-receptor antagonists. The intrinsic bursting property of the PNs, resulting from these additional modeled currents, give rise to another network feature that was seen experimentally in locusts: A relatively small increase in the number of additional generated PN action potentials when LN input is blocked. Consequently, the major effect of network inhibition is to redistribute the action potentials of the PNs from bursting to one action potential per cycle of the oscillations.

Action Potentials↗
PubMed2005

Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network.

The oriens-lacunosum moleculare (O-LM) subtype of interneuron is a key component in the formation of the theta rhythm (8-12 Hz) in the hippocampus. It is known that the CA1 region of the hippocampus can produce theta rhythms in vitro with all ionotropic excitation blocked, but the mechanisms by which this rhythmicity happens were previously unknown. Here we present a model suggesting that individual O-LM cells, by themselves, are capable of producing a single-cell theta-frequency firing, but coupled O-LM cells are not capable of producing a coherent population theta. By including in the model fast-spiking (FS) interneurons, which give rise to IPSPs that decay faster than those of the O-LM cells, coherent theta rhythms are produced. The inhibition to O-LM cells from the FS cells synchronizes the O-LM cells, but only when the FS cells themselves fire at a theta frequency. Reciprocal connections from the O-LM cells to the FS cells serve to parse the FS cell firing into theta bursts, which can then synchronize the O-LM cells. A component of the model O-LM cell critical to the synchronization mechanism is the hyperpolarization-activated h-current. The model can robustly reproduce relative phases of theta frequency activity in O-LM and FS cells.

Animals↗
PubMed2005

Encoding and retrieval in the CA3 region of the hippocampus: a model of theta-phase separation.

Past research conducted by Hasselmo et al. in 2002 suggests that some fundamental tasks are better accomplished if memories are encoded and recovered during different parts of the theta cycle. A model of the CA3 subfield of the hippocampus is presented, using biophysical representations of the major cell types including pyramidal cells and two types of interneurons. Inputs to the network come from the septum and the entorhinal cortex (directly and by the dentate gyrus). A mechanism for parsing the theta rhythm into two epochs is proposed and simulated: in the first half, the strong, proximal input from the dentate to a subset of CA3 pyramidal cells and coincident, direct input from the entorhinal cortex to other pyramidal cells creates an environment for strengthening synapses between cells, thus encoding information. During the second half of theta, cueing signals from the entorhinal cortex, by the dentate, activate previously strengthened synapses, retrieving memories. Slow inhibitory neurons (O-LM cells) play a role in the disambiguation during retrieval. We compare and contrast our computational results with existing experimental data and other contemporary models.

Animals↗
PubMed2005

Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons.

Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between E-cells and Icells (excitatory and inhibitory cells). The I-cells gate and synchronize the E-cells, and the E-cells drive and synchronize the I-cells. We refer to rhythms generated in this way as PING (pyramidal-interneuronal gamma) rhythms. The PING mechanism requires that the drive I(I) to the I-cells be sufficiently low; the rhythm is lost when I(I) gets too large. This can happen in at least two ways. In the first mechanism, the I-cells spike in synchrony, but get ahead of the E-cells, spiking without being prompted by the E-cells. We call this phase walkthrough of the I-cells. In the second mechanism, the I-cells fail to synchronize, and their activity leads to complete suppression of the E-cells. Noisy spiking in the E-cells, generated by noisy external drive, adds excitatory drive to the I-cells and may lead to phase walkthrough. Noisy spiking in the I-cells adds inhibition to the E-cells and may lead to suppression of the E-cells. An analysis of the conditions under which noise leads to phase walkthrough of the I-cells or suppression of the E-cells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism does not work far above the gamma range in the presence of heterogeneity, this justifies the "G" in "PING."

Action Potentials↗
PubMed2004

Mechanism and circuitry for clustering and fine discrimination of odors in insects.

Odor recognition encompasses both clustering and fine discrimination. Clustering joins together sets of odors, and fine discrimination distinguishes between odors belonging to the same cluster. We hypothesize that these two aspects of odor recognition are encoded in parallel by two brain areas of the insect olfactory system. Population activity of neurons in the lateral horn encodes the odor cluster, and population activity of neurons in the mushroom body encodes the fine identity of the odor. Our mechanism is based on the hypothesis that the underlying network of the insect olfactory system consists of a repetitive, hard-wired substructure whose anatomy we describe. We show that these suggested mechanisms and circuitry explain not only the observed numbers and connections of neurons in the system, but also the observed activity of these neurons, and why oscillations are critical for fine discrimination but not for clustering of odors.

Animals↗
PubMed2004

Synchronization in hybrid neuronal networks of the hippocampal formation.

Understanding the mechanistic bases of neuronal synchronization is a current challenge in quantitative neuroscience. We studied this problem in two putative cellular pacemakers of the mammalian hippocampal theta rhythm: glutamatergic stellate cells (SCs) of the medial entorhinal cortex and GABAergic oriens-lacunosum-molecular (O-LM) interneurons of hippocampal region CA1. We used two experimental methods. First, we measured changes in spike timing induced by artificial synaptic inputs applied to individual neurons. We then measured responses of free-running hybrid neuronal networks, consisting of biological neurons coupled (via dynamic clamp) to biological or virtual counterparts. Results from the single-cell experiments predicted network behaviors well and are compatible with previous model-based predictions of how specific membrane mechanisms give rise to empirically measured synchronization behavior. Both cell types phase lock stably when connected via homogeneous excitatory-excitatory (E-E) or inhibitory-inhibitory (I-I) connections. Phase-locked firing is consistently synchronous for either cell type with E-E connections and nearly anti-synchronous with I-I connections. With heterogeneous connections (e.g., excitatory-inhibitory, as might be expected if members of a given population had heterogeneous connections involving intermediate interneurons), networks often settled into phase locking that was either stable or unstable, depending on the order of firing of the two cells in the hybrid network. Our results imply that excitatory SCs, but not inhibitory O-LM interneurons, are capable of synchronizing in phase via monosynaptic mutual connections of the biologically appropriate polarity. Results are largely independent of synaptic strength and synaptic kinetics, implying that our conclusions are robust and largely unaffected by synaptic plasticity.

Animals↗
PubMed2004

Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks.

Electrical and chemical synapses exist within the same networks of inhibitory cells, and each kind of synapse is known to be able to foster synchrony among oscillating neurons. Using numerical and analytical techniques, we show here that the electrical and inhibitory coupling play different roles in the synchronization of rhythms in inhibitory networks. The parameter range chosen is motivated by gamma rhythms, in which the gamma-aminobutyric acid type A (GABAA)-mediated inhibition is relatively strong. Under this condition, addition of a small electrical conductance can increase the degree of synchronization far more than a much larger increase in inhibitory conductance. The inhibitory synapses act to eliminate the effects of different initial conditions, whereas the electrical synapses mitigate suppression of firing due to heterogeneity in the network. Analytical techniques include tracking trajectories of coupled cells between spikes; the analysis shows that, in networks in which the degree of excitability is heterogeneous, inhibition can increase the dispersion of the voltages between spikes, whereas electrical coupling reduces such dispersion.

Action Potentials↗
PubMed2003

Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus-pallidal circuits.

The motor symptoms of Parkinson's disease (PD) implicate the basal ganglia (BG) in some aspect of motor control, although the role the BG play in regulation of motor behavior is not completely understood. The modeling study presented here takes advantage of available cellular, systems, and clinical data on BG and PD to begin to build a biophysically based network model of pallidosubthalamic circuits of BG, to integrate this information and better understand the physiology of the normal BG and PD pathophysiology. The model reflects the experimentally supported hypothesis that the BG are involved in facilitation of the desired motor program and inhibition of competing motor programs that interfere with the desired movement. Our model network consists of subthalamic and pallidal (both external and internal segments) neural assemblies, with inputs from cortex and striatum. Functional subsets within each of the BG nuclei correspond to the desired motor program and the unwanted motor programs. A single compartment conductance-based model represents each subset. This network can discriminate between competing signals for motor program initiation, thus facilitating a single motor program. This ability depends on metabotropic gamma-aminobutyric acid B projections from the external pallidum to subthalamic nucleus and rebound properties of subthalamic cells, as well as on the structure of projections between pallidum and subthalamus. The loss of this ability leads to hypokinesia, known PD motor deficits characterized by a slowness or inability to switch between motor programs.

Animals↗
PubMed2003

Gamma oscillations induced by kainate receptor activation in the entorhinal cortex in vitro.

Gamma frequency (30-80 Hz) oscillations are recordable from human and rodent entorhinal cortex. A number of mechanisms used by neuronal networks to generate such oscillations in the hippocampus have been characterized. However, it is as yet unclear as to whether these mechanisms apply to other anatomically disparate brain regions. Here we show that the medial entorhinal cortex (mEC) in isolation in vitro generates gamma frequency oscillations in response to kainate receptor agonists. Oscillations had the same horizontal and laminar spatiotemporal distribution as seen in vivo and in the isolated whole-brain preparation. Oscillations occurred in the absence of input from the hippocampal formation and did not spread to lateral entorhinal regions. Pharmacological similarities existed between oscillations in the hippocampus and mEC in that the latter were also sensitive to GABAA receptor blockade, barbiturates, AMPA receptor blockade, and reduction in gap junctional conductance. Stellate and pyramidal neuron recordings revealed a large GABAergic input consisting of gamma frequency IPSP trains. Fast spiking interneurons in the superficial mEC generated action potentials at gamma frequencies phase locked to the local field. Stellate cells also demonstrated a subthreshold membrane potential oscillation at theta frequencies that was temporally correlated with a theta-frequency modulation in field gamma power. Disruption in this stellate theta frequency oscillation by the hyperpolarisation activated current (Ih) blocker ZD7288 also disrupted theta modulation of field gamma frequency oscillations. We propose that similar cellular and network mechanisms to those seen in the hippocampus generate and modulate persistent gamma oscillations in the entorhinal cortex.

Action Potentials↗
PubMed2003

Coordination of cellular pattern-generating circuits that control limb movements: the sources of stable differences in intersegmental phases.

Neuronal mechanisms in nervous systems that keep intersegmental phase lags the same at different frequencies are not well understood. We investigated biophysical mechanisms that permit local pattern-generating circuits in neighboring segments to maintain stable phase differences. We use a modified version of an existing model of the crayfish swimmeret system that is based on three known coordinating neurons and hypothesized intersegmental synaptic connections. Weakly coupled oscillator theory was used to derive coupling functions that predict phase differences between neurons in neighboring segments. We show how features controlling the size of the lag under simplified network configurations combine to create realistic lags in the full network. Using insights from the coupled oscillator theory analysis, we identify an alternative intersegmental connection pattern producing realistic stable phase differences. We show that the persistence of a stable phase lag to changes in frequency can arise from complementary effects on the network with ascending-only or descending-only intersegmental connections. To corroborate the numerical results, we experimentally constructed phase-response curves (PRCs) for two different coordinating interneurons in the swimmeret system by perturbing the firing of individual interneurons at different points in the cycle of swimmeret movement. These curves provide information about the contribution of individual intersegmental connections to the stable phase lag. We also numerically constructed PRCs for individual connections in the model. Similarities between the experimental and numerical PRCs confirm the plausibility of the network configuration that has been proposed and suggest that the same stabilizing balance present in the model underlies the normal phase-constant behavior of the swimmeret system.

Action Potentials↗
PubMed2003

Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity.

In model networks of E-cells and I-cells (excitatory and inhibitory neurons, respectively), synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions-homogeneity in relevant network parameters and all-to-all connectivity, for instance-this mechanism can yield perfect synchronization. We find that approximate, imperfect synchronization is possible even with very sparse, random connectivity. The crucial quantity is the expected number of inputs per cell. As long as it is large enough (more precisely, as long as the variance of the total number of synaptic inputs per cell is small enough), tight synchronization is possible. The desynchronizing effect of random connectivity can be reduced by strengthening the E --> I synapses. More surprising, it cannot be reduced by strengthening the I --> E synapses. However, the decay time constant of inhibition plays an important role. Faster decay yields tighter synchrony. In particular, in models in which the inhibitory synapses are assumed to be instantaneous, the effects of sparse, random connectivity cannot be seen.

Animals↗
PubMed2002

Synchronizing genetic relaxation oscillators by intercell signaling.

The ability to design and construct synthetic gene regulatory networks offers the prospect of studying issues related to cellular function in a simplified context; such networks also have many potential applications in biotechnology. A synthetic network exhibiting oscillatory behavior has recently been constructed [Elowitz, M. B. & Leibler, S. (2000) Nature (London) 403, 335-338]. It has also been shown that a natural bacterial quorum-sensing mechanism can be used in a synthetic system to communicate a signal between two populations of cells, such that receipt of the signal causes expression of a target gene [Weiss, R. & Knight, T. F. (2000) in DNA6: Sixth International Meeting on DNA-Based Computers, June 13-17, 2000, Leiden, The Netherlands]. We propose a synthetic gene network in Escherichia coli which combines these two features: the system acts as a relaxation oscillator and uses an intercell signaling mechanism to couple the oscillators and induce synchronous oscillations. We model the system and show that the proposed coupling scheme does lead to synchronous behavior across a population of cells. We provide an analytical treatment of the synchronization process, the dominant mechanism of which is "fast threshold modulation."

Bacterial Proteins↗
PubMedDate not supplied

New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm.

Gamma (30-80 Hz) and beta (12-30 Hz) oscillations such as those displayed by in vitro hippocampal (CA1) slice preparations and by in vivo neocortical EEGs often occur successively, with a spontaneous transition between them. In the gamma rhythm, pyramidal cells fire together with the interneurons, while in the beta rhythm, pyramidal cells fire on a subset of cycles of the interneurons. It is shown that gamma and beta rhythms have different properties with respect to creation of cell assemblies. In the presence of heterogeneous inputs to the pyramidal cells, the gamma rhythm creates an assembly of firing pyramidal cells from cells whose drive exceeds a threshold. During the gamma to beta transition, a slow outward potassium current is activated, and as a result the cell assembly vanishes. The slow currents make each of the pyramidal cells fire with a beta rhythm, but the field potential of the network still displays a gamma rhythm. Hebbian changes of connections among the pyramidal cells give rise to a beta rhythm, and the cell assemblies are recovered with a temporal separation between cells firing in different cycles. We present experimental evidence showing that such a separation can occur in hippocampal slices.

Animals↗
PubMedDate not supplied

Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics.

Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex. SCs are thought to contribute to the mammalian theta rhythm (4-12 Hz), and are notable for the slow ionic conductances that constrain them to fire at rates within this frequency range. We apply "spike time response" (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies. Predictions from STR methods are verified using network simulations. Slow conductances often make small inputs "effectively large"; we suggest that this is due to reduced attractiveness or stability of the spiking limit cycle. When inputs are (effectively) large, changes in firing times depend nonlinearly on synaptic strength. One consequence of nonlinearity is to make a periodically firing model skip one or more beats, often leading to the elimination of the anti-synchronous state in bistable models. Biologically realistic membrane noise makes such "cycle skipping" more prevalent, and thus can eradicate bistability. Membrane noise also supports "sparse synchrony," a phenomenon in which subthreshold behavior is uncorrelated, but there are brief periods of synchronous spiking.

Animals↗
PubMedDate not supplied

Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit.

Changes in behavioral state are typically accompanied by changes in the frequency and spatial coordination of rhythmic activity in the neocortex. In this article, we analyze the effects of neuromodulation on ionic conductances in an oscillating cortical circuit model. The model consists of synaptically-coupled excitatory and inhibitory neurons and supports rhythmic activity in the alpha, beta, and gamma ranges. We find that the effects of neuromodulation on ionic conductances are, by themselves, sufficient to induce transitions between synchronous gamma and beta rhythms and asynchronous alpha rhythms. Moreover, these changes are consistent with changes in behavioral state, with the rhythm transitioning from the slower alpha to the faster gamma and beta as arousal increases. We also observe that it is the same set of underlying intrinsic and network mechanisms that appear to be simultaneously responsible for both the observed transitions between the rhythm types and between their synchronization properties. Spike time response curves (STRCs) are used to study the relationship between the transitions in rhythm and the underlying biophysics.

Action Potentials↗