Neural Dynamics

Ion Concentration Dynamics as a Mechanism for Neuronal Bursting
Journal of Biological Physics 37, 361-373 (2011)
Ernest Barreto and John R. Cressman

We describe a simple conductance-based model neuron that includes intra- and extra-cellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables, and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.

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Synchronized Changes to Relative Neuron Populations in Postnatal Human Neocortical Development
Cognitive Neurodynamics 4, 151-163 (2010)
David L. Cooper, James E. Gentle, Ernest Barreto, and James L. Olds

Mammalian prenatal neocortical development is dominated by the synchronized formation of the laminae and migration of neurons. Postnatal development likewise contains "sensitive periods" during which functions such as ocular dominance emerge. Here we introduce a novel neuroinformatics approach to identify and study these periods of active development. Although many aspects of the approach can be used in other studies, some specific techniques were chosen because of a legacy dataset of human histological data (Conel in The postnatal development of the human cerebral cortex, vol 1–8. Harvard University Press, Cambridge, 1939–1967). Our method calculates normalized change vectors from the raw histological data, and then employs k-means cluster analysis of the change vectors to explore the population dynamics of neurons from 37 neocortical areas across eight postnatal developmental stages from birth to 72 months in 54 subjects. We show that the cortical "address" (Brodmann area/ sub-area and layer) provides the necessary resolution to segregate neuron population changes into seven correlated "k-clusters" in k-means cluster analysis. The members in each k-cluster share a single change interval where the relative share of the cortex by the members undergoes its maximum change. The maximum change occurs in a different change interval for each k-cluster. Each k-cluster has at least one totally connected maximal "clique" which appears to correspond to cortical function.

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The Influence of Sodium and Potassium Dynamics on Excitability, Seizures, and the Stability of Persistent States: I. Single Neuron Dynamics
Journal of Computational Neuroscience 26 159-170 (2009)
John R. Cressman Jr., Ghanim Ullah, Jokubas Ziburkus, Steven J. Schiff, and Ernest Barreto

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia,and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.

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The Influence of Sodium and Potassium Dynamics on Excitability, Seizures, and the Stability of Persistent States: II. Network and Glial Dynamics
Journal of Computational Neuroscience 26 171-183 (2009)
Ghanim Ullah, John R. Cressman Jr., Jokubas Ziburkus, Steven J. Schiff, and Ernest Barreto

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin– Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations.

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Interneuron and Pyramidal Cell Interplay During In Vitro Seizure-like Events
Journal of Neurophysiology 95 3948 (2006)
Jokubas Ziburkus, John R. Cressman, Ernest Barreto, and Steven J. Schiff

Excitatory and inhibitory (EI) interactions shape network activity. However, little is known about the EI interactions in pathological conditions such as epilepsy. To investigate EI interactions during seizure-like events (SLEs), we performed simultaneous dual and triple whole cell and extracellular recordings in pyramidal cells and oriens interneurons in rat hippocampal CA1. We describe a novel pattern of interleaving EI activity during spontaneous in vitro SLEs generated by the potassium channel blocker 4-aminopyridine in the presence of decreased magnesium. Interneuron activity was increased during interictal periods. During ictal discharges, interneurons entered into long-lasting depolarization block (DB) with suppression of spike generation; simultaneously, pyramidal cells produced spike trains with increased frequency (6-14 Hz) and correlation. After this period of runaway excitation, interneuron postictal spiking resumed and pyramidal cells became progressively quiescent. We performed correlation measures of cell-pair interactions using either the spikes alone or the subthreshold postsynaptic interspike signals. EE spike correlation was notably increased during interneuron DB, whereas subthreshold EE correlation decreased. EI spike correlations increased at the end of SLEs, whereas II subthreshold correlations increased during DB. Our findings underscore the importance of complex cell-type-specific neuronal interactions in the formation of seizure patterns.

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Control of Traveling Waves in Mammalian Cortex
Physics Review Letters 94 028103 (2005)
Kristen A. Richardson, Steven J. Schiff, and Bruce J. Gluckman

Neural activity can propagate as waves in the brain. Such waves of activity may be important in processing of sensory information when awake, are present during deep sleep, and may be involved with spread of epileptic seizures. In this present paper, we predicted from a mathematical model of wave propagation, then confirmed experimentally, that externally applied electrical fields can slow such waves sufficiently to stop them. Specifically, we demonstrated that by using electric fields to modulate neuronal excitability, we can speed up, slow down and even halt propagation of seizure-like waves of activity in rat brain slices. An important application of such control over the propagation of waves of activity in human brain would allow for the development of implantable seizure control electrical devices that can be used to contain seizure activity within a small localized region and thereby prevent such seizures from spreading throughout the brain.

Abstract: We experimentally confirmed predictions that modulation of neuronal threshold with electrical fields can speed up, slow down, and even block traveling waves in neocortical slices. The predictions are based on a Wilson-Cowan type integrodifferential equation model of propagating neocortical activity. Wave propagation could be modified quickly and reversibly within targeted regions of the network. To the best of our knowledge, this is the first example of direct modulation of threshold to control wave propagation in a neural systems.

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