THEMATIC PROGRAMS

November 27, 2014
THE FIELDS INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES
Focus Program on "Towards Mathematical Modeling of Neurological Disease from Cellular Perspectives"
Epilepsy Workshop
May 29-30, 2012


Abstracts

Peter Carlen, Toronto Western Research Institute
Seizure transitions: a failure of presynaptic release

How the brain transitions into and out of a seizure is mysterious. Using the intact mouse hippocampus preparation, recurrent seizure-like events (SLEs) in low Mg2+/high K+ perfusate were measured in the CA3 region. The SLE was characterized by a "preictal phase", which abruptly turns into a higher frequency "ictal" phase. Blockade of GABAA receptors shortened the preictal phase, abolished interictal bursts, attenuated the slow preictal depolarization, but with no effect on the ictal duration. On the other hand, SLEs were blocked by glutamate receptor blockade, whereas the interictal activity remained intact. In CA3 pyramidal cells and stratum oriens non-fast and fast spiking interneurons, recurrent GABAergic inhibitory postsynaptic currents (IPSCs) predominated interictally and during the early preictal phase, synchronous with extracellularly measured recurrent field potentials (FPs). These IPSCs then decreased to zero or reversed polarity by the onset of the higher frequency ictal phase. However, postsynaptic muscimol-evoked GABAA responses remained intact. Simultaneously, excitatory postsynaptic currents (EPSCs) synchronous with the FPs, markedly increased to a maximum at the ictal onset. The reversal potential of the compound postsynaptic currents (PSCs: combined simultaneous EPSCs and IPSCs) became markedly depolarized during the preictal phase, but the muscimol-evoked GABAA reversal potential remained unchanged, implying increasing glutamatergic input during this phase and not a further depolarization of the GABAA reversal potential. During the late preictal phase, interneuronal excitability was high, but IPSCs, evoked by local stimulation, or osmotically by hypertonic sucrose application, were diminished, disappearing at the ictal onset. EPSCs evoked by hypertonic sucrose application, were maximal at ictal onset, disappearing at the the end of the ictus. We conclude that the interictal and early preictal states are dominated by GABAergic activity, with the onset of the ictus heralded by exhaustion of presynaptic release of GABA, and unopposed increased glutamatergic responses. The ictus stops when presynaptic release of glutamate is exhausted. Supported by the CIHR.

Robert Clewley, Georgia State University
Beyond simulation and Big Data: How informatics and dynamics might merge to shape the future of modeling multi-scale diseases

Our modeling community has built a jumble of models for neural processes at different scales using different abstractions, amenable to different scientific questions and constraints by different kinds of data. In the bigger picture of understanding a multi-scale disease such as epilepsy, determining the compatibility and consistency of those models and the available data poses a huge meta-scientific challenge. Our current approaches to this challenge rely on simulation, toy mathematical models, superficial metadata, and a limited conception of "parameter fitting". I suggest that we will not be able to build useful, large data-driven models of disease that we adequately understand using these approaches. In particular, I will argue that we will struggle to make robust predictions about affecting macroscopic outcomes due to microscopic changes.

I will discuss emerging strategies from various sources across the computational sciences that could change this picture over the next decade, and provide some early prototypical examples of how we could model multi-scale disease mechanisms differently. Using one modest example, I will illustrate a strategy that is leading to a detailed mathematical explanation of the familiar Phase Response Curve (PRC) for a single neuron in terms of underlying ionic mechanisms. The PRC is used in many modeling studies associated with network synchronization despite its poorly understood causal origins. A clearer understanding of this issue will better connect microscopic and macroscopic processes relevant to dynamic, multi-scale diseases.

Alain Destexhe, Centre national de la recherche scientifique/Unité de Neurosciences Information et Complexité
Role of corticothalamic feedback in generating hypersynchronized 3Hz discharges by intact thalamic networks: a mechanism of absence seizures?

Absence seizures are characterized by a sudden change of cortical activity into hypersynchronized discharges at around 3Hz. Thalamic networks with altered inhibition have been shown to generate hypersynchronized 3Hz oscillations, but experimental models of absence seizure suggest that the thalamus is physiologically intact. Computational models of the thalamocortical system were used to resolve this contradiction. The models predicted that a strong corticothalamic feedback should be able to switch intact thalamic networks into a 3Hz hypersynchronized mode, but only if the biophysical details of the cellular intrinsic properties and synaptic receptors are taken into account. In particular, if GABA(B) receptors have highly nonlinear activation properties, the model can reproduce all experimental observations. Such nonlinear properties were later identified and measured experimentally. The model made the clear prediction that a switch to synchronized 3Hz rhythms should be observable if thalamic circuits are subject to strong stimulation of corticothalamic fibers. The latter prediction was confirmed by two independent studies. Collectively, these results suggest that hypersynchronized thalamocortical oscillations at 3Hz can result from an augmentation of cortical excitability with physiologically inact thalamus, in agreement with some experimental models of absence seizures.
Reference:
http://www.scholarpedia.org/article/Spike-and-Wave_Oscillations
(all original articles available in PDF in http://cns.iaf.cnrs-gif.fr in "publications")

Mark Kramer, Boston University
Multi-scale seizure dynamics

A seizure represents an extreme deviation from normal brain activity. In this talk, we will consider some characteristics of the seizure as observed across spatial and temporal scales in human patients. We will focus specifically on changes in the rhythmic voltage activity, and consider techniques to characterize these changes. We will also discuss a mathematical model consistent with the stereotyped dynamics observed at seizure termination.

J. Lawrence, University of Montana
Cell type-specific cholinergic modulation in the hippocampus: roles in normal and disease states

Acetylcholine (ACh) release from the medial septum-diagonal band of Broca (MS-DBB) to the hippocampus profoundly alters cellular excitability, network synchronization, and behavioral state. Deficits in cholinergic function are associated with memory impairments, such as in Alzheimer’s disease, while excessive cholinergic activity, such as in organophosphate exposure, can induce
seizures and lead to neuronal death. ACh has diverse pre- and postsynaptic targets onto both glutamatergic and GABAergic cell populations in the hippocampus. Recent evidence has emerged indicating that the actions of ACh can be highly specific, altering the excitability of distinct GABAergic circuits in a cell type-specific manner. Although cholinergic activation of interneurons and
principal cells are thought to generate theta oscillations, molecular and cellular details regarding cholinergic transmission onto specific hippocampal target cells remain poorly understood. Using a combination of immunocytochemical, electrophysiological, transgenic mouse, optogenetic, and computational modeling approaches, we are currently defining the relationship between the spatial
localization of MS-DBB afferents and the physiological consequence of cell typespecific cholinergic modulation, with the ultimate goal of developing mathematical models of cell type-specific cholinergic transmission. Fast spiking parvalbumincontaining (PV+) neurons will be discussed in particular. Muscarinic acetylcholine receptor (mAChR) activation generates a large depolarizing current in PV basket cells that is absent in global M1 mAChR KO mice (Cea del Rio et al. 2010). We have now selectively ablated M1 mAChRs from PV+ cells by crossing PVCRE+/+
and floxed M1+/+ mice. The resulting PV-Cre/fM1 mice showed reduced frequency and amplitude of spontaneous inhibitory postsynaptic currents compared to their wild type (WT) littermates, suggesting that tonic activation of M1 mAChRs on PV+ cells is important for normal GABAergic transmission. In behavioral tasks, while PV-CRE/fM1 mice exhibited deficits in working and
recognition memory, normal locomotion and spatial memory remained intact. Finally, we examined PV-CRE/fM1 mice in the development of pilocarpineinduced seizures. Following pilocarpine administration, a less severe phenotype was observed in PV-CRE/fM1 than WT, suggesting that M1 mAChRs on PV cells contributes to pilocarpine-induced epileptogenesis in WT mice. We conclude that cholinergic receptors on inhibitory interneurons play key roles in normal and pathophysiological disease processes.

Tim Lewis, UC Davis
The theory of weakly coupled oscillators: Can it be used to gain insight into the mechanisms underlying epileptic activity?

The theory of weakly coupled oscillators has been widely used to study the synchronization properties of neuronal networks. The theory allows one to significantly reduce the complexity of neuronal and synaptic dynamics, making it possible to identify some of the mechanisms that shape network activity. Not surprisingly, there are several assumptions that must hold for the theory to apply quantitatively. In this talk, I will give a tutorial on the theory of weakly coupled oscillators, pointing out the assumptions in the theory. I will then pose the question: Do these assumptions hold in neuronal networks that display epileptiform activity?

Erin Munro, RIKEN, Tokyo
How Very Fast Oscillations may lead to Epilepsy

Very fast oscillations (VFOs, >80 Hz) are seen in normal neocortex during the up-state of slow oscillations and cortical activations. However, VFOs are seen more frequently in seizure onset zones, especially at the beginning of seizures. Previous models show that an axonal plexus (network of axons coupled by gap junctions) can easily produce VFOs. Moreover, VFOs and seizures can be blocked by gap junction blockers in experiment. I will present a model of a neocortical axonal plexus, which shows that the somatic voltage can control AP propagation across gap junctions on the main axon but not side collaterals. Therefore, axonal sprouting may lead to many uncontrollable gap junctions which can generate persistent VFOs. Hence, networks of sprouted axons connected by gap junctions may kindle postsynaptic cells, leading to epilepsy.

S. Schiff, Penn State University
Towards Model-Based Observation and Control of Seizures

In the past decade, we have seen the concurrent development of sophisticated control theoretic techniques suitable for nonlinear networked systems, as well as computational models of neuronal systems that have improving fidelity to the behavior of neuronal ensembles in health and disease. Using nonlinear ensemble Kalman filters, we have in recent years demonstrated that we can fuse computational neuroscience models with data from single cells, small network motifs, and larger scale neuronal network dynamics. Simultaneously, the ability to quantify both analytically and numerically the formal observability of nonlinear dynamical systems has been developed using several approaches. Such metrics of observability define how much of the experimentally inaccessible variables of a complex system can be reconstructed from measurements of only a subset of the state variables, and whether different system trajectories are discriminable from measurement observations. I will show how model-based control principles can be applied to reconstruct seizure dynamics at the cellular and network level. I will also discuss some of the open questions in structural observability and controllability, and symmetry, where mathematical developments are needed.

Ivan Soltesz, University of California, Irvine
Functional network connectivity of the epileptic hippocampus

A major challenge in understanding the neurobiological basis of epilepsy stems from the fact that numerous molecular, cellular, synaptic and network properties undergo significant, simultaneous alterations during epileptogenesis. The close integration of experimental findings with large-scale, data-driven computational simulations of control and epileptic neuronal networks offers a powerful tool towards the identification of key circuit parameters that may be particularly effective in controlling epileptic circuit behavior. To this end, we have been developing realistic microcircuit-based network models of the control and injured hippocampus in order to investigate questions related to normal hippocampal microcircuit function and the mechanistic bases of epilepsy. We will discuss the conceptual framework and biological basis of model development and show specific applications, including computational and experimental results concerning model validation, cell type specific hippocampal chronocircuit properties and the role of hub neurons in seizures. The talk will highlight the predictive and analytic power of freely shared, highly realistic, large-scale computational models in understanding normal circuit function and temporal lobe epilepsy.

Roger Traub, IBM TJ Watson Centre and Columbia University
Cellular mechanisms of epilepsy: chemical synapses and gap junctions

During brief epileptic bursts, principal neurons fire together for tens to hundreds of milliseconds, producing a large extracellular potential ("field"). Superimposed on this large field are high-frequency oscillations, from ~100 to several hundred Hz. Two distinctive means of coupling between neurons cooperate to generate the event. Recurrent excitatory synaptic connections shape the overall event, but gap junction coupling produces the fast oscillations. I will describe the dissection of the cellular mechanisms via in vitro experiments and via computer modeling and network theory. Experimentally, the fast oscillations can be evoked alone, during blockade of chemical synapses; but blockade of gap junctions abolishes BOTH the fast oscillations and the larger burst. These data suggest that a targeted manipulation of selected gap junctions might prevent certain seizure events.

 

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