April 18, 2014

May 14-June 15, 2012
Focus Program on "Towards Mathematical Modeling of Neurological Disease from Cellular Perspectives"

Poster Abstracts

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Performance limitations of relay neurons
Rahul Agarwal
Johns Hopkins University
Coauthors: Sridevi Sarma

Relay cells are prevalent throughout sensory systems and receive two types of inputs: driving and modulating. The driving input contains receptive field properties that must be transmitted while the modulating input alters the specifics of transmission. For example, the motor thalamus contains relay neurons that receive a driving input from motor cortex which encodes a motor plan, and a modulating input from the basal ganglia, which suppress/facilitate movements that are not intended/intended. In this paper, we analyze a biophysical based model of a relay cell and use systems theoretic tools toconstruct analytic bounds on how well the cell transmits a driving input as a function of the neuron's electrophysiological properties, the modulating input, and the driving signal parameters. We assume that the modulating input belongs to a class of sinusoidal signals and that the driving input is an irregular train of pulses with inter-pulse intervals obeying an exponential distribution. Our analysis applies any nth order model as long as the neuron does not spike without a driving input pulse and exhibits a refractory period. Our bounds on relay reliability contain performance obtained through simulation of a second and third order model, and suggest, for instance, that if the frequency of the modulating input increases and the DC offset decreases, then relay increases. Our analysis shows how the biophysical properties of the neuron (e.g. ion channel dynamics) define the oscillatory patterns needed in the modulating input (e.g. cells local field potentials) for appropriately timed relay of sensory information. We show how our bounds predict experimentally observed neural activity in the basal ganglia in (i) health, (ii) in Parkinson's disease (PD), and (iii) in PD during therapeutic deep brain stimulation. Our bounds also predict different rhythms that emerge in the lateral geniculate nucleus in the thalamus during different attentional states.

Synchrony control in a population of bursting neurons using a common input, a mathematical study.
Guillaume Lajoie
University of Washington
Coauthors: Eric Shea-Brown

Intrinsically bursting neurons arise in many contexts.

The governing equations for models of such cells usually have multiple timescales, giving rise to solutions that have complex responses to perturbations. I will present a mathematical study of a population of elliptic bursting neurons driven by a common input. In particular, we investigate the effects of the driving signal’s attributes (strength, periodicity, etc.) on the synchronization and desynchronization of the population. This study suggests possible applications to therapeutic methods based on electrical stimulation of neural areas. Such treatments, sometimes known as deep brain stimulation, are often used as treatments of disorders such as Parkinson’s disease.

High Frequency STN DBS Elicits Reinforcement Mechanisms in the Motor Striatum in Normal and MPTP Non-Human Primates
Sabato Santaniello
Johns Hopkins University
Coauthors: Erwin B. Montgomery Jr. (University of Alabama at Birmingham), John T. Gale (Cleveland Clinic), and Sridevi V. Sarma (Johns Hopkins University)

We investigate the effects of subthalamic nucleus (STN) Deep Brain Stimulation (DBS) on striatum in the normal and Parkinsonian state by using single unit recordings and point process modeling tools. In particular, two non-human primates (macaca mulata) were treated with STN DBS (25 up to 130 pulses-per-second [pps]) while microelectrode recordings were acquired in striatum. In one animal, recordings were acquired before and after treatment with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), which induced Parkinson’s disease-like movement disorders. 185 neurons (118 normal, 67 MPTP) were collected and, for each neuron, a point process model captured DBS-induced discharge patterns.

We found that, in normal animals, spike trains at rest were Poisson processes with non-stationary recurrent patterns (RPs, period: 3-7ms), and were mildly changed by DBS below 100pps (<30% of neurons affected). With 130pps DBS, instead, up to 57% of neurons either increased or decreased the discharge rate and 66% had significant post-stimulus response. The population-mean rate decreased, the RPs were reduced, and the neuronal discharge patterns were significantly different from Poisson processes. MPTP lowered the population-mean rate and evoked significant inter-neuronal dependencies (INDs) at rest. Compared to normal, DBS below 100pps in the MPTP-treated animal increased RPs and INDs over the value at rest, while 130pps DBS elicited faster and wider post-stimulus activation.

In conclusion, 130pps STN DBS reduced non-stationary dynamics by regularizing the discharge patterns both in normal and MPTP-treated striatum, while the combination of dopamine depletion and DBS below 100pps enhanced such dynamics. This suggests that pattern regularization in striatum might contribute to the therapeutic effect of STN DBS, presumably by reinforcing the orthodromic effects along the basal ganglia-thalamo-cortical loop.


Modulations in Oscillatory Activity of the Globus Pallidus internus Neurons During a Directed Hand Movement Task – A Primary Mechanism for Motor Planning
Shreya Saxena
Department of Electrical Engineering, Massachusetts Institute of Technology
Coauthors: Shaun R. Patel, Sabatino Santaniello, John A. Assad, Emad Eskandar, Sridevi V. Sarma, John T. Gale

Globus Pallidus internus (GPi) neurons in the basal ganglia are traditionally thought to play a significant role in the promotion and suppression of movement via a change in firing rates. Here, we hypothesize that a primary mechanism of movement control by GPi neurons is through particular modulations in their oscillatory patterns.We built point process models of the neuronal spiking activity for 83 GPi neurons recorded from two healthy nonhuman primates executing a radial center-out motor task. We then analyzed the parameters of these models and (i) identified which neurons are task-related,i.e., directionally tuned, and (ii) assessed modulation of oscillations in the beta and gamma bands for non-task related and task-related neurons separately.We found that, during the planning stages of movement, a significant number of directionally tuned neurons display an increase in gamma oscillations and a suppression of beta oscillations (a “cross-over effect”). This cross-over effect is not observed in the non-directionally tuned neurons. These results suggest that, during movement planning, information encoding by GPi neurons may be governed by a sudden emergence and suppression of oscillatory activities, rather than simply by a change in average firing rates. Moreover our findings, taken together with previous work, suggest that increased beta band oscillations prevalent throughout the basal ganglia in Parkinson’s disease patients are more difficult to suppress, limiting the occurrences of the cross-over effect during movement planning and thereby impairing movements in patients.


Fine temporal patterning of intermittent synchronized oscillations in hippocampal and prefrontal circuits of the rat under repeated use of amphetamine
Sungwoo Ahn
Coauthors: Christopher C. Lapish and Leonid L. Rubchinsky

Characterizing how neural processing regimes facilitate communication within and between the prefrontal cortex (PFC) and hippocampus (HC) has received considerable attention due to the well-established roles of each structure in the control of behavior and cognitive functions. The neural processing regimes that mediate communication within, and between, each of these regions are hypothesized to be critically impaired in schizophrenia. Schizophrenia is associated with elevated synaptic dopamine concentrations which is often modeled via administration of dopamine releasing agents, such as amphetamine.

Here we used repeated intermittent injections of the psychostimulant d-amphetamine (d-AMPH) to awake freely moving rats resulting in behavioral sensitization to assess how neural dynamics across these regions are altered. Sensitization is an often-used model of schizophrenia that evokes a number of alterations in the neurobiology of the PFC and HC and the behaviors they mediate. As such, exploring how neural dynamics in these regions are altered after a sensitizing regime of d-AMPH will inform our understanding of the systems-level processes that are necessary to facilitate behavior and how they are altered in pathological states. The fine temporal structure of synchrony in delta and theta bands between these brain regions was examined to characterize how phase synchronization was altered by each day of d-AMPH relative to control groups (saline treated rats). Recent developments in nonlinear time-series analysis of phase-locking allowed for discrimination of the temporal patterns of dynamics with otherwise identical average synchrony level.

Differences were observed in the average level of phase-locking and in the variation of temporal patterns of synchrony on short (sub-second) time scales (including the distribution of durations of desynchronization events). Sensitization to d-AMPH induced alternations in prefronto-hippocampal synchrony at both delta and theta bands. Sensitization also altered the relationship between the behavior of the animal and the temporal dynamics from strong to weak correlation. This study further calls for mathematical exploration of dynamical aspects of mechanisms by which network dynamics is transformed under the action of methamphetamine.


Effects of Disinhibition in a Cortical Working Memory Circuit with Relevance to Schizophrenia
John D. Murray
Yale School of Medicine
Coauthors: Alan Anticevic Philip R. Corlett John H. Krystal Xiao-Jing Wang

Cortical working memory circuits generate stimulus-selective persistent activity through the interplay of recurrent excitation and inhibition. The balance of excitation and inhibition is critical for the function of cortical circuits, and disruption of this balance is believed to underlie multiple mental disorders such as schizophrenia. In particular, the cognitive dysfunction of schizophrenia, with a core deficit in working memory, is hypothesized to be due to the synapse-level antagonism of NMDA receptors onto inhibitory interneurons. This hinders the recruitment of feedback inhibition by local pyramidal-cell activity. However, it is poorly understood how synaptic disinhibition leads to specific behavioral deficits in working memory. To elucidate this connection, we incorporate this synaptic disinhibition mechanism into a computational model of spatial working memory, implemented with spiking neurons and realistic synaptic conductances.

We find that working memory function is very sensitive to the balance of excitation and inhibition, with even a small reduction in the strength of feedback inhibition recruitment degrading neural activity and behavior in a pronounced way. At the neural level, disinhibition broadens the tuning curves of working memory cells, and decreases the signal-to-noise ratio of the population code. At the behavioral level, we characterize two specific deficits. First, behavioral variability, due to drift of the population firing pattern over time, is increased by disinhibition, degrading performance. Second, resistance to intervening distractors is degraded by disinhibition, due to an increased overlap in the neural representations of the target and the distractor. We also present experimental support for the idea neural disinhibition by ketamine induces broadening of spatial working memory representations.

Our findings detail the importance of excitation-inhibition balance for the cognitive function of cortical microcircuits. The model makes specific predictions for the neural and behavioral effects of synaptic disinhibition, which can be tested in humans and animal models under pharmacological manipulation or in disease states. We propose important features of experimental task design for sensitive probing of these effects.


CPP alters hippocampal CA1 oscillations in rat: simulation and experiment
Mohamed A. Sherif
SUNY Downstate Medical Center - Dept of Psychiatry & Neurosimulation lab
Coauthors: Jeremy M. Barry (Darmouth Hitchcock Medical Center) Samuel A. Neymotin (SUNY Downstate Medical Center) William W. Lytton (SUNY Downstate Medical Center, Kings County Hospital)

Several different NMDA receptor (NMDAR) antagonists are used to produce pharmacological models for schizophrenia. These antagonists have different molecular mechanisms of action: uncompetitive (e.g. ketamine, which blocks the receptor pore) and competitive (e.g.CPP, which displaces glutamate). Because competitive antagonism results in more glutamate availability, glutamate receptors can be activated in excess on the same synapses. In this study, we modeled the effects of competitive blockade by simultaneously blocking NMDAR and increasing activity of AMPAR. We looked at alterations of network oscillations and synchronization using our biophysical model of the CA1 region of hippocampus using the NEURON simulator. We then compared the results with data obtained from the CA1 region of hippocampus in rats injected with CPP.

Our network consisted of 800 five-compartment pyramidal cells (PYR), 200 one-compartment basket cell interneurons (BAS), and 200 one-compartment oriens lacunosum-moleculare interneurons (OLM) [1]. All cells contained leak current, transient sodium current and delayed rectifier current. Additionally, pyramidal cells contained potassium type A current and pyramidal and OLM cells had Ih current. Cell classes were interconnected probabilistically with AMPA/NMDA synapses, and two classes of GABAa synapses. The OLM cells formed synapses on the distal dendrites of pyramidal cells, while the basket cells synapsed proximally on pyramidal and other basket cells. Pyramidal cells synapsed on both types of interneurons with AMPA/NMDA synapses. All synapses were bombarded with external Poisson inputs to generate network activity. Competitive inhibition was modeled by setting the conductance across NMDAR to zero, and increasing current conductance across AMPAR on the same set of synapses. We modeled this on synaptic sites on all cell populations. Also, given the possible variation of the affinity of competitive inhibitors to NMDAR on different cells, we studied this effect when it took place at the receptors of the 3 different cell populations separately. Experimental recordings were made from tetrode arrays implanted in the CA1 region of Long Evans rats chasing sugar pellets in a box. CPP at a dose of 5 mg/kg was injected intraperitoneally in the rats. Recordings were for 16 min sessions, separated by 30 min breaks during which the rats were returned to their cages.

Recordings from CA1 of rat hippocampus under the effect of CPP, showed that there is a reduction in theta and an increase in gamma. Modeling competitive inhibition to glutamate at all synapse locations (on OLM, BAS, and PYR) (model 1) resulted in a reduction in the theta power and an increase in gamma power, differing from the noncompetitive effect with ketamine, which reduced both theta and gamma when given across all synapses. However, reduction of theta and increase in gamma was also seen when the effect of competitive inhibition was restricted to only OLM cell NMDARs (model 2). Our simulations predict that model 1would be associated with shift in the peak of gamma to lower frequency, while model 2 would not be associated with any shift in gamma peak.


Supported by NIMH (R01MH086638). The authors would like to thank Larry Eberle (SUNY Downstate) for assistance with computer programming and Neurosimulation Lab computer support; Michael Hines (Yale) and Ted Carnevale (Yale) for NEURON simulator support.


1. Neymotin SA, Lazarewicz MT, Sherif M, Contreras D, Finkel LH, Lytton WW: Ketamine disrupts ? modulation of ? in a computer model of hippocampus. J Neurosci 2011, 31(32):11733–11743.

Date received: March 19, 2012


Default mode network connectivity indicates episodic memory capacity in patients with temporal lobe epilepsy
Cornelia McCormick
Toronto Western Hospital, Krembil Neuroscience Center
Coauthors: Maher Quraan, Melanie Cohn, Taufik A. Valiante, and Mary Pat McAndrews

FMRI resting state connectivity holds great promise for assessing cognitive capacities in patients with neuropsychiatric or neurological diseases because it is relatively easy to acquire and shows reliable changes in several patient populations. The main goal of this study was to evaluate the clinical utility of the default mode network (DMN), a robust resting state network, in assessing episodic memory capacity in patients with unilateral mesial temporal lobe epilepsy (mTLE) who have focal damage to, and in some cases surgical removal of, one node of the DMN, the hippocampus (HC).

We used six-minutes fMRI resting state data to evaluate functional connectivity from a seed (i.e., posterior cingulate cortex, PCC) in 19 healthy participants and 20 patients with right and 18 patients with left seizure onset. First, we examined changes in connectivity between patients and controls and second, we correlated PCC connectivity with presurgical memory performance and postsurgical memory decline in patients with mTLE.

We found that stronger PCC-HC connectivity in the damaged hemisphere was associated with better presurgical memory and also predicted greater postsurgical memory decline. Unexpectedly, stronger PCC-HC connectivity in the contralateral hemisphere was associated with less postsurgical memory decline, indicating functional reserve. This prediction was corroborated by showing that postsurgical PCC connectivity to the remaining HC increased and supported postsurgical memory function.

Our findings indicate the capability of a short resting state scan to accurately reflect episodic memory capacity in patients with selective impairment in this domain. These findings demonstrate the clinical significance of the brain’s intrinsic activity and connectivity in evaluating functional integrity and cognitive capacity.


A Multivariate Bayesian Framework for Modeling Brain Dynamics at Seizure Onsets in Drug-Resistant Epilepsy Patients
Sabato Santaniello
Johns Hopkins University
Coauthors: Samuel P. Burns (Johns Hopkins University), Alexandra J. Golby (Brigham and Women’s Hospital), Jedediah M. Singer (Children’s Hospital), William S. Anderson (Johns Hopkins Hospital), and Sridevi V. Sarma (Johns Hopkins University)

The onset of an unequivocal electrographic seizure in epileptic subjects is associated with multiple nonlinear and spatially distributed changes in brain dynamics, whose identification and detection are currently challenging problems. We hypothesize that early seizure-related (i.e., ictal) changes in the brain dynamics can be captured by (i) combining information from multiple simultaneously recorded intra-cortical electroencephalographic signals (iEEG) from the affected brain, (ii) by computing a network-based statistic that describes the dynamics of such signals, and (iii) by modeling the temporal evolution of this statistic as a function of the current and past observations.

In particular, we first compute a time-varying cross-power-based connectivity matrix that combines multiple iEEG channels to map the whole brain. Then, we extract from this matrix the temporal sequence of leading singular values (one value for each instance of the connectivity matrix) and corresponding sequence of leading singular vectors. We assume that these sequences are stochastic processes generated by hidden Markov models (HMM) with two hidden clinical states (normal and ictal) in each HMM. Each sequence has a time-varying stochastic characterization that depends on the hidden clinical state and is described by a history-dependent generalized linear model. Finally, the Bayesian a posteriori probability of being in the ictal state is introduced and is conditioned on the HMM dynamics, the stochastic model of the sequence of singular values and vectors, and the past observations of singular values and vectors.

We apply our framework to iEEG recordings from four drug resistant epileptic patients (168 hours of continuous recordings, 26-44 electrodes, 33 clinically-annotated seizures) and show that the proposed statistics significantly modulate in normal vs. ictal state while the Bayesian a posteriori probability is generally low (i.e., <0.5) and selectively increases (i.e., almost 1) only at the onset of the annotated seizures, thus accurately capturing the change in brain dynamics.

Date received: March 1, 2012


Genesis of interictal spikes in CA1: A computational Investigation
Sachin Talathi
Department of Pediatrics, Division of Neurology, University of Florida
Coauthors: R.G. Shivakeshavan, Stefanescu R.A., Khargonekar P., Carney P.R.,

Interictal spikes (IIS) refer to abnormal synchronized neuronal discharges, which are hallmarks of epilepsy and can be confirmed through electroencephalography (EEG) [1]. In vitro analysis of resected temporal lobe tissue from patients with refractory temporal lobe epilepsy of hippocampal origin has revealed the presence of IIS in the CA1 subfield. IIS are abolished when the Schaffer collateral (SC) input from the CA3 subfield is cut [2]. The CA1 undergoes morphological changes including cell death and the emergence of recurrent connections between excitatory neurons following brain injury that triggers epileptic seizures [3].A question then arises: How are the morphological network changes and input variability through SC related to the CA1’s ability to generate IIS? To address this issue, we develop a computational model of the CA1 network.

We characterize the morphological changes within the CA1 network by changing the percentage of recurrent synaptic connections (average number of incoming synapses onto CA1 pyramidal cells). Input variability is studied in two ways: (i) By changing the fraction of CA1 pyramidal cells that receive input from SC, and (ii) by changing the synchronization of incoming input by varying the temporal window in which SC input arrives. The CA1 computational network is comprised of 280 neurons of which 80% are pyramidal (excitatory) and 20% are inhibitory interneurons. Each neuron is modeled using the Hodgkin-Huxley framework of conductance based point neuron models.

Since pathological burst firing of pyramidal neurons, referred to as the paroxysmal depolarization shift (PDS) are known as the cellular correlates for IIS, we begin by identifying a typical temporal profile of a cellular PDS event that contributes to an observed IIS. We begin with experimental data on IIS recorded from the CA1 subfield of an in vivo self-sustaining status electrical status epilepticus animal model of chronic limbic epilepsy [4]. We then generate template IIS events using a subset of artificial PDS constructs. By matching the temporal profile of the template IIS with the experimental IIS, we identify the characteristics for PDS constructs that can generate experimentally observable IIS. We then use this information to tune the synaptic parameters of a minimal network of a pyramidal cell coupled with interneurons that is capable of generating a PDS event that matches the temporal profile of the artificial PDS construct in response to stimulation from external synaptic input. The minimal model parameters are then incorporated into a detailed CA1 network model to study conditions under which experimentally observable IIS are produced.

We find that the CA1 network with low recurrent connectivity, mimicking the topology of a normal brain, has a very low probability of producing an IIS except when a large fraction of CA1 neurons (>80%) receives a quasi-synchronous barrage of input (events occurring within a temporal window of 20 ms) via SC. However, as we increase recurrent connectivity of CA1 (>40%) we find that an IIS can be evoked in the CA1 network even in the presence of low synchrony SC input (>80 ms temporal window) and a low fraction of SC input to CA1 pyramidal cells (>30%). For sufficiently high recurrent connections (40%), the model produces a sequence of IIS in response to sparse asynchronous SC input. These results indicate that as the CA1 becomes increasingly excitable resulting from recurrent excitatory connections, the ability to produce IIS increases with less dependence on input variability. This in turn, suggests that the CA1’s susceptibility to produce IIS increases following brain injury, a finding that has been reported in earlier experimental studies [5].

1. Staley K, Hellier J, Dudek F: Do interictal spikes drive epileptogenesis? The Neuroscientist 2005, 11(4): 272-276

2. Dzhala V I, Staley K J: Transition from interictal to ictal activity in limbic networks in vitro. Journal of Neuroscience 2003, 23(21):7873-7880

3. Lehmann T N, Gabriel S, Kovacs R, Eilers A, Kivi A, Schulze K, Lanksch W R, Meencke H J, Heinemann U: Alterations of neuronal connectivity in area CA1 of hippocampal slices from temporal lobe epilepsy patients and from pilocarpine-treated epileptic rats. Epilepsia 2000, 41(Suppl. 6):S190-S194

4. Talathi S.S., Hwang D.U., Ditto W.L., Mareci T., Sepulveda H., Spano M., Carney P.R., Circadian control of neural excitability in an animal model of temporal lobe epilepsy, Neurosci Lett, 2009, 455:145-9

5. Buzsaki G, Hsu M, Slamka C, Gage F H, Horvath Z: Emergence and Propagation of Interictal Spikes in the Subcortically Denervated Hippocampus. Hippocampus 1991. 1(2): 163 – 180


Mollecular mechanisms of synaptic plasticity at CA3-CA1 synapses define the properties of learning during theta cycles in a model of the hippocampal CA1 microcircuit
Ausra Saudargiene
Department of Informatics, Vytautas Magnus University, Kaunas, Lithuania
Coauthors: Bruce P Graham, Institute of Computer Science and Mathematics, University of Stirling, UK

Hippocampal CA1 pyramidal neurons can oscillate in a theta rhythm (4-10Hz) integrating excitatory synaptic inputs from entorhinal cortex (EC) and CA3 neurons, inhibitory synaptic inputs from many classes of interneuron such as axo-axonic, basket, bistratified, oriens lacunosum-moleculare cells. Pattern storage due to synaptic changes at CA3-CA1 Schaffer collateral synapses is induced by the associated EC and CA3 pattern presentation and occurs most strongly out-of-phase with the peak of CA1 pyramidal cell activity during theta oscillations. Pattern recall is triggered by the CA3 inputs only and it is observed in phase with the firing of pyramidal neurons. It is not known precisely how synaptic learning is induced during these theta cycles.

We model synaptic modifications at CA3-CA1 Schaffer collateral synapses using a detailed model of CA1 pyramidal neuron microrcircuit (Cutsuridis et al, 2010; Poirazzi et al, 2003) and a combined model of synaptic plasticity based on the CaMKII and PP2A biochemical network (Graupner and Brunel, 2007; Pi and Lisman, 2008). The results show that synaptic changes are induced by complex nonlinear interactions between kinase CaMKII, phosphatase PP2A and other numerous molecules. Tristable behaviour of the CaMKII and PP2A system and the resulting potentiation, depression or basal level of the synapse depends not only on the postsynaptic intracellular calcium amplitude, but also on the overall time course of the calcium signal. Strong CA3 inputs alone or paired with the EC inputs evoke large long-lasting calcium transients and result in potentiation of the CA1-CA3 synapses, even when somatic spiking is inhibited by perisomatic basket cell inhibition. Weak CA3 inputs paired with the EC inputs cause synaptic potentiation as well due to high calcium signal provided by the EC inputs. However, weak CA3 inputs alone result in depression of a synapse as the calcium signal is not strong enough to maintain high CaMKII activity but it is long-lasting enough to trigger PP2A activation. Removing dendritic inhibition reverts this weak CA3 input-induced depression to potentiation.

The results inply that molecular mechanisms of synaptic plasticity together with the spatio-temporal pattern of synaptic inputs define the properties of associative learning in the CA1 region of the hippocampus.

This research was funded by a grant (No. MIP-93/2010) from the Research Council of Lithuania.

Cutsuridis V, Cobb S, Graham BP. Encoding and retrieval in a model of the hippocampal CA1 microcircuit. Hippocampus, 20:423-446, 2010.

Graupner M, Brunel N. STDP in a Bistable Synapse Model Based on CaMKII and Associated Signaling Pathways. PloS Computational Biology 3: 2299-2323, 2007.

Pi HJ, Lisman JE. Coupled Phosphatase and Kinase Switches Produce the Tristability Required for Long-Term Potentiation and Long-Term Depression. Journal of Neuroscience 28(49):13132-13138, 2008.

Poirazi P, Brannon T, Mel BW. Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell. Neuron 37:977-987, 2003.


Control of slow population activities by fast-spiking interneurons via network multistability
Ernest Ho
Coauthors: Liang Zhang and Frances Skinner

Slow population activities (SPAs) exist in the brain and have frequencies below approximately 5 Hz. Despite SPAs being prominent in several cortical areas and serving many putative functions, their mechanisms are not well understood. We study a specific type of in vitro GABAergic, inhibitory-based SPAs exhibited by rodent hippocampus. We use a multi-pronged approach consisting of experiment, simulation and mathematical analyses to uncover mechanisms responsible for hippocampal SPAs. Our results show that hippocampal SPAs are an emergent phenomenon where the “slowness” of the network is due to interactions between synaptic and cellular characteristics of individual fast-spiking, inhibitory interneurons. Our simulations quantify characteristics underlying hippocampal SPAs. In particular, for hippocampal SPAs to occur, we predict that (i) individual fast-spiking interneurons should have frequency-current (f-I) curves that exhibit a suitably sized “kink” where the slope of the curve decreases more abruptly in the gamma frequency range with increasing current, and (ii) be well-connected with one another. Our mathematical analyses show that the combination of synaptic and intrinsic conditions as predicted by our simulations promote network multistability. Population slow time scales occur when excitatory fluctuations drive the network between different stable network firing states. Since many of the parameters we use are extracted from experiments, we propose that our network models capture a fundamental, operating mechanism in biological, hippocampal networks.

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