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G Bard Ermentrout

Publications and source records attributed to G Bard Ermentrout.

16 recordsLinked to original sources
PubMed2006

A homeostatic rule for inhibitory synapses promotes temporal sharpening and cortical reorganization.

Experience with transient stimuli leads to stronger neural responses that also rise and fall more sharply in time. This sharpening enhances the processing of transients and may be especially relevant for speech perception. We consider a learning rule for inhibitory connections that promotes this sharpening effect by adjusting these connections to maintain a target homeostatic level of activity in excitatory neurons. We analyze this rule in a recurrent network model of excitatory and inhibitory units. Strengthening inhibitory-->excitatory connections along with excitatory-->excitatory connections is required to obtain a sharpening effect. Using the homeostatic rule, we show that repeated presentations of a transient signal will "teach" the network to respond to the signal with both higher amplitude and shorter duration. The model also captures reorganization of receptive fields in the sensory hand area after amputation or peripheral nerve resection.

Amputation, Surgical↗
PubMed2006

Correlation-induced synchronization of oscillations in olfactory bulb neurons.

Oscillations are a common feature of odor-evoked and spontaneous activity in the olfactory system in vivo and in vitro and are thought to play an important role in information processing and memory in a variety of brain areas. Theoretical and experimental studies have described several mechanisms by which oscillations can be generated and synchronized. Here, we investigate the hypothesis that correlated noisy inputs are able to generate synchronous oscillations in olfactory bulb mitral cells in vitro. We consider several alternative mechanisms and conclude that olfactory bulb synchronous oscillations are likely to arise because of the response of uncoupled oscillating neurons to aperiodic but correlated inputs. This mechanism has been described theoretically, but we provide the first experimental evidence that such a mechanism may underlie synchronization in real neurons. In physiological experiments, we show that this mechanism can generate gamma-band oscillations in populations of olfactory bulb mitral cells. This mechanism synchronizes oscillatory firing by using shared fast fluctuations in stochastic inputs across neurons, without requiring any synaptic or electrical coupling. We discuss the properties and limitations of synchronization by this mechanism and suggest that it may underlie fast oscillations in many brain areas.

Action Potentials↗
PubMed2006

Actin filament branching and protrusion velocity in a simple 1D model of a motile cell.

We formulate and analyse a 1D model for the spatial distribution of actin density at the leading edge of a motile cell. The model incorporates nucleation, capping, growth and decay of actin filaments, as well as retrograde flow of the actin meshwork and known parameter values based on the literature. Using a simplified geometry, and reasonable assumptions about the biochemical processes, we derive PDEs for the density of actin filaments and their tips. Analytic travelling wave solutions are used to predict how the speed of the cell depends on rates of nucleation, capping, polymerization and membrane resistance. Analysis and simulations agree with experimental profiles for measured actin distributions. Extended versions of the model are studied numerically. We find that our model produces stable travelling wave solutions with reasonable cell speeds. Increasing the rate of nucleation of filaments (by the actin related protein Arp2/3) or the rate of actin polymerization leads to faster cell speed, whereas increasing the rate of capping or the membrane resistance reduces cell speed. We consider several variants of nucleation (spontaneous, tip, and side branching) and find best agreement with experimentally measured spatial profiles of filament and tip density in the side branching case.

Actin Cytoskeleton↗
PubMed2006

A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation.

The acute inflammatory response, triggered by a variety of biological or physical stresses on an organism, is a delicate system of checks and balances that, although aimed at promoting healing and restoring homeostasis, can result in undesired and occasionally lethal physiological responses. In this work, we derive a reduced conceptual model for the acute inflammatory response to infection, built up from consideration of direct interactions of fundamental effectors. We harness this model to explore the importance of dynamic anti-inflammation in promoting resolution of infection and homeostasis. Further, we offer a clinical correlation between model predictions and potential therapeutic interventions based on modulation of immunity by anti-inflammatory agents.

Acute Disease↗
PubMed2005

Persistent synchronized bursting activity in cortical tissues with low magnesium concentration: a modeling study.

We explore the mechanism of synchronized bursting activity with frequency of approximately 10 Hz that appears in cortical tissues at low extracellular magnesium concentration [Mg2+]o. We hypothesize that this activity is persistent, namely coexists with the quiescent state and depends on slow N-methyl-D-aspartate (NMDA) conductances. To explore this hypothesis, we construct and investigate a conductance-based model of excitatory cortical networks. Population bursting activity can persist for physiological values of the NMDA decay time constant (approximately 100 ms). Neurons are synchronized at the time scale of bursts but not of single spikes. A reduced model of a cell coupled to itself can encompass most of this highly synchronized network behavior and is analyzed using the fast-slow method. Synchronized bursts appear for intermediate values of the NMDA conductance g(NMDA) if NMDA conductances are not too fast. Regular spiking activity appears for larger g(NMDA). If the single cell is a conditional burster, persistent synchronized bursts become more robust. Weakly synchronized states appear for zero AMPA conductance g(AMPA). Enhancing g(AMPA) increases both synchrony and the number of spikes within bursts and decreases the bursting frequency. Too strong g(AMPA), however, prevents the activity because it enhances neuronal intrinsic adaptation. When [Mg2+]o is increased, higher g(NMDA) values are needed to maintain bursting activity. Bursting frequency decreases with [Mg2+]o, and the network is silent with physiological [Mg2+]o. Inhibition weakly decreases the bursting frequency if inhibitory cells receive enough NMDA-mediated excitation. This study explains the importance of conditional bursters in layer V in supporting epileptiform activity at low [Mg2+]o.

Action Potentials↗
PubMed2005

Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling.

The phase-resetting curve (PRC) of a neural oscillator describes the effect of a perturbation on its periodic motion and is therefore useful to study how the neuron responds to stimuli and whether it phase locks to other neurons in a network. Combining theory, computer simulations and electrophysiological experiments we present a simple method for estimating the PRC of real neurons. This allows us to simplify the complex dynamics of a single neuron to a phase model. We also illustrate how to infer the existence of coherent network activity from the estimated PRC.

Computer Simulation↗
PubMed2005

Phase-response curves give the responses of neurons to transient inputs.

Neuronal firing is determined largely by incoming barrages of excitatory postsynaptic potentials (EPSPs), each of which produce a transient increase in firing probability. To measure the effects of weak transient inputs on firing probability of cortical neurons, we compute phase-response curves (PRCs). PRCs, whose shape can be related to the dynamics of spike generation, document the changes in timing of spikes caused by an EPSP in a repetitively firing neuron as a function of when it arrives in the interspike interval (ISI). The PRC can be exactly related to the poststimulus time histogram (PSTH) so that knowledge of one uniquely determines the other. Typically, PRCs have zero values at the start and end of the ISI, where EPSPs have minimal effects and a peak in the middle. Where the peak occurs depends in part on the firing properties of neurons. The PRC can have regions of positivity and negativity corresponding respectively to speeding up and slowing down the time of the next spike. A simple canonical model for spike generation is introduced that shows how both the background firing rate and the degree of postspike afterhyperpolarization contribute to the shape of the PRC and thus to the PSTH. PRCs in strongly adapting neurons are highly skewed to the right (indicating a higher change in probability when the EPSPs appear late in the ISI) and can have negative regions (indicating a decrease in firing probability) early in the ISI. The PRC becomes more skewed to the right as the firing rate decreases. Thus at low firing rates, the spikes are triggered preferentially by inputs that occur only during a small time interval late in the ISI. This implies that the neuron is more of a coincidence detector at low firing frequencies and more of an integrator at high frequencies. The steady-state theory is shown to also hold for slowly varying inputs.

Animals↗
PubMed2004

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice.

OBJECTIVE: To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation. METHODS: A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT. RESULTS: This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion. CONCLUSIONS: A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

Animals↗
PubMed2004

Inflammatory modulation of hepatocyte apoptosis by nitric oxide: in vivo, in vitro, and in silico studies.

Nitric oxide (NO*) and its reaction products are key players in the physiology and pathophysiology of inflammatory settings such as sepsis and shock. The consequences of the expression of inducible NO* synthase (iNOS, NOS-2) can be either protective or damaging to the liver. We have delineated two distinct hepatoprotective actions of NO*: the stimulation of cyclic guanosine monophosphate and the inhibition of caspases by S-nitrosation. In contrast, iNOS/NO* promotes hepatocyte death under conditions of severe redox stress, such as hemorrhagic shock or ischemia/reperfusion. Redox stress activates an unknown molecular switch that transforms NO*, which is hepatoprotective under resting conditions, into an agent that induces hepatocyte death. We hypothesize that the magnitude of the redox stress is a major determinant for the effects of NO* on cell survival by controlling the chemical fate of NO*. To address this hypothesis, we have carried out studies in relevant in vivo and in vitro settings. Moreover, we have constructed an initial mathematical model of caspase activation and coupled it to a model describing some of the reactions of NO* in hepatocytes. Our studies suggest that modulation of iron, oxygen, and superoxide may dictate whether NO* is hepatoprotective or hepatotoxic.

Animals↗
PubMed2003

Detecting instabilities of cardiac rhythm.

Diminished beat-to-beat variations in cardiac cycle lengths (CLs) are associated with poor prognosis after acute myocardial infarction and in patients with heart failure. Short-long-short sequences of cardiac cycles, or ultra-short rhythm instabilities, precede initiation of ventricular tachyarrhythmias in some patients. However, little is known about clinical or prognostic significance of abrupt short-term instabilities in CL (AICL) that occur minutes to hours before the event, in part because appropriate analytical methods are lacking. Although various techniques have been used to analyze CL changes, methods for analysis of AICL are limited. We compared performance of time domain, spectral, nonlinear, and pattern recognition techniques with respect to the detection and quantification of AICL. Because of high intra- and inter-subject variability of CL, pattern recognition techniques compared favorably to other studied methods. In continuous ambulatory ECG recordings, AICL occurred hours before spontaneous initiation of sustained atrial and ventricular arrhythmias in different patient populations. AICL were also found prior to the onset of spontaneous ventricular arrhythmias in a mouse model of congestive heart failure. To quantify AICL, we used the number of unstable orthogonal projection coefficients; this number gradually increased hours before the event. Removal of ectopic beats reduced but did not eliminate AICL. To illustrate potential physiological effects and temporal evolution of AICL, we used a simple, continuous, two-dimensional model of cardiac tissue governed by the Morris-Lecar equations. Computer simulations in this model showed that AICL may lead to gradual accumulation of spatial irregularities of the propagation wavefront giving rise to the initiation of reentry. Time-frequency analysis of the most significant eigenvectors of cardiac rhythm in subjects undergoing head-up tilt showed that AICL could indicate instabilities and unsuccessful adaptation of autonomic nervous system activity to physiological stimuli.

Animals↗
PubMed2002

Slow excitation supports propagation of slow pulses in networks of excitatory and inhibitory populations.

We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory neurons. Each neuron is represented by the integrate-and-fire model, and is allowed to fire only one spike. Two types of propagating pulses are observed. During fast pulses, inhibitory neurons fire a short time before or after the excitatory neurons. During slow pulses, inhibitory cells fire well before neighboring excitatory cells, and potentials of excitatory cells become negative and then positive before they fire. There is a bistable parameter regime in which both fast and slow pulses can propagate. Fast pulses can propagate at low levels of inhibition, are affected by fast excitation but are almost unaffected by slow excitation, and are easily elicited by stimulating groups of neurons. In contrast, slow pulses can propagate at intermediate levels of inhibition, and are difficult to evoke. They can propagate without slow excitation, but slow excitation makes their propagation substantially more robust. Fast pulses can propagate in a wider parameter regime if inhibition decays slowly with time, whereas slow pulses can propagate in a wider parameter regime if the passive time constant of inhibitory cells is large. Strong inhibitory-to-inhibitory conductance eliminates the slow pulses and converts the fast traveling pulses into irregular pulses, in which the inhibitory neurons segregate into two groups that have different firing delays with respect to their neighboring excitatory cells. In general, the velocity of the fast pulse increases with the axonal conductance velocity c, but there are cases in which it decreases with c. We suggest that the fast and slow pulses observed in our model correspond to the fast and slow propagating activity observed in experiments on neocortical slices.

Biophysical Phenomena↗
PubMed2002

Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators.

We investigate the dynamics of a recurrent network of coupled heterogeneous neural oscillators with experimentally observed spike-timing-dependent synaptic plasticity. We show both theoretically and by computer simulations that, in a regime of a balance between synaptic potentiation and depression, the network of such oscillators converges to a stable synchronous state. The stability of this state is fostered by flexible synaptic weights which adjust themselves based on the relative timing of firing of pre- and postsynaptic oscillators.

Animals↗
PubMed2002

Modeling neural oscillations.

A brief review of oscillatory activity in neurons and networks is given. Conditions required for neural oscillations are provided. Three mathematical methods for studying the coupling between neural oscillators are described: (i) weak coupling, (ii) firing time maps, and (iii) leaky integrate-and-fire methods. Several applications from macroscopic motor behavior to slice phenomena are provided.

Algorithms↗
PubMedDate not supplied

An introduction to simulation and visualization of biological systems at multiple scales: a summer training program for interdisciplinary research.

Advances in biomedical research require a new generation of researchers having a strong background in both the life and physical sciences and a knowledge of computational, mathematical, and engineering tools for tackling biological problems. The NIH-NSF Bioengineering and Bioinformatics Summer Institute at the University of Pittsburgh (BBSI @ Pitt; www.ccbb.pitt.edu/bbsi) is a multi-institutional 10-week summer program hosted by the University of Pittsburgh, Duquesne University, the Pittsburgh Supercomputing Center, and Carnegie Mellon University, and is one of nine Institutes throughout the nation currently participating in the NIH-NSF program. Each BBSI focuses on a different area; the BBSI @ Pitt, entitled "Simulation and Computer Visualization of Biological Systems at Multiple Scales", focuses on computational and mathematical approaches to understanding the complex machinery of molecular-to-cellular systems at three levels, namely, molecular, subcellular (microphysiological), and cellular. We present here an overview of the BBSI @ Pitt, the objectives and focus of the program, and a description of the didactic training activities that distinguish it from other traditional summer research programs. Furthermore, we also report several challenges that have been identified in implementing such an interdisciplinary program that brings together students from diverse academic programs for a limited period of time. These challenges notwithstanding, presenting an integrative view of molecular-to-system analytical models has introduced these students to the field of computational biology and has allowed them to make an informed decision regarding their future career prospects.

Computational Biology↗
PubMedDate not supplied

Spike generating dynamics and the conditions for spike-time precision in cortical neurons.

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.

Animals↗