Abstract: In auditory cortex, firing patterns distributed across populations of pyramidal cells are postulated to represent features of the acoustic environment. We are interested in how GABAergic interneurons shape these firing patterns. Interneurons regulate spike timing by inhibiting target cells for brief periods of time, and they coordinate spike timing across cell populations via divergence. These rules apply as well in interneuronal networks in which cells are coupled by inhibitory synapses and/or gap junctions. Spike times in these networks are constrained by synaptic coupling parameters whose modulation alters the dynamics of observed firing patterns. For example, synchrony in interneuronal networks is modulated in frequency and coherence by anesthetic agents that prolong inhibition. We investigated the types of firing patterns exhibited by two-cell networks of layer I interneurons in brain slices coupled via dynamic clamp under control conditions and under conditions mimicking modulation by the anesthetic agent isoflurane. We found that these networks exhibited bistable behavior in response to DC current pulses, firing either in phase or in antiphase, and that the stability of these stable states is shifted in a predictable fashion by prolonging inhibition. Experiments with Poisson input trains show that these networks can be biased to follow either the timing of transients in the input train or by intra-network firing transients, and suggest a mechanism whereby anesthetic agents may decouple cortical circuits from sensory inputs.

Robert Butera (Georgia Institute of Technology, GA) (Joint work with Amanda Preyer).

Title: Weak coupling and neuronal oscillators - is it valid and is it relevant?

Abstract: Many theoretical studies in computational neuroscience utilize phase oscillator models and the assumptions of weak coupling. While most modern approaches are based upon the work of Kuramoto (1984), the fundamental assumptions were put forth earlier by Winfree (1967). Here we review some recent work of ours (Preyer and Butera, 2005) where we validate the weak coupling assumption in the context of phase response curves and small perturbations to repetitively spiking neurons. We applied weak stimuli to neuronal oscillators in Aplysia californica and deconvolved infinitesimal phase response curves (IPRCs) that describe the phase response of a neuron. We show that these IPRCs reliably predict the phase response for weak stimuli, independent of the stimulus waveform used. These weak stimuli are in the range of normal synaptic activity for these neurons, suggesting that weak coupling is a likely mechanism. However, this work was done solely using PRCs, and not in the context of a real or artificial (dynamic clamp) network.

Carmen C. Canavier

Title: Phase Resetting: Phenomenology and Applications.

Abstract: Phase resetting theory assumes that coupled oscillators continue to traverse their intrinsic limit cycles when coupled in a pulsatile fashion, except that the inputs received can advance or delay the progress on that limit cycle. This assumption is quite accurate for Type I oscillators that arise from a saddle node bifurcation. It is not so accurate for Type II oscillators (Hopf bifurcation) or for relaxation oscillators. However, as long as the trajectory of each component oscillator returns to near the limit cycle between inputs, the phase resetting curve (PRC) can be used to predict the patterns that will be produced by the coupled oscillators. One further assumption is required, that the input received in the closed loop is similar to the input with which the PRC was generated. The AB/PD complex is the main oscillator in the pyloric circuit of the stomatogastric ganglion of the lobster. It's response to inhibitory pulses can be predicted by presuming that it is a relaxation oscillator with a single slow variable (Oprisan et al 2003). An inhibition switches the trajectory in a normal direction between the depolarized and hyperpolarized branches of the limit cycle, and prevents a transition to the depolarized branch during its duration. Recent work shows that the response to an excitatory pulse is more complex. The inhibitory PRCs were successfully used to predict phase-locking in a circuit composed of the AB/PD complex coupled to a model neuron via the Dynamic Clamp (Oprisan et al 2004). One reason that it is important to understand the phenomenology of resetting in bursting neurons is that the coupling may truncate or elongate the burst, so that a PRC generated using the intrinsic burst duration of the presynaptic neuron may be inadequate for prediction purposes without better understanding of the phenomenology.

Roberto Fernández Galán (Joint work with G. Bard Ermentrout and Nathaniel N. Urban)

Title: Phase-response curves: predicting network dynamics from a single cell feature.

Abstract: The knowledge of the phase response permits us to reduce the complex dynamics of N real neurons to simple phase-oscillator models with N coupled, first-order differential equations. This enables efficient and fast simulations of large network models as well as their analytical treatment. Recently, several authors have proposed complementary methods of estimating the phase response in real neurons. I have used some of these techniques to build a simple, but realistic dynamical model of a real neuronal network (the olfactory bulb) that predicts the formation of synchronized neural assemblies in the gamma band. I will also show how these dynamics can be used to encode and discriminate odors. Finally, I will show the role of the phase response in spike-timing reliability and stochastic synchronization.

Mate Lengyel (GATSBY, UCL, UK) (Joint work Peter Dayan, Jeehyun Kwag and Ole Paulsen)

Title: Matching storage and recall: spike timing-dependent plasticity and phase response curves in the hippocampus.

Abstract: Hippocampal area CA3 is widely considered to function as an autoassociative memory. However, it is insufficiently understood how it does so. In particular, the extensive experimental evidence for the importance of carefully regulated spiking times poses the question as to how spike timing-based dynamics may support memory functions. Here, we develop a normative theory of autoassociative memory encompassing such network dynamics. Our theory specifies the way that the synaptic plasticity rule of a memory constrains the form of neuronal interactions that will retrieve memories optimally. If memories are stored by spike timing-dependent plasticity, neuronal interactions should be formalized in terms of a phase response curve, indicating the effect of presynaptic spikes on the timing of postsynaptic spikes. We show through simulation that such memories are competent analog autoassociators and demonstrate directly that the attributes of phase response curves of CA3 pyramidal cells recorded in vitro qualitatively conform with the theory.

Theoden Netoff (Boston University, MA) (Joint work with Lisa Giacomo and John A. White)

Title: Mechanisms of Carbachol oscillations.

Abstract: Carbachol (CCh) is a cholinergic agonist that causes spontaneous theta frequency oscillations in the entorhinal cortex and hippocampus. To better understand the mechanism by which these oscillations are generated, we measured the effect of CCh on phase response curves from pyramidal neurons and stellate cells in the entorhinal cortex. Based on the measurements, it was predicted that CCh would facilitate synchronization of a network of pyramidal neurons but would have little or even a desynchronizing effect on stellate cells. The pyramidal cell results were then confirmed by coupling pairs of pyramidal neurons using the dynamic clamp and measuring their synchrony in control and CCh conditions.

Bart Sautois (Ghent University, Belgium)

Title: Phase response curves, delays and synchronization.

Abstract: Phase response curves, delays and synchronization MatCont is a Matlab software package for the study of dynamical systems through continuation and bifurcation analysis. We have developed a new and very fast way to compute PRCs as a byproduct of a continuation algorithm. We found that delays can be crucial for the synchronizing abilities of networks of neurons through excitatory connections. Using the PRC of a neural model, one can quickly compute the necessary delay to allow synchronization or phase locking.

Ruedi Stoop (Institute of Neuroinformatics, Zurich, Switzerland)

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