High-frequency forced oscillations in neuronlike elements.

We analyzed a generic relaxation oscillator under moderately strong forcing at a frequency much greater that the natural intrinsic frequency of the oscillator. Additionally, the forcing is of the same sign and, thus, has a nonzero average, matching neuroscience applications. We found that, first, the transition to high-frequency synchronous oscillations occurs mostly through periodic solutions with virtually no chaotic regimes present. Second, the amplitude of the high-frequency oscillations is large, suggesting an important role for these oscillations in applications. Third, the 1:1 synchronized solution may lose stability, and, contrary to other cases, this occurs at smaller, but not at higher frequency differences between intrinsic and forcing oscillations. We analytically built a map that gives an explanation of these properties. Thus, we found a way to substantially "overclock" the oscillator with only a moderately strong external force. Interestingly, in application to neuroscience, both excitatory and inhibitory inputs can force the high-frequency oscillations.

Universality in spectral statistics of open quantum graphs.

The quantum evolution maps of closed chaotic quantum graphs are unitary and known to have universal spectral correlations matching predictions of random matrix theory. In chaotic graphs with absorption the quantum maps become nonunitary. We show that their spectral statistics exhibit universality at the soft edges of the spectrum. The same spectral behavior is observed in many classical nonunitary ensembles of random matrices with rotationally invariant measures.

Spectral properties and dynamical tunneling in constant-width billiards.

We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model for systems with violated time-reversal invariance and a mixed dynamics. Furthermore, we investigate tunneling in terms of the splittings of the doublet partners. On the basis of the random-matrix model we derive an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.

Co-activation of VTA DA and GABA neurons mediates nicotine reinforcement.

Smoking is the most important preventable cause of mortality and morbidity worldwide. This nicotine addiction is mediated through the nicotinic acetylcholine receptor (nAChR), expressed on most neurons, and also many other organs in the body. Even within the ventral tegmental area (VTA), the key brain area responsible for the reinforcing properties of all drugs of abuse, nicotine acts on several different cell types and afferents. Identifying the precise action of nicotine on this microcircuit, in vivo, is important to understand reinforcement, and finally to develop efficient smoking cessation treatments. We used a novel lentiviral system to re-express exclusively high-affinity nAChRs on either dopaminergic (DAergic) or γ-aminobutyric acid-releasing (GABAergic) neurons, or both, in the VTA. Using in vivo electrophysiology, we show that, contrary to widely accepted models, the activation of GABA neurons in the VTA plays a crucial role in the control of nicotine-elicited DAergic activity. Our results demonstrate that both positive and negative motivational values are transmitted through the dopamine (DA) neuron, but that the concerted activity of DA and GABA systems is necessary for the reinforcing actions of nicotine through burst firing of DA neurons. This work identifies the GABAergic interneuron as a potential target for smoking cessation drug development.

A reduced model of DA neuronal dynamics that displays quiescence, tonic firing and bursting.

Midbrain dopaminergic neurons send numerous projections to cortical and sub-cortical areas, and in a manner dependent upon their activities, diffusely release dopamine (DA) to their targets. Recent experimental studies have shown that DAergic neuronal bursting is associated with a significantly greater degree of DA release than an equivalent tonic activity pattern. Past computational models for DA cell activity relied upon somatodendritic mechanisms in order to generate DA neuronal bursting. However, recent experimental studies indicate that burst firing can be generated somatically with the dendrites silenced. These somatically induced bursts have characteristics consistent with normal bursting, suggesting that a single-compartmental model should be sufficient for generating the observed DA neuronal dynamics. In this work, we introduce such a model for DA neuronal dynamics and demonstrate that this model captures the qualitative behavior of DAergic neuronal dynamics: quiescence, tonic firing and bursting. In our conductance-based approach, the interplay between the L-type calcium and the calcium dependent SK potassium channel provides a scaffold for the underlying oscillation for the pacemaker-like firing patterns. The model includes terms which can selectively block the SK conductance, which would correspond to pharmacological manipulations using the drug apamin. Our modeling studies are in line with experimental evidence that a reduction of the SK conductance often induces DA neuronal bursting. Moreover, our model can reproduce findings that burst firing can be elicited via stimulus driven events, manifested by rises in the amount of NMDA. This model for DA cell activity could be further sculpted to include more detailed second messenger signaling processes in order to elucidate key differences between the two principal classes of midbrain DA neurons: those of the ventral tegmental area and the substantia nigra pars compacta.

Computational approaches to the neurobiology of drug addiction.

To increase our understanding of drug addiction--notably its pharmacological and neurobiological determinants--researchers have begun to formulate computational models of drug self-administration. Currently, one can roughly distinguish between three classes of models which all have in common to attribute to brain dopamine signaling a key role in addiction. The first class of models contains quantitative pharmacological models that describe the influence of pharmacokinetic and pharmacodynamic factors on drug self-administration. These models fail, however, to explain how the drug self-administration behavior is acquired and how it eventually becomes rigid and compulsive with extended drug use. Models belonging to the second class circumvent some of these limitations by modeling how drug use usurps the function of dopamine in reinforcement learning and action selection. However, despite their behavioral plausibility, these latter models lack neurobiological plausibility and ignore the potential role of opponent processes in addiction. The third class of models attempts to surmount these pitfalls by providing a more realistic picture of the midbrain dopamine circuitry and of the complex action of drugs of abuse in the output of this circuitry. Here we provide a brief overview of these different models to illustrate the potential contribution of mathematical modeling to our understanding of the neurobiology of drug addiction.

Adiabatic swimming in an ideal quantum gas.

Interference effects are important for swimming of mesoscopic systems that are small relative to the coherence length of the surrounding quantum medium. Swimming is geometric for slow swimmers and the distance covered in each stroke is determined, explicitly, in terms of the on-shell scattering matrix. Remarkably, for a one-dimensional Fermi gas at zero temperature we find that slow swimming is topological: the swimming distance covered in one stroke is quantized in half integer multiples of the Fermi wavelength. In addition, a careful choice of the swimming stroke can eliminate dissipation.

Turning on and off with excitation: the role of spike-timing asynchrony and synchrony in sustained neural activity.

Delay-related sustained activity in the prefrontal cortex of primates, a neurological analogue of working memory, has been proposed to arise from synaptic interactions in local cortical circuits. The implication is that memories are coded by spatially localized foci of sustained activity. We investigate the mechanisms by which sustained foci are initiated, maintained, and extinguished by excitation in networks of Hodgkin-Huxley neurons coupled with biophysical spatially structured synaptic connections. For networks with a balance between excitation and inhibition, a localized transient stimulus robustly initiates a localized focus of activity. The activity is then maintained by recurrent excitatory AMPA-like synapses. We find that to maintain the focus, the firing must be asynchronous. Consequently, inducing transient synchrony through an excitatory stimulus extinguishes the sustained activity. Such a monosynaptic excitatory turn-off mechanism is compatible with the working memory being wiped clean by an efferent copy of the motor command. The activity that codes working memories may be structured so that the motor command is both the read-out and a direct clearing signal. We show examples of data that is compatible with our theory.

The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators.

There are several different biophysical mechanisms for spike frequency adaptation observed in recordings from cortical neurons. The two most commonly used in modeling studies are a calcium-dependent potassium current I(ahp) and a slow voltage-dependent potassium current, I(m). We show that both of these have strong effects on the synchronization properties of excitatorily coupled neurons. Furthermore, we show that the reasons for these effects are different. We show through an analysis of some standard models, that the M-current adaptation alters the mechanism for repetitive firing, while the afterhyperpolarization adaptation works via shunting the incoming synapses. This latter mechanism applies with a network that has recurrent inhibition. The shunting behavior is captured in a simple two-variable reduced model that arises near certain types of bifurcations. A one-dimensional map is derived from the simplified model.

Conditions for noise reduction and stable encoding of spatial structure by cortical neural networks.

Cortical circuits have been proposed to encode information by forming stable spatially structured attractors. Experimentally in the primary somatosensory cortex of the monkey, temporally invariant stimuli lead to spatially structured activity patterns. The purpose of this work is to study a recurrent cortical neural network model with lateral inhibition and examine what effect additive random noise has on the networks' ability to form stable spatially structured representations of the stimulus pattern. We show numerically that this network performs edge enhancement and forms statistically stationary, spatially structured responses when the lateral inhibition is of moderate strength. We then derive analytical conditions on the connectivity matrix that ensure stochasticly stable encoding of the stimulus spatial structure by the network. For stimuli whose strength falls in the near linear region of the sigmoid, we are able to give explicit conditions on the eigenvalues of the connection matrix. Finally, we prove that a network with a connection matrix, where the total excitation and inhibition impinging upon a neural unit are nearly balanced, will yield stable spatial attractor responses.

Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics.

We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the theta-neuron. The theta-neuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude "kicks" to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the Morris-Lecar (M-L) neural model with random synaptic inputs: type I M-L yields high CVs. When this model is modified to have type II dynamics (periodicity arises via a Hopf bifurcation), however, it gives regular spike trains (CV below 0.3). Our results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by "random" inputs. In contrast, neural oscillators or neurons exhibiting type II excitability should produce regular spike trains.

Analysis of stutterers' voice onset times and fundamental frequency contours during fluency.

The purpose of this study was to examine stutterers' and nonstutterers' fluent voice onset time (VOT) and fundamental frequency (Fo) contour measures from target syllables located at the beginning of a carrier phrase. Ten adult male stutterers were matched within one year of age with 10 adult male nonstutterers. Oscillographic and spectrographic analyses of subjects' VOT and Fo at vowel onset, average vowel Fo, and speed and range of Fo change were obtained from fluent productions of 18 stop consonant-vowel syllables. Results showed that VOTs for voiced stops and the range of Fo change for voiceless stops were associated with significant between-group differences. All other dependent measures were not significantly different between the two groups. When compared with past research, these findings indicate that greater differences emerge between stutterers and nonstutterers when measures of fluency are taken at the beginning than in the middle of a carrier phrase. Implications for future research are discussed.