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.

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.

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.

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.