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A recent theoretical emphasis on complex interactions within neural systems underlying consciousness has been accompanied by proposals for the quantitative characterization of these interactions. In this article, we distinguish key aspects of consciousness that are amenable to quantitative measurement from those that are not. We carry out a formal analysis of the strengths and limitations of three quantitative measures of dynamical complexity in the neural systems underlying consciousness: neural complexity, information integration, and causal density. We find that no single measure fully captures the multidimensional complexity of these systems, and all of these measures have practical limitations. Our analysis suggests guidelines for the specification of alternative measures which, in combination, may improve the quantitative characterization of conscious neural systems. Given that some aspects of consciousness are likely to resist quantification altogether, we conclude that a satisfactory theory is likely to be one that combines both qualitative and quantitative elements.

The functional and biophysical properties of a persistent sodium current (I(NaP)) previously proposed to participate in the generation of subthreshold oscillations and burst discharge in mesencephalic trigeminal sensory neurons (Mes V) were investigated in brain stem slices (rats, p7-p12) using whole cell patch-clamp methods. I(NaP) activated around -76 mV and peaked at -48 mV, with V1/2 of -58.7 mV. Ramp voltage-clamp protocols showed that I(NaP) undergoes time- as well as voltage-dependent inactivation and recovery from inactivation in the range of several seconds (tau(onset) = 2.04 s, tau(recov) = 2.21 s). Riluzole (< or =5 microM) substantially reduced I(NaP), membrane resonance, postinhibitory rebound (PIR), and subthreshold oscillations, and completely blocked bursting, but produced modest effects on the fast transient Na+ current (I(NaT)). Before complete cessation, burst cycle duration was increased substantially, while modest and inconsistent changes in burst duration were observed. The properties of the I(NaT) were obtained and revealed that the amplitude and voltage dependence of the resulting "window current" were not consistent with those of the observed I(NaP) recorded in the same neurons. This suggests an additional mechanism for the origin of I(NaP). A neuronal model was constructed using Hodgkin-Huxley parameters obtained experimentally for Na+ and K+ currents that simulated the experimentally observed membrane resonance, subthreshold oscillations, bursting, and PIR. Alterations in the model g(NaP) parameters indicate that I(NaP) is critical for control of subthreshold and suprathreshold Mes V neuron membrane excitability and burst generation.

A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.

We propose a novel architecture of an oscillatory neural network that consists of phase-locked loop (PLL) circuits. It stores and retrieves complex oscillatory patterns as synchronized states with appropriate phase relations between neurons.

Many scientists believe that all pulse-coupled neural networks are toy models that are far away from the biological reality. We show here, however, that a huge class of biophysically detailed and biologically plausible neural-network models can be transformed into a canonical pulse-coupled form by a piece-wise continuous, possibly noninvertible, change of variables. Such transformations exist when a network satisfies a number of conditions; e.g., it is weakly connected; the neurons are Class 1 excitable (i.e., they can generate action potentials with an arbitrary small frequency); and the synapses between neurons are conventional (i.e., axo-dendritic and axo-somatic). Thus, the difference between studying the pulse-coupled model and Hodgkin-Huxley-type neural networks is just a matter of a coordinate change. Therefore, any piece of information about the pulse-coupled model is valuable since it tells something about all weakly connected networks of Class 1 neurons. For example, we show that the pulse-coupled network of identical neurons does not synchronize in-phase. This confirms Ermentrout's result that weakly connected Class 1 neurons are difficult to synchronize, regardless of the equations that describe dynamics of each cell.

We study pulse-coupled neural networks that satisfy only two assumptions: each isolated neuron fires periodically, and the neurons are weakly connected. Each such network can be transformed by a piece-wise continuous change of variables into a phase model, whose synchronization behavior and oscillatory associative properties are easier to analyze and understand. Using the phase model, we can predict whether a given pulse-coupled network has oscillatory associative memory, or what minimal adjustments should be made so that it can acquire memory. In the search for such minimal adjustments we obtain a large class of simple pulse-coupled neural networks that can memorize and reproduce synchronized temporal patterns the same way a Hopfield network does with static patterns. The learning occurs via modification of synaptic weights and/or synaptic transmission delays.