Oscillations in many regions of the cortex have common temporal characteristics with dominant frequencies centered around the 40 Hz (gamma) frequency range and the 5-10 Hz (theta) frequency range. Experimental results also reveal spatially synchronous oscillations, which are stimulus dependent (Gray & Singer, 1987; Gray, Konig, Engel, & Singer, 1989; Engel, Konig, Kreiter, Schillern, & Singer, 1992). This rhythmic activity suggests that the coherence of neural populations is a crucial feature of cortical dynamics (Gray, 1994). Using both simulations and a theoretical coupled oscillator approach, we demonstrate that the spike frequency adaptation seen in many pyramidal cells plays a subtle but important role in the dynamics of cortical networks. Without adaptation, excitatory connections among model pyramidal cells are desynchronizing. However, the slow processes associated with adaptation encourage stable synchronous behavior.

We have examined a model by Holmes and Levy (1990) of the induction of associative long-term potentiation (LTP) by a rise in the free Ca2+ concentration ([Ca2+]) after synaptic activation of dendritic spines. The previously reported amplification of the change in [Ca2+] caused by coactivation of several synapses was found to be quite sensitive to changes in the permeability of the N-methyl-D-aspartate (NMDA) receptor channels to Ca2+. Varying this parameter indicated that maximum amplification is obtained at values that are close to Ca2+ permeabilities reported in the literature. However, amplification failed if permeability is reduced by more than 50%. We also found that the maximum free [Ca2+] reached in an individual spine during synaptic coactivation of several spines depended on the location of that spine on the dendritic tree. Distal spines attained a higher [Ca2+] than proximal ones, with differences of up to 80%. The implications of this result for the uniformity of induction of associative LTP in spines in different regions of the dendrite are discussed.

Periodic variations in correlated cellular activity have been observed in many regions of the cerebral cortex. The recent discovery of stimulus-dependent, spatially-coherent oscillations in primary visual cortex of the cat has led to suggestions of neural information encoding schemes based on phase and/or frequency variation. To explore the mechanisms underlying this behavior and their possible functional consequences, we have developed a realistic neural model, based on structural features of visual cortex, which replicates observed oscillatory phenomena. In the model, this oscillatory behavior emerges directly from the structure of the cortical network and the properties of its intrinsic neurons; however, phase coherence is shown to be an average phenomenon seen only when measurements are made over multiple trials. Because average coherence does not ensure synchrony of firing over the course of single stimuli, oscillatory phase may not be a robust strategy for directly encoding stimulus-specific information. Instead, the phase and frequency of cortical oscillations may reflect the coordination of general computational processes within and between cortical areas. Under this interpretation, coherence emerges as a result of horizontal interactions that could be involved in the formation of receptive field properties.

Head movements in vertebrates give rise to involuntary eye movements that stabilize visual images on the retina. Previous models of the vestibulo-ocular reflex (VOR), one of the neural mechanisms responsible for stabilizing the eyes during head movements, have assumed that the VOR transfer function should have unity gain and 180° phase shift. Experimental measurements of VOR gain and phase, however, exhibit frequency dependencies that are not easily interpreted within the framework of existing models. We reanalyze the problem of VOR control using stochastic optimal estimation theory and show that VOR dynamics, in general, should differ from the "ideal" unity-gain, 180° phase shift transfer function. We illustrate this approach by computing the optimal VOR transfer function for a simple, second-order dynamical model of a head–neck system. Despite its simplicity, this model is able to give some insight into the dynamical properties of the VOR. In particular, it qualitatively reproduces an experimentally observed gain peak in monkey VOR at high frequencies. The model also predicts that the gain and phase characteristics of the optimal VOR transfer function should depend on the spectrum of natural head movements, possibly giving rise to species-dependent and gait-dependent differences in the VOR transfer function. We suggest that the applicability of optimal estimation extends beyond the control of compensatory eye movements and that it is probably a universal component of movement control in the nervous system.