1. The effect of cholinergic modulation on cortical oscillatory dynamics was studied in a computational model of the piriform (olfactory) cortex. The model included the cholinergic suppression of neuronal adaptation, the cholinergic suppression of intrinsic fiber synaptic transmission, the cholinergic enhancement of interneuron activity, and the cholinergic suppression of inhibitory synaptic transmission. 2. Electroencephalographic (EEG) recordings and field potential recordings from the piriform cortex were modeled with a simplified network in which cortical pyramidal cells were represented by excitatory input/output functions with gain parameters dependent on previous activity. The model incorporated distributed excitatory afferent input and excitatory connections between units. In addition, the model contained two sets of inhibitory units mediating inhibition with different time constants and different reversal potentials. This model can match effectively the patterns of cortical EEG and field potentials, showing oscillatory dynamics in both the gamma (30-80 Hz) and theta (3-10 Hz) frequency range. 3. Cholinergic suppression of neuronal adaptation was modeled by reducing the change in gain associated with previous activity. This caused an increased number of oscillations within the network in response to shock stimulation of the lateral olfactory tract, effectively replicating the effect of carbachol on the field potential response in physiological experiments. 4. Cholinergic suppression of intrinsic excitatory synaptic transmission decreased the prominence of gamma oscillations within the network, allowing theta oscillations to predominate. Coupled with the cholinergic suppression of neuronal adaptation, this caused the network to shift from a nonoscillatory state into an oscillatory state of predominant theta oscillations. This replicates the longer term effect of carbachol in experimental preparations on the EEG potential recorded from the cortex in vivo and from brain-slice preparations of the hippocampus in vitro. Analysis of the model suggests that these oscillations depend upon the time constant of neuronal adaptation rather than the time constant of inhibition or the activity of bursting neurons. 5. Cholinergic modulation may be involved in switching the dynamics of this cortical region between those appropriate for learning and those appropriate for recall. During recall, the spread of activity along intrinsic excitatory connections allows associative memory function, whereas neuronal adaptation prevents the spread of activity between different patterns. During learning, the recall of previously stored patterns is prevented by suppression of intrinsic excitatory connections, whereas the response to the new patterns is enhanced by suppression of neuronal adaptation.

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This report describes a three-dimensional computer model of the olfactory cortex developed for the study of cortical oscillations and their biological significance. The model was designed with the intention of investigating the relative role of network circuitry and network unit properties, resulting in a model complexity between simple Hopfield nets and detailed realistic simulations. Network connections are essentially the same as in a detailed simulation of the olfactory (piriform) cortex by Wilson and Bower (1989), but the network units are here modeled with continuous output functions and single compartments. It is shown that the present model is capable of reproducing all major results of the more complex model, corresponding to spatiotemporal patterns found in the actual cortex (Freeman 1975). This indicates that action potentials and the geometry of cells are not needed per se for explaining certain cortical activities. In contrast, connections between units, in particular feedforward and feedback inhibitory loops and long-range, excitatory-excitatory connections, are found to be crucial for the dynamical behavior of this system. The model describes intrinsic oscillatory properties of olfactory cortex and reproduces response patterns associated with a continuous random-input signal and with a shock pulse given to the cortex. In the latter case, waves of activity move across the model cortex in a way similar to the detailed simulations by Wilson and Bower, and consistent with corresponding global dynamic behavior of the functioning cortex. For a constant random input, the network is able to oscillate with two separate frequencies simultaneously, purely as a result of its intrinsic network properties. A delicate balance between inhibition and excitation, in terms of connection strength and timing of events, is necessary for coherent frequency and phase of the oscillating neural units. The analytical equations used in this model seem an adequate representation of olfactory cortex for mathematical analysis of its computational function.