1. The detailed visualization of membrane currents over time and depth provided by current source-density (CSD) analysis was used as the basis for development of a system model that reproduces the response of piriform cortex to afferent fiber stimulation. This model has allowed the testing and substantial revision of previous hypotheses concerning the sequence of neuronal events underlying this response, has enabled net membrane currents visualized by CSD analysis to be separated into active and passive components, and has generated predictions for important axonal and synaptic parameters as well as for the behavior of piriform cortex as a system. 2. The model was developed in three steps. Activity in excitatory fiber systems was first represented with continuous distributions. The ''population conductances'' due to the activation of excitatory fiber systems were then computed from the distribution of action-potential arrival times and the conductance waveform for excitatory synapses. Finally, these temporally dispersed excitatory conductances and locally mediated inhibitory conductances were introduced at appropriate locations on a compartmentalized cable that simulated the passive response of the pyramidal cell population. 3. After the simulation of membrane currents at one site, all parameters in the model were fixed so that it could be used to predict the variation in the time course of membrane currents at additional recording sites; comparison with the results of CSD analysis at these sites provided the primary validation of the model. Additional validation included the simulation of membrane potentials derived by intracellular recording, including the effects of manipulating somatic potential with current injection. 4. Several conclusions have emerged from the mathematical description of activity in fiber systems. Propagation of activity in both afferent and association (corticocortical) fiber systems is ''dispersive'' as a result of a wide spectrum of axon conduction velocities. The characteristically different time courses of afferent and association fiber-mediated responses are largely determined by the focal, shock-evoked origin of the volley in afferent fibers as opposed to the spatially distributed disynaptic origin of activity in association fibers. Conduction velocity distributions for afferent and association fiber systems are skewed and can be approximated with lognormal distributions. 5. General solutions, which relate an arbitrary conduction velocity distribution to arrival time and spatial distributions of action potentials, were used to generate specific solutions describing the effects of dispersive propagation. This approach allowed the derivation of conduction velocity distributions from the membrane currents at a single recording site, the prediction of the time course of the response at different recording sites, and the prediction of spatial distributions of activity across fiber systems. This theoretical development revealed that estimates of conduction velocities of fiber pathways from the propagation velocity of the peak of postsynaptic responses can result in overestimates of greater-than-or-equal-to 30%. 6. For excitatory processes, previous conclusions were confirmed that afferent fiber stimulation evokes a monosynaptic excitatory postsynaptic current (EPSC) in distal dendritic segments of pyramidal cells and a strong disynaptic EPSC in middle dendritic segments mediated by long association fibers that originate in the anterior piriform cortex. Second, it was concluded that the small inward current in proximal apical dendrites (deep layer Ib sink) that follows the strong disynaptic EPSC may be mediated by association fibers originating from cells in either the posterior piriform cortex or the dorsal part of the anterior piriform cortex, but not a voltage-dependent Na+ conductance extending into apical dendrites. Third, in the pyramidal cell model the fall-off of peak post-synaptic potential at the level of cell bodies from dendritic EPSCs was 75% for the monosynaptic EPSC on distal segments, 50% for the disynaptic EPSC in middle segments, and 20% for the disynaptic EPSC in proximal segments. Finally, it was concluded that the synaptic conductances mediated by both afferent and association fibers have similar fast time courses (time to peak less-than-or-equal-to 1 ms; time constant of decay on the order of 1 ms). 7. Two previous hypotheses concerning the Cl--mediated inhibitory postsynaptic potential (IPSP) were not confirmed: that it is responsible for a shift in location of source current for the mono-synaptic EPSC, and that it exerts a strong shunting action on excitatory postsynaptic potentials (EPSPs) at resting membrane potential. It was concluded that the shift in source current is a result of passive membrane properties, and that the blockage of EPSPs by the Cl--mediated IPSP is only substantial at depolarized membrane potentials. 8. Decomposition of the net membrane current into active (synaptic) and passive current components provided conclusions with general relevance for the interpretation of results of CSD analysis. First, the duration of active synaptic currents can be substantially less than the duration of net membrane currents detected by CSD analysis as a result of capacitative current generated by the equalization of membrane potential over depth. Second, Cl--mediated IPSPs can have little effect on membrane currents as a result of the proximity of their reversal potential to resting membrane potential. Third, CSD analysis does not visualize membrane currents that occur during equipotential repolarization because they consist of equal and opposite capacitative and resistive components.
