Recently, Markram et al. (2015) presented a model of the rat somatosensory microcircuit (Markram model). Their model is high in anatomical and physiological detail, and its simulation requires supercomputers. The lack of neuroinformatics and computing power is an obstacle for using a similar approach to build models of other cortical areas or larger cortical systems. Simplified neuron models offer an attractive alternative to high-fidelity Hodgkin-Huxley-type neuron models, but their validity in modeling cortical circuits is unclear. We simplified the Markram model to a network of exponential integrate-and-fire (EIF) neurons that runs on a single CPU core in reasonable time. We analyzed the electrophysiology and the morphology of the Markram model neurons with eFel and NeuroM tools, provided by the Blue Brain Project. We then constructed neurons with few compartments and averaged parameters from the reference model. We used the CxSystem simulation framework to explore the role of short-term plasticity and GABA and NMDA synaptic conductances in replicating oscillatory phenomena in the Markram model. We show that having a slow inhibitory synaptic conductance (GABA allows replication of oscillatory behavior in the high-calcium state. Furthermore, we show that qualitatively similar dynamics are seen even with a reduced number of cell types (from 55 to 17 types). This reduction halved the computation time. Our results suggest that qualitative dynamics of cortical microcircuits can be studied using limited neuroinformatics and computing resources supporting parameter exploration and simulation of cortical systems. The simplification procedure can easily be adapted to studying other microcircuits for which sparse electrophysiological and morphological data are available.